WORKS OF
PROFESSOR CECIL H. PEABODY
PUBLISHED BY
JOHN WILEY & SONS.
Thermodynamics of the Steamengine and other
Heatengines.
This work is intended for the use of students in
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THERMODYNAMICS
OF THE
STEAMENGINE
AND
OTHER HEATENGINES
BY
CECIL H.
PROFESSOR OF NAVAL ARCHITECTURE AND MARINE ENGINEERING^
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
FIFTH EDITION, REWRITTEN
SECOND THOUSAND
PROPERTY OF
IHSTITJiF OF TECai,310]Y
NEW YORK
JOHN WILEY & SONS
LONDON: CHAPMAN ft HALL, LIMITED
1908
>O I J
'. ^C'
COPYRIGHT 1889, 1898, 1907
BY
CECIL H. PEABODY
PREFACE TO FIFTH EDITION.
WHEN this work was first in preparation the author had before
him the problem of teaching thermodynamics so that students in
engineering could use the results immediately in connection with
experiments in the Engineering Laboratories of the Massachu
setts Institute of Technology. The acceptance of the book by
teachers of engineering appears to justify its general plan, which
will be adhered to now that the development of engineering calls
for a complete revision.
The author is still of the opinion that the general mathematical
presentation due to Clausius and Kelvin is most satisfactory and
carries with it the ability to read current thermodynamic inves
tigations by engineers and physicists. At the same time it is
recognized that recent investigations of superheated steam are
presented in such a way as to narrow the applications of the
general method so that there is justification for those who prefer
special methods for those applications. To provide for both
views of this subject, the general mathematical discussion is
presented in a separate chapter, which may be omitted at the
first reading (or altogether), provided that the special methods,
which also are given in the proper places, are taken to be sufficient.
The first edition presented fundamental data not generally
accepted at that time, so that it was considered necessary to
justify the data by giving the derivation at length; much of this
matter, which is no longer new, is removed to an appendix, to
relieve the student of discussions that must appear unnecessary
and tedious.
The introduction of the steamturbine has changed adiabatic
calculations for steam, from an apparent academic abstraction, to
a common necessity. To meet this changed condition, the Tables of
iii
IV
PREFACE
Properties of Saturated Steam have had added to them columns
of entropies of vaporization; and further there has been
computed a table of the quality (or dryness factor) the heat
contents and volume at constant entropy, for each degree
Fahrenheit. This table will enable the computer to deter
mine directly the effect of adiabatic expansion to any pres
sure or volume, and to calculate with ease the external work
in a cylinder or the velocity of flow through an orifice or nozzle
including the effect of friction; and also to determine the distri
bution of work and pressure for a steamturbine. For the
greater part of practical work this table may be used without
interpolation, or by interpolation greater refinement may be had.
Advantage is taken of recent experiments on the properties of
superheated steam and of the application to tests on engines to
place that subject in a more satisfactory condition. Attention,
is also given to the development of internal combustion engines
and to the use of fuel and blastfurnace gas. A chapter is given
on the thermodynamics of the steamturbine with current method
of computation, and results of tests.
So far as possible the various chapters are made independent,
so that individual subjects, such as the steamengine, steamtur
bine, compressedair and refrigerating machines, may be read
separately in the order that may commend itself.
PREFACE TO FIRST EDITION.
THIS work is designed to give instruction to students It
technical schools in the methods and results of the application
of thermodynamics to engineering. While it has been considerec
desirable to follow commonly accepted methods, some part
differ from other textbooks, either in substance or in manner q
presentation, and may require a few words of explanation.
The general theory or formal presentation of thermodynamic
PREFACE V
is that employed by the majority of writers, and was prepared
with the view of presenting clearly the difficulties inherent in the
subject, and of giving familiarity with the processes employed.
In. the discussion of the properties of gases and vapors the
original experimental data on which the working equations,
whether logical or empirical, must be based are given quite
fully, to afford an idea of the degree of accuracy attainable in
calculations made with their aid. Rowland's determination of
the mechanical equivalent of heat has been adopted, and with it
his determination of the specific heat of water at low tempera
tures. The author's "Tables of the Properties of Saturated
Steam and Other Vapors" were calculated to accompany this
work, and may be considered to be an integral part of it.
The chapters on the flow of gases and vapors and on the
injector are believed to present some novel features, especially
in the comparisons with experiments.
The feature in which this book differs most from similar
works is in the treatment of the steamengine. It has been
deemed advisable to avoid all approximate theories based on
the assumption of adiabatic changes of steam in an engine
cylinder, and instead to make a systematic study of steam
engine tests, with the view of finding what is actually known on
the subject, and how future investigations and improvements
may be made, For this purpose a large number of tests have
been collected, arranged, and compared, Special attention is
given to the investigations of the action of steam in the cylinder
of an engine, considerable space being given to Hirn's researches
and to experiments that provide the basis for them. Directions
are given for testing engines, and for designing simple and com
pound engines.
Chapters have been added on compressedair and refrigerating
machines, to provide for the study of these important subjects
in connection with the theory of thermodynamics.
Wherever direct quotations have been made, references have
been given in footnotes, to aid in more extended investigations.
It does not appear necessary to add other acknowledgment of
VI
PREFACE
assistance from wellknown authors, further than to say that
their writings have been diligently searched in the preparation
of this book, since any textbook must belargely an adaptation of
their work to the needs of instruction.
C. H. P.
MASSACHUSETTS INSTITUTE or TECHNOLOGY,
May, 1889.
PREFACE TO FOURTH EDITION.
A THOROUGH revision of this work has been made to bring
it into accord with more recent practice and to include later
experimental work. Advantage is taken of this opportunity to
make changes in matter or in arrangement which it is believed
will make it more useful as a textbook.
C.H. P.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
July, 1898.
TABLE OF CONTENTS.
CHAl'THU
_,I^ THERMAL CAPACITIES I
/ II. JFIRST LAW OF THERMODYNAMICS *3
'"Til" SECOND LAW OF THERMODYNAMICS 22
IV. GENERAL THKRMODYNAMIC METHOD 43
V. PKRFKCT CASKS 54
VI. SATURATED VAPOR 7 6
VII. SUPERHEATED, VAPORS 10
VIII, THE STEAIMCNOINK Ia8
IX, COMPOUND EMOIMKB J S 6
X. TESTING STKAMKNOINES .....' l8 3
XL INFLUENCE OF TOR CYLINDER WALLS *99
XII. ECONOMY OF STKAMENOINKS 2 37
XIII. FRICTION OF KNCMNEB a8 S
XIV. INTERNALCOMBUSTION ENGINES 2 9 8
XV. COMPRISED AIR 35 8
XVI. REFRIGERATING MACHINES 39 6
XVII. FLOW OF FLUIDS 42 3
XVIIL INJECTORS  447
XIX STBAMTORBINES 47
vii
THERMODYNAMICS OF THE STEAMENGINE,
CHAPTER I.
THERMAL CAPACITIES.
THE object of thermodynamics, or the mechanical theory of
heat, is the solution of problems involving the action of heat,
and, for the engineer, more especially those problems presented
by the steamengine and other thermal motors. The substances
in which the engineer has the most interest are gases and vapors,
more especially air and steam, Fortunately an adequate treat
ment can be given of these substances for engineering purposes.
First General Principle. In the development of the theory
of thermodynamics it is assumed that if any two characteristics
or properties of a substance are known these two, treated as
independent variables, will enable us to calculate any third
property.
As an example, we have from the combination of the laws of
Boyle and GayLussae the general equation for gases,
pv RT,
in which f is the pressure, v is the volume, T is the absolute
temperature by the airthermometer, and R is a constant which
for air has the value 53,35 when English units are used. It is
probable that thin equation led to the general assumption just
quoted, That assumption is purely arbitrary, and is to be justi
fied by its results, It may properly be considered to be the first
general principle of the theory of thermodynamics; the other
two general principles are the nocalled first and second laws of
thermodynamics, which will be stated and discussed later.
2 THERMAL CAPACITIES
Characteristic Equation. An equation which gives th
relations of the properties of any substance is called the charac
tcristic equation for that substance. The properties appcarin
in a characteristic equation are commonly pressure, volunV'
and temperature, but other properties may be used if convcnierj
The form of the equation must be determined from experiment
cither directly or indirectly.
The characteristic equation for a gas is, as already quote"'
pv = RT.
The characteristic equation for an imperfect gas, like supc
heated steam, is likely to be more complex; for example, t!
equation given by Knoblauch, Linde, and KIcbe is
3r#(iMi
On the other hand, the properties of saturated steam, cspccla
if mixed with water, cannot be represented by a single cquatk
Specific Pressure. The pressure is assumed to be a hydi
static pressure, such as a fluid exerts on the sides of the CC
taining vessel or on an immersed body. The pressure
consequently the pressure exerted by the substance under cc
sideration rather than the pressure on that substance. I
example, in the cylinder of a steamengine the pressure of '
steam is exerted on the piston during the forward stroke a
docs work on the piston; during the return stroke, when
steam is expelled from the cylinder, it still exerts pressure
the piston and abstracts work from it.
For the purposes of the general theory pressures
expressed in terms of pounds on the square foot for the Engl
system of units. In the metric system the pressure is cxprcs
in terms of kilograms on the square metre. A pressure t
expressed is called the specific pressure. In engineering prac
other terms are used, such as pounds on the square inch, inc
of mercury, millimetres of mercury, atmospheres, or kilogra
on the square centimetre.
TEMl'KRATURE 3
Specific Volume. It is convenient to deal with one unit of
weight of the substance under discussion, and to consider the
volume occupied by one pound or one kilogram of the substance;
this is called the specific volume, and is expressed i'n cubic feet or
in cubic metres. The specific volume of air at freezingpoint
and under the normal atmospheric pressure is 12.39 cubic feet;
the specific volume of saturated steam at 212 F. is 26.6 cubic
feet; and the specific volume of water is about . or nearly
62.4
0.016 of a cubic foot.
Temperature is commonly measured by aid of a mercurial
thermometer which has for its reference points the freezing
point and boilingpoint of water. A centigrade thermometer
has the volume of the stem between the referencepoints divided
into one hundred equal parts called degrees. The Fahrenheit
thermometer differs from the centigrade in having one hundred
and eighty degrees between the freezingpoint ;md the boiling
point, and in having its zero thirtytwo degrees below freezing.
The scale of a mercurial thermometer is entirely arbitrary,
and its indications depend on the relative expansion of glass and
mercury. Indications of such thermometers, however carefully
made, differ appreciably, mainly on account of the varying
nature of the glass. For refined investigations thermomelric
readings are reduced to the airthermometer, which has the
advantage that the expansion of air is so largo compared with
the expansion of glass that the latter has little or no effect.
It is convenient in making calculations of the properties of
air to refer temperatures to the absolute zero of the scale of the
airthermometer. To gel a conception of what is meant by this
expression we may imagine the airthcrmomctcr to be made of
a uniform glass tube with a proper index to show the volume
of the air. The position of the index may be marked at boiling
point and at freezingpoint as on the mercurial thermometer,
and the space between may be divided into one hundred parts
or degrees. If the graduations arc continued to the closed end
of the lube there will be found to be 273 of them. It will be
THERMAL CAPACITIES
shown later that there is reason to suppose that the absolute
zero of temperature is 273 centigrade below the freezingpoint
of water. Speculations as to the meaning of absolute zero and
discussions concerning the nature of substances at that temper
ature arc not now profitable. It is sufficient to know that
equations are simplified and calculations arc facilitated by this
device. For example, if temperature is reckoned from the
arbitrary zero of the centigrade thermometer, then the charac
teristic equation for a perfect gas becomes
in which a is the coefficient of dilatation and  = 273 nearly.
a
In order to distinguish the absolute temperature from the
temperature by the thermometer we shall designate the former
by T and the latter by t, bearing in mind that
T = t + 273 centigrade,
T = t + 459.5 Fahrenheit.
Physicists give great weight to the discussion of a scale of
temperature that can be connected with the fundamental units
of length and weight like the foot and the pound. Such a scalo,
since it docs not depend on the properties of any substance
(glass, mercury, or air), is considered to be the absolute scale of
temperature. The differences between such a scale and thd
scale of the airthermometer are very small, and arc difficult to
determine, and for the engineer arc o Utllc moment. A.t tho
proper place the conception of the absolute scale can be easily
slated.
Graphical Representation of the Characteristic Equation.
Any equation with three variables may be represented by ft.
geometrical surface referred to coordinate axes, of which surface
the variables arc the coordinates. In the case of a perfect gas
which conforms to the equation
pv = RT t
STANDARD TEMPERATURE
FIG.
the surface is such thai each scclion perpendicular to the axis
of T is a rectangular hyperbola (Fig. i).
Returning now lo the general case,
it is apparent that the characteristic
equation of any substance may be repre
sented by a geometrical surface referred
to coordinate axes, since the equation is
assumed to contain only three variables;
hut the surface will in general be less
simple in form than that representing the
combined laws of Hoyleand GayLussac.
If one of the variables, as 7', is given a special constant value,
it is equivalent lo taking a section perpendicular lo the axis of
T\ and a plane curve will be cut from the surface, which may
he conveniently projected on Ihc (/, T) plane. The reason for
choosing liic (^ v) plane is lliat the curves correspond with
those drawn by the steamengine indicator.
Considerable use is made of such thermal curves in explaining
thermodynamic conceptions. As a rule, a graphical process
or representation in merely another wity of presenting nn idea
that has been, or may be, presented analytically } there is, how
ever, an advantage in representing a condition or EV change to
the eye by a diagram, especially in a discussion which appears
to be abstract. A number of thermal curves are explained on
page 16.
Standard Temperature. For many purposes it is convenient
lo l/ike ilio freezing point of water for iJic standard lempcrnlurcj
since it Is one of the referencepoints on the thcrmometric scale;
this is especially true for air, Rut ihe properties of water change
rapidly at and near freezingpoint and arc very imperfectly
known. H has consequently become customary to take 6aF,
for Ihc standard temperature for the English system of units;
there is a convenience in this, inasmuch as the pound and yard
arc aiandardfl ftt tlint cm)craturc. For the mclric system 15 C.
is used, though the kilogram and metre are standards at freezing
point.
thermal units (u. T. u.). A British thermal unit is tl
required to raise one pound of water from 62 F. to 63'
like manner a calorie is the heat required to raise one k
of water from 15 C. to i6C.
Specific Heat is the number of thermal units required
a unit of weight of a given substance one degree of tcmp<
The specific heat of water at the standard tcmpcratun
course, unity.
If the specific heat of a given substance is constant, tl
heat required to raise one pound through a given range
perature is the product of the specific heat by the incr
temperature. Thus if c is the specific heat and t ^ is Ih
of temperature the heat required is
Q = c (t ~~ /,), and c
JL.
If the specific heat varies the amount of heat must bo oi
by integration that is,
Q  fcdt,
and conversely
ffl.
dt
It is customary to distinguish two specific heats for
gases; specific heat at constant pressure* and speqific t
constant volume, which may be represented by
c a =
andc.
the subscript attached to the parenthesis indicates the pj
which is constant during the change. It is evident tr,
specific heats just expressed are partial differential coefiic
Latent Heat of Expansion is the amount of heat requ
increase the volume of a unit of weight of the substance
cubic fooi ; or one cubic metre, at consianl temperature. It
may be represented by
I*
Thermal Capacities. The two specific heals and the latent
heat of expansion are known as thermal capacities. It is cus
lomary to use three other properties suggested by (hose just
named which are represented as follows;
m
and o
The first represents the amount of heat thai must be applied
to one pound of a substance (such as air) to increase the pressure
by the amount of one pound per square foot at consianl tem
perature; this property is usually negative and represents the
heat that must be abstracted to prevent the temperature from
rising, The other two can be defined in like manner if desired,
but it is not very important to stale the definitions nor to try to
gain a conception (is to what they mean, as it is easy to express
(hem in terms of the first three, for which the conceptions are
not difficult. They have no names assigned lo them, winch is,
on the whale, fortunate, tts, of the first three, two have names that
have no real significance, and the third is a misnomer.
General Equations of the Effects Produced by Heat. In
order lo be able lo compute the amount of heat required to
produce a change in a substance by aid of the characteristic
equation, it Is necessary to admit that there is a functional rela
tion between the heat applied and some Iwo of the properties
that enter into the characteristic equation. It will appear later
in connection with the discussion of the firsl law of thermody
namics that an integral equation cannot in general be written
directly, but we may write a differential equation in one of tho
three following forms;
I 1
or substituting for the partial differential coefficients the letters
which have been selected to represent them,
dQ = c v dt + ldv
dQ  c p dl + mdp
dQ = ndp + odv
(3)
This matter may perhaps be
clearer if it is presented graph
ically as in Fig. 2, where ab is
intended to represent the path
of a point on the characteristic
surface in consequence of the
addition of the heat dQ. There
will in general be a change of
temperature volume and pres
sure as indicated on the figure.
Now the path ab, which
for a small change may
Plo . ,. be considered to be a straight
line, will be projected on
the three planes at a'b' } a"b" and o!"V". The projection on the
(y.T) plane may be resolved into the components Sy and' &T',
the first represents a change of volume at constant temperature
requiring the heat ldv t and the second represents a change of tem
perature at constant volume requiring the heat yti. Conse
quently the heat required for the change in terms of the volume
and temperature is
dQ = c v dl t
RELATIONS OF TIIK THKRMAL CAPACITIES g
Relations of the Thermal Capacities. The three equations
(i), (2), and (3), show the changes produced by the addition of
an amount of heal <1Q to a unit of weight of a substance, the
difference coming from the methods of analyzing the changes.
We may conveniently find the relations of the several thermal
capacities by the method of undetermined coefficients. Thus
equating the lighthaml members of equations (i) and (2),
c v <lt I Idv *= c p (U '] mdl> ..... (4)
From the characteristic equation we shall have in general
v F (/>, T),
us, for example, for air we have
t,
XT
,
and consequently we may write
Sv
which substituted in equation U) gives,
c v (!l I
cjli
f
(S)
It will be noted that, as T differs from t only by the addition
of a constant, the differential <lt may be used in till cases, whether
we arc dealing with absolute temperatures, or temperatures on
the ordinary thermometer.
In equation (5) p and T arc independent variables, and each
may have all possible values; consequently we may equate like
coefficients.
. Sv ,,\
,'. c p ** c 9 \ i jr (0)
Also, equating the remaining
(7)
If the characteristic equation is solved for the pressure we
shall have
so that
^dv (8)
which substituted in equation (4) gives
Equating like coefficients,
S/>
+ m 4, = e >
= c n
(9)
(10)
From equations (2) and (3)
c p dt + mdp = fw
+
and from an equation
(v,
which latter substituted in equation (11) gives
t, j ' JA i J
p &V O/>
Equating coefficients of dv,
C = Cn R
(12)
RELATIONS OK THE THERMAL CAPACITIES
II
Finally, from equations (i) and (3),
c v dt h Itlv ='iidf t odv (13)
Substituting for dt as above,
?
5v
I c v fT" dp  Itlv <= ndp \ odv,
op l
Equaling coefficients of dp,
'xr (14)
For convenience the several relations of the thermal capacities
may be assembled as follows:
w= /
They arc tlic necessary algebraic relations of the literal func
tions growing out of the first general principle, and arc inde
pendent of the scale of temperature, or of tiny other theoretical
or experimental principle of thermodynamics other than the one
already slated namely, llmt any two properties of a given
substance, treated as independent variables, arc sufficient lo
allow us to calculate any third property.
Of the six thermal capacities the specific heat at constant
pressure is the only one thnl is commonly known by direct
experiment. For perfect gases this thermal capacity is a con
stant, and, further, the ratio of the specific heals
CMS K
is a constant, so that c v is readily calculated. The relation? of
the thermal capacities allow us to calculate values for tho
other thermal capacities, /, , , and o, provided that we
first determine the several partial differential coefficients w!
appear in the proper equations. But for a perfect gas
characteristic equation is
pit  RT t
from which we have
*ST ~~ p ' S/ ~ v '
8p R' &v JR.
Substituting these values in the equations for the tho
capacities, we have
i i (c _ c v _ w H. f c _ tf V
' ' y? (Cp ^' m R (Cp v) >
v p
0= C n ',
by aid of which the several thermal capacities may be calcul
numerically, or, what is the usual procedure, may be represo
in terms of the specific heats.
CHAPTER II.
FIRST LAW 01' TUKUMOIWNAMICS.
Tire formal statement of the first law of thermodynamics is:
Heat and mechanical energy are mutually convertible, and
heal requires for its product ion and produces by its disappearance
a definite number of units of work for each thermal writ,
This law, winch may he considered to be (he second general
principle of thermodynamics, is the statement of a welldeter
mined physical hut. H is a special statement of the general
law of (he conservation of energy, i.e., that energy may be trans
formed from one form to another, but can ncilhcr be crcnled
nor destroyed. Jt should lie slated, however, that the general
law of conservation of energy, tjiough universally accepted, has
not been proved by direct experiment in till cases; there may be
cases that are not susceptible of so direct, a proof as we have for
the transformation of heat into work.
The best determinations of the mechanical equivalent of heat
were made by Rowland, whose work will be considered in detail
in connection with the properties of steam and water. From
his work it appears that 778 footpounds of work are required to
raise one pound of water from 62 to 0,j Fahrenheit; this value
of the mechanical equivalent of heat is now commonly accepted
by engineers, and is verified by the latest determinations by
Joule and oilier experimenters.
The values of the mechanical equivalent of heal for the Eng
lish system and for the metric system are:
i i). T. u. 778 footpounds.
i calorie 126.9 metrekilograms.
This physical constant is commonly represented by the letter
/; the reciprocal is represented by A.
'J
monly quoted as 772 for the English system and 424 for the
metric system. The error of these values is about one per cent.
Effects of the Transfer of Heat. Let a quantity of any sub
stance of which the weight is one unit i.e., one pound or one
kilogram receive a quantity of heat dQ. It will, in general,
experience three changes, each requiring an expenditure of
energy. They are: (i) The temperature will be raised, and,
according to the theory that sensible heat is due to the vibra
tions of the particles of the body, the kinetic energy will be
increased. Let dS represent this change of sensible heat or
vibration work expressed in units of work. (2) The mean
positions of the particles will be changed; in general the body
will expand. Let dl represent the units of work required for
this change of internal potential energy, or work of disgrcgation.
(3) The expansion indicated in (2) is generally against an exter
nal pressure, and to overcome the same that is, for the change
in external potential energy there will be required the work
dW.
If during the transmission no heat is lost, and if no heat is
transformed into other forms of energy, such as sound, electricity,
etc., then the first law of thermodynamics gives
dQ = A(dS + dl
(15)
It is to be understood that any or all of the terms of the equa
tion may become zero or may be negative. If all the terms
become negative heat is withdrawn instead of added, and dQ is
negative. It is not easy to distinguish between the vibration'
work and the disgrcgation work, and for many purposes It is
unnecessary; consequently they are treated together under the
name of intrinsic energy, and we have
dQ = A(dS + dl + dW) = A(dE + dW)
(16)
The inner work, or intrinsic energy, depends on the state of
the body, and not at all on the manner by which it arrived at
cncc to a given plane consisting of kinetic energy and potential
energy, depends on ihc velocity of the body and the height
above ihc plane, .and not on the previous history of the body.
The external work is assumed lo be done by a fluidpres
sure; consequently
rflK pdv
W
(18)
where u 3 and u, arc the final and initial volumes.
In order lo find the value of the integral v in equation (18) it
is necessary lo know the manner in which the pressure varies*
with the volume. Since the pressure may vary in different ways,
the external work cannot be determined from the initial and
final slates of the body; consequently ihe heat required to effect
a change from one slate lo another depends on the manner in
which the change is effected .
Assuming the law of ihc variation of the pressure and volume
lo be known, we may inlcgralc thus:
r" a ^
2,. I / pito)
*/i>i /
(19)
In order lo determine E for any stale of a body ii would be
necessary lo deprive it entirely of vibration and disgrcgntion
energy, which would of course involve reducing it to a^stalc of
absolute cold; consequently ihc direct determination is impossi
ble. However, in all our work the substances operated on arc
changed from one slate lo another, and in each state the intrinsic
energy depends on Ihc slate only; consequently the change of
intrinsic energy may be determined from the initial and final
states only, without knowing the manner of change from one lo
ihc other.
In general, equations will be arranged lo involve differences
vibration and disgrcgation work avoided.
Thermal Lines. The external work can be determined only
when the relations of p and v arc known, or, in general, when
the characteristic equation is known. It has already been
shown that in such case the equation may be represented by a
geometrical surface, on which socalled thermal lines can bo
drawn representing the properties of the substance under con
sideration. These lines arc commonly projected on the (p t v)
plane. It is convenient in many cases to find the relation of />
and v under a given condition and represent it by a curve drawn
directly on the (p, v) plane.
Lines of Equal Pressure. The change of
aj . condition takes place at constant pressure, and
consists of a change of volume, as represented in
Fig. 3. The tracingpoint moves from a t to a,,
and the volume changes from u, to v z  Tlw
FIB.J. " work done is represented by the rectangular area
under d t a a) or by
W
fvt
= p I
Jo,
During the change the temperature may or may not change;
the diagram shows nothing concerning it.
Lines of Equal Volume. The pressure in
creases at constant volume, and the tracingpoint
moves from a t to o a . The temperature usually
increases meanwhile. Since dv is zero,
SSB Q
(21)
Pic.
Isothermal Lines, or Lines of Equal Temperature. The
temperature remains constant, and a line is drawn, usually
convex, toward the axis 0V. The pressure of a mixture of a
jiquiu ana its vapor is consumi lor u given temperature; con
sequently the isothermal for such a mixture is a line of equal
pressure, represented by Fig. 3. The iso
thermal of a perfect gas, on the other hand, is
an equilateral hyperbola, as appears from the
law of Boyle, which may be written
laodynamlc or Isoenerglc Lines arc lines representing changes
during which Ihc intrinsic energy remains constant. Conse
quently all the heat received is transformed into external work.
It will be seen later that the isodynamic and isothermal lines
for a gas are the same.
Adiabatlc Lines. A very important problem in thermo
dynamics is to determine the behavior of a Kiihslancc when a
change of condition lakes place in a nonconducting vessel.
During the change for example, an increase of volume or
expansion some of the heat in ihc substance; may ho changed
into work; but no heat is transferred to or from the substance
through the walls of the containing vessel. Suck changes are
called adiabalic changes.
Very rapid changes of dry air in the cylinder of an aircom
pressor or a compressedair engine are very nearly adiabalic.
Adiabalic changes never occur in the; cylinder of a steamengine
on account of the rapidity with which aleam is condensed on or
vaporized from the castiron walls of the cylinder.
Since Ihcrc is no transmission of heal to (or from) ihc working
substance, equation (19) becomes
Q
, ~f / ' fitto)
C/"l
fitlv
(22)
(23)
that is, the external work is clone wholly at the expense of Ihc
intrinsic energy of the working substance, as musl be ihc case
in conformily wilh the assumption of an adiabalic change,
Relation of Adiabatic and Isothermal Lines. An important
property of acliabatic lines can be shown to advantage at this
place, namely, that such a lino
is sleeper than an isothermal
line on the (p, v) plane where
they cross, as represented in
Fig. 6. The essential feature of
adiabalic expansion is that no
heat is supplied and that conse
quently the external work of
expansion is done at the expense
of the intrinsic energy which
consequently decreases. The
intrinsic energy is ihc sum of
PlD . 6 . Ihc vibration energy and I he
disgrcgaiion energy, both of
which m general decrease during an adiabalic expansion; in partic
ular the decrease of vibration energy means a loss of temperature.
Conversely an adiabatic compression is accompanied by an in
crease of temperature. If an isothermal compression is rcpre
scnted by cl, then an adiabatic compression will be represented
by a sleeper line like ca, crossing the constant pressure line fo to
the right of 6, and thus indicating that at that pressure ihcro is
a greater volume, as must be the case for a body which expands
during a rise of temperature at constant pressure.
It is very instructive to note the relation of these lines on the
surface which represents the characteristic equation for a perfect
gas. In Fig. 6, which is an isometric projection, the general
form of the surface can be recognized from the following condi
tions: a horizontal section representing constant pressure
cuts the surface in a straight line which indicates that the volume
increases proportionally to the absolute temperature, and this
line is projected as a horizontal line on the (p, ) plane; a vertical
section parallel to the (p t l) plane shows that the pressure in
this case increases as the absolute temperature, and the line of
intersection with the surface is projected as a vertical line on the
(/j, y) plane; finally vortical sections parallel to the (p, v] plane
arc rectangular hyperbola? which arc projected in their true
form on the (/>, i>) plane. If AC is an adiabalic curve on the
characteristic surface, its loss of temperature is properly repre
sented by the fact that it crosses a scries of isolhcrmals in passing
from A lo C; Aft is a line of constant pressure showing a decrease
of temperature between the isothcrmaLs through A ami through
C; finally the projection of ABC on to the (/>, v) plane shows that
the adiabalic line ac is steeper than the isothermal line be.
Addition .should be called to the fad lhal the first sta Lenient
of this relation is the more general as it holds for all substances
that expand with rise of temperature ul constant pressure what
ever may be ihe form of the characteristic oriuuion.
Thermal Linos and their Projections, The treatment given
of thermal lines is believed to be the simplest and to present
ihc features that nrc most useful in practice. There is, how
ever, both Interest and instruction in considering their relation
in space and their projections on the three thermal planes. Jt
is well lo look attentively at Fig. C, which is n correct isometric
projection of the characteristic surface of a gas following the
law of lioylo and GayLussac, noting that every section by a
plane parallel lo the (/*, v) plane is
a rectangular hyperbola which has
the same form in space find when
projected on the (/, v) plane. The
sections by a plane parallel lo the
(/;, plane are straight lines and arc
of course projected as straight lines
on that plane ami on the (p t v] plane;
in like manner [be sections by plnnc
parallel to the (/, v) plane nre straight
lines. The adiabalic. line In space
and fts projected on the {/>, v) plane is probably drawn a little
loo sleep, bul the divergence from truth is not evident to Ihc eye.
In l'ig. 7 the same method of projection iy used, bul other
lines arc added together with their projections on Ihc several
rP
umi.a. jjtgiiiiinig UL un. jiuiiu i* in ajj ( ii.i, uiw jmu ow
isothermal which Js projected as a rectangular hypcrbol
on the (p, v) plane, and as straight lines a"b" and a'"L
the (p, 1) and (/, v) plane. The adiabalic line ac is s
than the isothermal, bolh in space and on the (p, v) pla
already explained; it is projected as a curve (a"c" or a"'c'
the other planes. The section showing constant prcssi
represented in space by the straight line ae which project
the (/>, plane is parallel to the axis ot, and on the
plane is parallel to the line itself in space; on the (p, v) plan
horizontal, as shown in Fig. 3. In much the same way ad
section by a plane parallel to the (I, v) plane, and a'd',
and a'"d" f arc its projections.
Graphical Representations of Change of Intrinsic Enerj
Professor Rankinc first used a graphical method of rcprese
a change of intrinsic energy, employing adiabalic lines on
follows :
Suppose that a substance is originally in the state A (Fij
and that it expands acllabalically; then the external work is
at the expense of the intrinsic energy; hence if the expa
has proceeded to A l the area AA l a l a ) which represent;
external work, also represents the change of intrinsic en
Suppose lhat the expansion were to continue indefinitely;
the adiabatic will approach the axis
indefinitely, and the area representing
work will be included between the curve
produced indefinitely, the ordinatc Aa,
the axis OV; this area will represent al
work that can be obtained by the cxpai
of the substance; and if it be admitted
during the expansion all the intrinsic energy is transfoi
into work, so that at the end the intrinsic energy is zero, it
resents also the intrinsic energy. In cases for which the c
lion of the aaiabatic can be found it is easy to show that
/i
J..
on
oti
IB
on
v )
ne
m
ev
icl
1C*
n
it
is a finite quantity; and in any case, if we admit an absolute xcro
of temperature, it is evident that the intrinsic energy cannot
be infinite. On the olhcr hand, if an isothermal curve were
treated in the same way the area would be infinite, since beat
would be continually added during the expansion.
Now suppose the body to pass from the condition represented
by A to that represented by #, by any path whatever that is,
by any succession of changes whatever /or example, that
represented by the irregular curve AJ). The intrinsic energy
in the stale ft is represented by the area VkBfi. The change of
intrinsic energy is represented by the urea ftRbfiAa t and this
area does not depend on the form of the curve AJi. This graph
ical process is only another way of saying thai ihe intrinsic
energy depends on the slate of the subslunce only, and that
change of intrinsic energy depends on the final and initial slates
only.
Another way of representing change of intrinsic energy by
aid of isodynamie lines avoids an infinite diagram. Suppose
the change of slate to be represented by the
curve AH (Kip;, g). Draw an isodynamic
line AC through the point A t and an adia
balic line RC through Ji t intersecting at C;
in general the Lsocnergic line is distinct,
from the isothermal line; for example, the
isothermal line for a saturated vapor is a
line parallel to the OV nxis, and
I'm g.
the isocnergic line ia represented approximately by the equation
c .Ortfl
const.
Then the atvu AJlba represents Ihe external work, and the area
bJRCc reprcsciixs the change of intrinsic energy; for if the body be
allowed lo expand adiabnticftlly till the intrinsic energy is reduced
to jifl original amount at the condition represented by A the
external work bBCc will be done at the expense of the intrinsic
energy.
CHAPTER HI.
SECOND LAW OF THEKMODYN/UfrCS.
Heatengines are engines by which heat is transformed into
work. All actual engines used as motors go through conlinuous
cycles of operations, which periodically return things to Iho
original conditions. All heatengines arc similar j n that (hoy
receive heat from some source, transform part of it into work,
and deliver the remainder (minus certain losses) to a ftfrigmriv.
The source and refrigerator of a condensing steamengine arc
he furnace and the condenser. The boiler is properly con!
in
to cliscuss a
Pro. ro.
v .,._.... ^M.iuui with nonconducting
s fitted a p,ston, also of nonconducting material,
and moving without friction; on the
other hand, the bottom of the cylinder
>s supposed to be of a material that is
a P erfcct conductor. There is a mm
conducting stand C on which the
Binder can be pi accd whilc ftdillbal , c
changes take place. The source of
heat A at a temperature
that in operat I'd !
and draws heat from "
frigerator B at , h " m
draw heat from the cvlinder ' mannCr can
constant tcmpemture ' *" " b P ' aced

* P ' aCCd " "
at a
ce of heat. ,, ace thcy
22
(Fig. TO), and let the substance expand at the constant tem
perature /, receiving heat from the source A.
If the first condition of the substance be
represented by A (Fig. n), then the second
will be represented by B> and AB will be an
isothermal. If E a and 4 are the intrinsic
energies at A and B, and if W ab , represented
by the area aABb, be the external work, the
hca( received from A will be
Flo . .
QA (>
( 25 )
Now place the cylinder on the stand C (Fig. 10), and let
the substance expand adiabatically until the temperature is
reduced to t lt that of the refrigerator, the change being rep
resented by the adiabatic BC (Fig. 11). If e is the intrinsic
energy at C, then, since no heat passes into or out of the
cylinder,
o = A (E c E b + WK) (26)
where W^ is the external work represented by the area bBCc.
Place the cylinder .on the refrigerator B, and compress the sub
stance tilt it passes through the change represented by CD,
yielding heat to the refrigerator so that the temperature remains
constant. If Ed is the intrinsic energy at D, then
is the heat yielded to the refrigerator, and W ed , represented by
the area cCDd, is the external work, which has a minus sign,
since it is done on the substance.
The point D is determined by drawing an adiabatic from A
to intersect an isothermal through C. The process is completed
by compressing the substance while the cylinder is on the stand
C (Fig. 10) till the temperature rises to t, the change being
represented by the adiabatic DA. Since there is no transfer
of heat,
o = A (E a E d W da ) (28)
Adding together the several equations, member to member,
Q _ Q, = A (W ail + H'fc  W c<l  Wto) . , (29)
or, if W be the resulting work represented by the area ABCB t
then
(30)
that is, the difference between the heat received and the heat
delivered to the refrigerator is the heat transformed into work.
A Reversible Engine is one that may run cither in the usual
manner, transforming heat into work, or reversed, describing
the same cycle in the opposite direction, and transforming work
into heat.
A Reversible Cycle is the cycle of a reversible engine.
Carnot's engine is reversible, the reversed cycle being
ADCBA (Fig. ii ), during which work is done by the cnglno
on the working substance. The engine then draws from tho
refrigerator a certain quantity of heat, it transforms a certain
quantity of work into heat, and delivers the sum of both to tho
source of heat.
No actual heatengine is reversible in the sense just staled,
for when the order of operations can be reversed, changing the
engine from a motor into a pump or compressor, the reversed
cycle differs from the direct cycle. For example, the valvo*
gear of a locomotive may be reversed while the train is running,
and then the cylinders will draw gases from the smokebox,
compress them, and force them into the boiler. The locomotive
as ordinarily built is seldom reversed in this way, as the hot
gases from the smokebox injure the surfaces of the valves and
cylinders. Some locomotives have been arranged so that the
exhaustnobles can be shut off and steam and water supplied
to the exhaustpipe, thus avoiding the damage from hot gases
when the engine is reversed in this way. Such an cnglno may
'then have a reversed cycle, drawing steam into' the cylinders,
compressing and forcing it into the boiler; but in any case the
reversed cycle differs from the direct cycle, and the engine is
nol properly a reversible engine.
A Closed Cycle is any cycle in which the final slate is the same
as the initial stale. Fig. 12 represents such a
cycle nnulu up of four curves of any nature
whatever. If the four curves arc of two species
on!}', ns in the diagram representing the cycle
of Carnol's engine, the cycle is said to be simple.
Jn general we shall have for u cycle like that of Fig, 12,
rm.
(?*  (?  (?*
W flt
A dosed curve of any form may be consid
ered lo be ihc general form of a closed cycle,
as that in Fig. 13. For such a cycle we have
Fio.i3> I dQ *= A IdW, which is one more way of
slating ihc first law of thermodynamics.
Tt may make this last clearer to consider the cycle of Fig, 14
composed of the isothermals AM, CD, and HG } and the
adialmtics BC t DK, and GA. The cycle
may be divided by drawing ihc curve
through from C lo P. ll is indifferent
whether the path followed be ARCDHGA
I Tl f ' T>Xf 1'\ V *f* 4 J ( Tl f~* J "*/*' t i
or A]tCl'CJ)hCrA) or, ngain, ABCJ'UA f
CDEJ'C.
Again, an irregular figure may be
imagined to be cut into elementary areas by Isoihcrnwls and
adiabalic lines, as in Fig. 15. The summation of the areas will
give the entire area, and the summation of the works represented
by these will give the entire work represented by ihc entire area,
The Efficiency of an engine is the ralio of ihe heat changed
into work lo the entire heat applied; so that if it be represented
by c,
AW ~' (30
Fin. 14.
Q
Q
for the heat Q> rejected to the refrigerator is what is left
AW thermal units have been changed into work. '
Carnot's Principle. It was first point*(
out by Carnol that the efficiency of **
reversible engine docs not depend tm
nature of the working substance, but
it depends on the temperatures of
L source of heat and the refrigerator.
FI. u. Let us sec what would be the
qucncc if this principle wore not iruCt
Suppose there arc two reversible engines R and A, each Inking
Q thermal units per second from the source of heat, of whtcH
A Is the more efficient, so that
is larger than
AW,
Q
Q
Q  Q
Q
Q
(33>
this can happen only because Q a ' is less than Q,', for Q is assumed
to be the same for each engine. Let the engine R be reversed
and coupled to A, which can run it and still have left the useful
work W a W r . This useful work cannot come from tho
source of heat, for the engine R when reversed gives to the sourCQ
Q thermal units per second, and A takes the same amount in Lhd
same time. It must be assumed to come from the refrigerator!
which receives Q a ' thermal units per second, and gives up Q r *
thermal units per second, so that it loses
Qr  Q a '  A (W a  Wr)
thermal units per second. This equation may be derived from
equations (32) and (33) by subtraction.
Now it cannot be proved by direct experiment that such an
action as that just described is impossible. Again, the first law
of thermodynamics is scrupulously regarded, and there is no
contradiction or formal absurdity of statement. And yd when
the consequences of lite negation of Cur not *s principles tire
clearly set forth they arc naturally rejected as improbable, if not
impossible. The justification of the principle is found in the
fact thai theoretical deductions from it arc confirmed by
experiments.
Second Law of Thermodynamics. The formal statement
of Carnot's principle is known us the second Inw of thermody
namics. Various forms arc given by different investigators,
none of which arc entirely satisfactory, for the conception is not
simple, as is that of the first law.
The folio wing nrc sonic of ihc statements of the second law;
(7) AH reversible engines working between the same source of
heat and refrigerator have the stnne efficiency,
(2) The efficiency of a reversible engine is independent of llio
working substance.
(3) A selfacting machine cannot convey heat frain one body
to another at a higher temperature.
The second law is the third general principle of thermody
namics; it dilTcrs from each of the others and is independent
of them. Summing up briefly, the first general principle is a
pure assumption that ihcrmodyrmmic equations may contain
only two independent variables; the second is the statement of
an experimental fact; the third is a choice of one of two
propositions of a dilemma. The first and third arc justified
by the results of the applications of the theory of thermo
dynamics.
So far as efficiency is concerned, lite second law of thermo
dynamics shows that it would be a umUcr of Indifference what
working substance should be chosen; we might use air or sicnm
in the same engine and get the same efficiency from cither;
there would, however, be a great difference in the power that
would be obtained. In order to obtain a diagram of convenient
size and distinctness, the adia balks are made much sleeper than
the isolhermals in Fig. n; as a matter of fact the diagram drawn
correctly is so long and attenuated that it would be practically
worthless even if it could be obtained with reasonable 
mation in practice, as the work of the cycle would hard
come the friction of [lie engine. The isothcrmals for a
of water and steam arc horizontal, and the diagram la
form shown by Fig. 16. In practice
gram closely resembling Garnet's c
chosen as the ideal, differing mainly
steam is assumed to be supplied a
hauslcd. In n particular case an
working between the temperatures 36
and 158 F. had an actual thermal efficiency of o.
ideal cycle had an efficiency of 0.23, and Carnot's cy
an efficiency of 0.25. The ratio of 0.18 to 0.23 is abot
which compares favorably with the efficiency of turbine
7 """ wheels.
/? i /
Carnot's Function.  Carnot's principle asserts th
efficiency of a reversible engine is independent of the na
the working substance; consequently the expression i
efficiency will not include such properties of the workir
stance as specific volume and specific pressure. But th
ciplo asserts also that the efficiency depends on the tempc
of the source of heat and the refrigerator, which indeed
only properties of the source and refrigerator that can
the working of the engine.
We may then represent the efficiency as a function of tl
peralures of the source of heat and the refrigerator, or
amounts to the same thing, as a function of the sup'cric
pcrature and the difference of fhc temperatures, and ma;
AW '
e Q
where Q is the heat received, Q' the heat rejected; and /
are the temperatures of the source of heat and of the refri$
on any scale whatsoever, absolute or relative.
, .If the temperature of the refrigerator approaches near t
[lie source of hcuLQ Q' and / f become A<7 and A/, and at
the limit dQ and <//, so that
(34)
It is convenient in assume thai the equation ctin he expressed
in the form
The function/ (0 is known as Carnot'a function, and physi
cists consider that the isolation of this function and the relation
of the function in temperature are of great theoretical importance.
Absolute Scale of Temperature, ft is convenient and cus
tomary to assign to Carnoi's function the form,;, whore T is
[lie temperature by the absolute scle referred to on page 3,
measured from the absolute xcro of temperature. '.Phis assump
tion is justified by the facts that the theory of thermodynamics
is much .simplified thereby, and (1ml the difference belwccn
such n scalp of temperature and the scale of the airlhcnnomcter
Is very small.
Kelvin's Graphical Method. This treatment of CA mot's
function was first proposed by Lord Kelvin, who illustrated the
general conception by the following graphical construction:
In J'ig. 17 let ak And bi be two ueliAbatic lines, and let the
substance have its condition
represented by the point fl.
Through a and d dmw iso
ihermallincs; then the diagram
abed represents the cycle of a
simple reversible engine. Draw
the isothermal line fc, so that
the area dcef shall be equal to
iii i ,< i f Vio. t?.
(toed; then the' diagram dccj
represents the cycle of a reversible engine, doing the same
Amount of work per stroke aa that engine whose cycle is rcpre
from the source and delivered lo the refrigerator i.e., the hen I
transformed into work is ihc same. The refrigerator of the
first engine might serve for the source of heat for the second.
Suppose that a series of equal areas arc cut oft by isothermal
lines, as/<2//, hgik^ etc., and suppose ihcrc arc a scries of reversible
engines corresponding; then there will be a scries of sources of
heat of determinate temperatures, which may be chosen lo
establish a thcrmometric scale. In order lo have ihc scale cor
respond with those of ordinary thcrmomclcrs, one of the sources
of heat must be at the temperature of boiling wnlcr, and one at
that of melting ice; and for the centigrade scale there will be one
hundred, and for the Fahrenheit scale one hundred and eighty,
such cycles, with the Appropriate sources othcal, between boiling
point and freezingpoint. To establish Ihc absolute zero of the
scale the scries must be imagined to be continued till the firca.
included between an isothermal and the two adiabalics, continued
indefinitely, shall not be greater than one of the equal arcns.
This conception of Ihc absolute 2cro
may bo made clearer by taking wide
intervals of temperature, as on Fig.
18, where the cycle abed is assumed
to extend between the isothcrmals of
o and 100 C.; that is, from frccfc
ingpoinl to boilingpoint. The
next cycle, cdef, extends ^o 100 C.,
and the third cycle, efgb t extends
to 200 C. The remaining area,
which is of infinite length and ex
tremely attenuated, is bounded by the
isothermal gk and the two adiabalics
ha and gfi, The diagram of course
cannot be completed, and conse
quently the area cannot bo measured;
but when the equations to the isothermal and the adiabatics
are known it can be computed. So computed, the area Is found
to bo^of one of the; three equal areas abctl, cr//e, and efhg.
100
The absolute xcro is consequently 273 C. below frccxingpoinl.
VuruVr discussion of the ubsohile scale will be deferred till
a comparison is made with the airthermometer.
Spacing of Adlabixtics.  Kelvin's graphical scale of temper
ature is clearly a method of spacing isothermal* which depends
only on our conceptions of thermodynamics siml on the funclii
menliil units of weight and length. Kvlrlenlly the same method
may be applied lo spucing iiclialmlics, i\nd thereby a new concep
tion of great importance may be introduced into (he theory of
thermodynamics. On this conception is based the method for
solving problems involving adiabalic expansion of steam, us
will bo explained in the discussion of that subject.
In Fig. ii) let tin and do
be two isolhermals, and let
ad, be, hit uml no be a series
of adiabalii's, so drawn that
llie areas of the figures ftbcd,
l>intc } and hiom are equal;
then we have u series of
adiabalics that are spaced in
the same manner as are the
isolhermals in Figs. 17 and
18, and, as wilh ihose iso
lhermals, the spacing depends only on our conceptions of ther
modynamics and ihe fundamental units of weight find length.
In the discussion of I'JKS. 17 and 18 it was shown lhat the area
of the Blrlp between the initial isothermal tib and the two adiabalic
lines must be treated (is finite, mid that in consequence the
graphical process leads to un absolute zero of temperature. On
the contrary! lite area between the acliabatic ad and the two
isoihcrmuls an and <h if extended Infinitely will be infinite, and
it will be found that there is no limit to the number of nelia
bntics that can be drawn with the spacing indicated. A like
result will follow if the isothcrnmls arc extended to the right and
SECOND LAW OF T1IKUMODYNAMICS
upward, and if adinbnlics ft re spucid off in the same marmot*.
This conclusion comes from the fact pointed out on page jj,
that the area under an isothermal curve which is extended with
out limit is infinite, because heat is continuously supplied,
part of which can be changed into work.
It is convenient to introduce a new function [
place which shall express the spacing of adiabalb
represented in Fig. K), nnd which will bo called
From what precedes it is evident tluit cniropy
same relations lo the ndinlwiiirs of Fitf 19 llmi
has to the isolhcrmals of Figs. 17 nnd 18, but that ihcrc la
radical difference, that while there is a natural absolute zero of
temperature, there is no aero of cniropy. Consequently In pro!~
Icms we shall always deal with di/l'mnccK of entropy, and tf ir*
find it convenient lo treat the entropy of a certain condition of (*
given substance as a jwro point it is only that we may count up
and down from that point.
If the adiubatic line ad in Fig. 19 should lie extended lo
right, it would clearly lie btnealh the ndmbalic no, which
with the tacit convention of that figure, i.e., that as spaced
adiabalics are lo be numbered toward the right and that
entropy increases from a toward n.
The simplest and the most natural definition of entropy
the present considerations, is that entropy is that function which
remains constant for any change represented by a
adiabatic expansion (or compression). With this definition
view, the adiabatic lines might be called iaoentropic lines*
should be borne in mind thai our present discussion is p
limited to expansion in a nonconducting cylinder closed
piston, or to like operations. More complex operations
that' just mentioned may require an extension of the conce
of entropy and lead to fuller definitions. Such extensions of lhi
conception of entropy have been found very fruitful In certain
physical invcsligations, and many writers on thcrmoclynamfc*
lor engineers consider that they get like advantages from thotn,
There is, however, an advantage in limiting the conception csf u
It
GRAIM1ICAI, KKI'KKHKNTATION OK KFKICIKNCY
33
new function, howcrcr simple [hat conception may he; and (here
is an added advantage in being able to return La a simple con
ception at will.
Efficiency of Reversible Engines. Returning to equation
(34) and replacing Cnrnot's function/ (1} by ?> a.s agreed, wo
have for the differential equation of the efficiency of a reversible
engine
tlO <ll
ii . i
Q V
or, integrating between limits,
Q
r
T'
and the efficiency for the cycle becomes
T
Q
This result might I wive been obtained before (or without) the
discussion of Kelvin's ^mphlcul method, and leads to the same
conclusion, that the absolute temperature cnn In; made to depend
on the efficiency of Carnol'.s cyclu, and may, llu'refort 1 , be inde
pendent of any thcrmomc'U'ic substance.
As has already been nairl, this conception
is more important on the physical side
than on the engineering aide, uncl its rtit
eration need not be considered to call fur
any speculation by thcflluek'ntauhis time.
Graphical Representation of Efficiency.
Let Klg. 20 represent, the cycle of
a reversible heatengine. For convenience
it is supposed there are four degrees of icmpertiluro from the
isothermal AB to the Isothermal DC t find thai there are three
Intervals or units of entropy between the adialmlics AD and
I'm. ao.
34
SECOND LAW OF THICHMOIJYNAMICS
BC. First it will be shown that all the srmill arcas into
the cycle is divided by drawing the intervening lulitiUitJ*'*
isolhcrmiils arc equal. Thus we have to begin with a ^
a = c by construction. But engines working on the
and b have the same efficiency ami reject ihc snmc
of heat. These heats rejected are equal to the hents
to engines working on the cycles cam] d } which
take in the same amounts of heat. Hut these
between the same limits of temperature and Iwvu
efficiency, and consequently change ihu same nmnuni
into work. Therefore the areas c and </ arc equal.
manner all the small areas arc equal, and each
thermal unit, or 778 foolpounds of work.
It is evident that the heat changed into work i.s
(T~T) (r//~r/,),
and, further, that the same expression would be obtain trc
similar diagram, whatever number of degrees there mi
between the isothcrmcils, or intervals of entropy brtwc
adiabalics, and that it is not invalidated by using rrnc't
degrees and fractions of units of entropy. Ji is con*?
the general expression for the heal changed into wnrk
engine having a reversible cycle.
It Is clear that the work done on such a cycle innpaw**
lower temperature T decreases, and that it is a maximum
T becomes zero, for which condition all of the hem np
changed into work. Therefore the heat applied is
Q  r &  0j,
and the efficiency of ilic engine working on the cycle
by Fig. 20 is
AW Q Q 1 (Tr) w  </>) r 
" J  v_ j . .
Q
Q
T
as found by equation (35). The deduction of this
integration is more simple and direct, but the uraphlcnl
* * n i ^
EXPRESSION FOR KNTKOPY
35
I' HI. 31.
is interesting and may give the student additional light on (hi.s
subject.
TemperatureEntropy Diagram. Thermal diagrams are com
monly drawn with pressure and volume for. (he coordinates,
but for some purposes il is convenient to use other properties
as coordinates, in particular temperature and entropy. For
example, Fig. 21 represents Carnal 'a cycle
drawn with entropies Cor abscissa. 1 and tem
peratures for ordinales, with the advantage (/j If> .
that indefinite extensions of the lines are
avoided, and ihc areas under consideration
are evidently finite and measurable. With
the exception that there appears now to be no
necessity to show that the areas obtained by subdivision are all
equal, the discussion for Fig. 20 drawn with pressures and vol
umes may be repealed with temperatures and entropies.
Expression for Entropy. One advantage of using the tem
pera lureentropy diagram is that il leads at once to a method
for computing changes of entropy. Thus in Fig. 22 let t(B
represent an isothermal change, and lei Aa
and Jib be adiabailcs drawn to ilic axis of </>;
then the diagram ABlia may be considered to
be the cycle for a Carnot's engine working
between the temperature 7' and the absolute
xero, and consequently having the efficiency
unity. The heal changed into work may there
fore be represented by
G r tf '  4) W
If we are dealing with a change under any other condition
than constant temperature, we may for an Infinitesimal change,
write the expression
d<[> ^ , (37)
J
and for ihc entire change may express the change of entropy by
,, L A/Q
/A' * tfy asa I **
r / I f f* '
Fl. 11.
36 SKCONI) LAW OK TIIKKMOUYNAM1CS
which should for any particular case either be integrated
between limits or else a constant of integration should be
determined.
Attention should be called to the fact that the conception of
the spacing of isoihermals and adiabalic.s is based fundamen
tally cm Carnol's cycle and the second law of thermodynamics,
which 1ms been applied only to reversible operations. The
method of calculating changes of entropy applies in like manner
to reversible operations; and when entropy is employed (or
calculations of operations that tiro not reversible, discretion
must be used to avoid inconsistency and error.
On the other hand, the entropy of a unit weight of a given
substance under certain conditions IK a perfectly definite quao*
tity and Ls independent of the previous history of the substance.
This nwy be made evident by the consideration that nny point
on the line no, Fig. icj, page 31, has n certain number of unlla of
entropy* (for example, three) more (ban that of any point tin
the ndiabalic (iff.
Example.  There may be an advantage in giving a calcu
lation of a change of entropy to emphasize the point that it eon
be represented by a number. Let it be required to find Ihts
change of entropy during an isothermal expansion of one pound
air from four cubic feet to eight cubic.
The heal applied may be obtained by integrating the expression
<!&
T
Itfa
T
" B) 7"
ille value of the latent heat having been taken from page
From the characteristic equation
t>v  itr
the above expression may be reduced to
dv
APPLICATION TO A RKVKRSI11I.K CVCI.K 37
 i ' I, i \ 1 v
. . t/> (p  (t jf ( v ) jojr^
(/,' t/j , ; (0.2375 o.ifiyo) lo& ~ =0.0475.
''"'
A problem for air is chosen because H can he readily worked
out at Ui is place; as Ji mailer of fuel, I here arc few occasions in
practice where there is reason lo refer to entropy of air.
Application to a Reversible Cycle. A very important result
is ohlaincd by the application of equation (37) to the calcula
tion of un l ropy during n reversible cycle. In the first place,
il is clear llmt the entropy of a substance having its condition
represenled ))y the point a (Kitf. 23), depends on tin mliabalic
line drawn through it; in other words, the entropy depends only
on ihe condition of liic siihslunee,
In this regard entropy i like intrin
sic energy and differs from cxtermd
uork. ,SupKWt' now ihtU I!K. sub
stance in made to pass through a
cycle of operations represented by
the point a lraein# the dw#wm on
l ; i}<. 23; it is clear that the entropy will lit ihc same at the end
of (he cycle us at (lie lie^inniiiK, for llic tntciriKpoim will ihen
be (in the original uditilmlic. line, As ihe tnicin^point moves
toward ihe ri^hl from adialmtic lo ntliiibalir Ihe onlropy
increases, and as it moves lo the left Ihe entropy d^creascH, (he
algebraic sum of chunks of eiUropy bcinK xero for the entire
cycle. This conclimion holds whclhei' ihe cycle is reversible
or nonreversible. The cycle represented by Fig. 23 in purposely
drawn like a sieamcngine indicator diagram (which is not
rc'vcrsihk') to emphasize die fticL thai llic cjiiinpic' of entropy is
/ero in tiny ciise.
If the cycle is reversible, then equation (37) may be used for
cnlcuhvlintf the. Hevcrul changes of cntrojiy, and for calculalinj;
the change for the entire cycle, giving for the cycle
/?
,g SECOND LA.W OF Til KKMODYNAMICS
This is a very important conclusion from the second law
thermodynamics, and is considered to represent that law.
second law is frequently applied by using this equation in can*
ncction with a general equation or a characteristic equation, fa
a manner to be explained later.
Though the discussion just given is simple and complete
there is some advantage in showing that equation (38)
for certain simple and complex reversible cycles.
Thus for Carnot's cycle, represented by Fig. 20, the i
of entropy during isothermal expansion is
because the temperature is constant. In like manner
decrease during isothermal compression is
**
so that the change of entropy for the cycle is
T 'J'
But from the efficiency of the cycle wu have
oQ' _ T  r . Q
Q
r
Q
r
T
Q,
T
r
A complex cycle like that represented by Fig. 24 may
broken up into two simple cycles A
and CDFE, for each of which individually
the same result will be obtained thai 1^
the increase of entropy from A to B b
equal to the decrease from F to 6\ afl4
the increase from C to 1) is equal lo lh
decrease from tt to F, so that the MIRH
mnlion of changes for the entire cycle gives xero.
Fin. 94,
MAXIMUM EFFICIENCY
39
Km.
Fig. 25 represents the simplified ideal diagram of a hotair
engine, in which by the aid of a regenerator the adiabatic lines
of Carnot*s cycle are replaced by
vertical lines without affecting the
reversibility or the efficiency of the
cycle. We may replace the actual
diagram by a series of simple cycles
made up of isothermals and ndia
batics, so drawn that the perimeter
of !hc complex cycle includes the
same area and corresponds ap
proximately with that of the
actual diagram. The summation of the change of entropy
for the complex cycle is clearly zero, as before. But by
drawing the adiabatic lines near enough together we may
make the perimeter approach that of the actual diagram as
nearly as we please, and we may therefore conclude that the
integration for the changes of entropy for that cycle is also zero.
Maximum Efficiency. Tn order (hat heat may be trans
formed into work with the greatest efficiency, all the heat should
be applied at the highest pniclicabic temperature, and the heat
rejected should be given up at the lowest practicable tempera
ture; this condition is found for Carnot's cycle, which serves
as the ideal type to which we approach as nearly as practical
conditions allow. Deviations from the ideal type arc of two
sorts, (i) commonly a different and inferior cycle is chosen as
being practically more convenient, and (2) the material of
which the working cylinder is made absorbs heat at high tem
perature and gives out heat at low temperature, thus interfering
with the attainment of the cycle selected.
The principle just stated must be accepted as immediately
evident; but there may be an advantage in giving an illustration.
The complex cycle of Fig. 24 is made up of two simple Carnot
cycles ABFG and CDEF; if two thirds of the heat is applied
during the isothermal expansion AB at 500 C, and one third
during the expansion CD, at 250 C., and if all the heat is re
40
SKCONI) LAW OK THERMODYNAMICS
jcctccl at 20 C., the combined dlinumy of the diagram
computed to be
^x
20
3 5 'I' 2 73 3
0.56;
250 I 273
had the heal been all applied nt 500 C., the efficiency
have been
500 20
*' ; fcj 0.62.
500 I 273
The loss in this case from applying pan, of the hcnl nt la
temperature is, therefore,
o.fia o.;6
; " " o.oo7.
0.02 "
Nonreversible Cycles. If a process or a cycle is nonre
siblc, then the change of entropy cannot be calculated ly et
lion (37), and equation (38) will not hold. The entropy '
indeed, be the same at the end as at the beginning of ihe cj
but the integration of ^ for the cycle will not give atero.
the contrary, it can be shown that the integration of % foi
entire cycle will give a negative quantity. Thus lei tlte 
reversible engine A take the same amount of heat per sarc*k
the reversible engine R which works on Gurnet's cycle* tew
it have a less efficiency, so thai
<J> Q '
where Q/ represents the heat rejected by the
Q C/ < 6  1>'  ('/'  r; C<A' 
Suppose now that r approaches xcro and that <jb'
then at the limit we shall have
ftj*prMiclj
or
i <
Ttty,
NONHHVKUSiniJi CYCLES 41
Integrating for ihc entire cycle., we shall have
C<1(\ ^ . CilO, Ar ' , .
Jr <0 ' ' J T"~* ' ' ' Ul)
where JV represents u negative quantity. The absolute
value of W will, of cuur.se, depend on the efficiency of Ihc non
reversil)lc engine. If ihe efficiency is small compared with llmt
of a reversible engine, then the value of W will bo large. Tf
(lit: efficiency approaches (hat nf a rcvcrsihle engine 1 , then N
approaches aero. Ft is scarcely necessary It) point out. that N
cannot be positive, for that would infer that ihe nonreversllilc
engine had a greater efluienry than a nvcrsiblc engine working
between the same lemperalures.
Some nonreversible operation*, like the /low of gus through
an orifice, result in the development of kinetic energy of motion.
In such ea.se the equation representing tin distribution of energy
contains a fourth term K to represent the kinetic: energy, and
equation (15) becomes
i/(j  A (rf.V I til ! tlW I rftf) . . . (42)
As before S represents vibration work, / represents disgreguLion
work, and W represents external work. If the vil)ratian and
disgrcgation work cannot be. separated, then we may write
tlQ  A (HE + d\\ r i(//C) (, 3 )
If a non reversible process like that just discussed takes place
in apparatus or appliances tlrnt are made of nonconcluciing
material, or if the action of the wills on ihc substance contained
can be neglected, the operation may properly be called adialwlic;
such a use fa clearly an extension of the idea Hlatetl on page 32,
and conclusions drawn from adiabatic expansion in a closed
cylinder cannot be directly extended Lo this new application,
Such a nonreversible operation is not likely to be isoeniropic,
and there is some advantage in drawing a distinction between
operations which are faocniroplc and those which are adfaballc.
SECOND IAW Of TtfKRMonVNAMICS
A nonreversible operation in nonconducting receptacles
isothermal, or may be with constant intrinsic energy,
appear in the discussion of flow of air in pipes on page
the discussion of the steam calorimeter, page ig lt Any
reversible process is likely tu be accompanied by nn Irtcrott
entropy; this will appear in special cases discussed * n
chapter on flow of fluids.
Since the entropy of a pound of :i given substance *.
given conditions, reckoned from an arbitrary /.urn, is ti pcrJ
definite numerical quantity, it is possible to determine its* en
for any scries of conditions, without regard to the melh<
passing from one condition tu another. Jt is, thmforc*, ctl
possible to represent any changes of a fixed weight f w.
stance, by a diagram drawn with temperatures and ertlf
for coordinates. If the diagram can be properly interp!
conclusions from it will be valid. It is, however, u> he Ir
mind that thermodynamics is essentially an analytical maltn
ical treatment; the treatment, so far as it applies to i?rififiKi
is neither extensive nor difficult. But the student in trmut
not to consider that because he has drawn u diagram repr
ing n given operation to the eye, he necessarily hit** a
conception of the operation. If any operation EnvtilvK
increase (or decrease) of weight of the substance npcrrntc
thermal diagrams are likely to be diflkuli to duvlac
to misinterpretation.
CHAPTER TV.
GENKRAT, TII1RMODYNAMIC METHOD.
IN the three preceding chapters a discussion lias been given
of the three fundamental principles of thermodynamics, namely,
(i) the assumption Unit the properties of any substance can
be represented by an equation involving three variables; (2) the
acceptance of the conservation of energy; and (3) the idea of
Carnol's principle. Jn the ideal case cfich of ihcsc principles
should be represented by an equation, and by the combination
of the three several equations all the relations of the properties
of a substance should be brought out so that unknown proper
tics may be computed from known properties, and in particular
advantage may be taken of opportunities to calculate such prop
erties us cannot be readily determined by direct experiment from
those which may be determined experimentally with precision.
Recent experiments have so far changed the condition of
affairs that there is less occasion than formerly for sucli a general
treatment. Of the three classes of substances that arc interest
ing to engineers, namely, gases, saturated vapors, and super
heated vapors, the conditions appear to be as follows. For
gases there arc sufficient experimental data to solve all problems
without referring to the gcncml method, though the ratio of the
specific heals is probably best determined by that method. For
saturated steam there is one property, namely, the specific vol
ume, which is computed by aid of the general method, but there
arc experimental determinations of volume which arc reliable
though less extensive. The characteristic equation of super
heated steam is now well determined, and the specific heat is
determined with sufficient precision for engineering purposes,
so that there is no difficulty to making the customary
calculations.
43
The one class of stiljslancvs for which (In necessary pr**? 1
must be computed by aid of the general meihod, art
tile fluids like ammonia and .sulphur dinxidc, w
for refrigerating machines.
On the whole, even with conditions as stated, it
that the student should master the gctmal iii
method, given in this chapler. Thai method in
nor hard, and is so commonly accepted lliut sludetiK
maslcrcd it will have no difliculiy in reading .sumd
and current literature involving thcrmodynainic !
Those cases remaining where the enenil nietlmil in
lent musl bo used, ure best Ireuled liy thul iiuiliod,
case of volatile fluids can lie treated only liy thui inr
The. case having been prescnled us fairly HH M>*^I
crction may be left wilh the student or his instructor
he shall read the remainder of tin's chapter Infurr
or whether the chapter ahull l>u altogether untilled.
The following method of comliiniiiK ilu* three H
ciplcs of thermodynamics, which is due to Lori) Kelt*! n
on the use of the expression
jf^sT" t "V"
oyoz 030 v
as the basis oC an operation, This expression is
as a criterion to determine whether a ctriuin
exact differential that am he inte^ivdcd ilinrdy,
some additional relation must IK stiii^hi liy aid of
expression may be transformed so ihul il ran lie
Conversely, if we .know, from the nature of it #k
like intrinsic energy, llmt il can be always ealctiljilce!
condition as represented by two variMi"i like umji
volume, then we are justified in concluding ihul lltr c
must be true and that we can use it its the Imsis of nn
Now in laying out a Ki'ncnil inclhocl it is impossible to s
uny parliiulur chiiraclerisiir equation, ami for that reason, it
nit ilu:r, the Ainu of (lie inugral equation connecting K with
fiindiuiinnul In assigned. Hut iho fact remains thai the pews!
bilily of working out uny mctlmrl depends on the ussumplion of
tin ultimate possibility of writing such an equation, and that
asHumplimi tiirrii's* with it the assumption that rf/i is an uxacl
clifTi'rrniiat.
Application of the First Law. .....  The first Kctienil principle
may be lulun u> be rrprcsinli;! by njuutiuu (i),
inul ilu fir.st law of lluTmodyiiiunicH by tciuation (16),
dQ A (<//; I r/HO A (<//M
i'su cqwvllous glvi*
,,; ., i ,/,
and comparing with ihc
ml form,
n< '< i, ,
rf/i v" '" "I
O/
U h cvltlcni tlmt
Now equation (,,) Is an abbreviated way of writing Iho
for continun] tllRcrvnilm'wn which may be expanded
to
;/:
4 5 GENERAL TIIKRMODYNAMIC METHOD
or replacing the first pnrtial clilTcrenlial coefficients by
equivalents,
8
a
8*
ihc subscripts being \vrillcn to avoid possible confusion
oilier partial different in I coefficients to he deduced laier.
From the first law of ihermodynumirs and equation (
have in like manner
dQ /I (<!E + pttv) Cj,'// I wfty.
Since the differential (/v is inconvenient, we may replace it
so that
17
Making use of Ihc equation
v *
8/
,
givcs
AITI.U'ATION ()! T1IK SKCUNIl LAW
Uui llu ithhumii(oti of u diimuUriHiii 1 . ajvmtitm c
f>, Vt ami / uirriis willi ii ilu usHumpliun llmL
Sj
in, fnnii tcuiiluih (.0 \vi* tntiy have
tl{>  A ((//;  {Hlr}  ml ft ! tnlv.
cr,
Appllcfliion of Iho Second Law. Tin 1 htitnu! inw of
clynnmici inn be cxprfwii'il liy ctjuwlion (.^H), PHKC 37i
T 1 '^
J ^
(.17)
which rmikrm * (trdtfi n t*xit<( dirfcrcnlln), i that we may
$v> ^v
' Daa _ "* .
'I'd prrpnrr rtimi[nn (i I for ihU iraUHftirmntUm, \vv mny
i. *'(i 'j j, B ' /
tlt} ; Jr ,y./ 6 rn',
so that the preceding equation gives
* f
or
*.(&
T\
T \8v/f ~YS
' 8 A ~ ( Sc \ i
W. UvA" T
(49)
on
( 2 ) we haw
m
m, from cquation
(So)
First and Second Laws Combined _Th
th the first and thc sccond  To
&
to the
Al.TKKNATtVK MKTIKW
iilioriK (1)1 ('*), nnd (3) may la oUainrd hy ctimliinin^ ilu
eiiuuinns rmillmtf from tin application nf llu laws MpurtiU'ly.
Thus ^illations (15) ami (.c)) give
' '
(50
And
and (so) uiv
t '
i tu
ill
.i7'
(.H)
}.',\i
ft is uitwiuVnl tn [ntnf(irin thU fa^l riiialinn Ity L
valuta of n and ti front pii^r i j, yuldiiij!
The rquntirin* (lctlticcl in tlin tliuptrr uluiw tlu rt
rctatiunn aiming lilt 1 lluTinal Mipmilin if llu U\VH of llirnno
dynarniri rr nuri(rd, Simtr itf iltrin, nr rttu.iliunn rlnltiinl
freim llum, liavi* IKTH MH liy wrllrrt un ihrriiUHlyimitiut in
(HlahlKli rrkilinn*! nr (iniHHr Jirtiprrlir, llml iiniu.l In rnitlily
olilaincd liy dim l r*K'rinu'm*>.
i'tir llic niudtnl familmriiy with the jir<nr^*. ii nf murv
imptirlitnrr ih.in ny nf \\w rriulu.
Alternntlve Metlmtl. Stunr uriirr* cm ilurrtHKlynnmlt^ rr
HTVC iln diit ii'rtjcin of ifnHT(iiiirt' until tin.) arc rtady tu
dflinc (if ii'^umr nil al^nluti wtilr jtidt'wndrni nf liny it
iinil dtpindiri^ unly nn tttr hinduimmal unit, nf length
wri(il. Hf tin ihrrr irllrral riunliimi (i), (j), and (0 lhr\
Uhf ill lirAt tmlv tin latter :
ml*.
go GENERAL THERMODYNAMIC METHOD
No\v from equation (16), representing the first law of thermo
dynamics,
dQ  A (dE, I pdv),
it is evident that dQ is not an exact differential, since the equa
tion cannot be integrated directly. The fact that in certain
cases p may be expressed as a function of v t and the integral
for external work can be deduced, docs not affect this general
statement. Suppose that there is some integrating factor,
which may be represented by , so that
o
may be integrated directly; we may then consider that we have
a scries of thermal lines represented by making
const.,
o
; const., etc.
const.,
These lines with a scries of adiabatic lines represented by
tf> = const., </>' = const., </>" * const., etc.,
allow us to draw a simple cycle of operations represented by Fig.
ssa, in which AB and CD arc represented by the equations
~  C, and ~  C',
while AD and BC arc adiabatlca. The cffi
h If tf ciency of a reversible engine receiving the
(I
FID.
heat Q during the operation AJi t and reject
ing the heat Q' during the operation CD, will be
Q
AW
Q
(10 .
But  is an exact differential, and depends on the state of
o
ZEUNKR'S EQUATIONS 51
the substance only, and consequently is the same at the end as
at the beginning of the cycle, so that for the entire cycle
5
Now during the operations represented by the adiabaiics AD
and BC no heat is transmitted, and during the operations rep
resented, by the lines AB and CD, is constant; consequently
the integration of the above equation for the cycle gives
0'
*= s = o,
S S'
.00' S$>
" Q S '
that is, the efficiency of an engine working on such a cycle depends
on 5 and S' } and on nothing else.
Zeuner's Equations. A special form of thermodynamic
equations has been developed by Zcuncr and through his influ
ence has been impressed to a large extent on German writings.
These equations can be deduced from those already given in
the following manner.
From the application of the first law of thermodynamics to
equation (3) we have equation (47), page 47,
Now
^, + g*
so that
n BE o BE
A~Sj' A*7
These properties Zcuner writes
52 GENERAL TIIKRMOUYNAMIC METHOD
Solving equation (54) first for o and then for w,
AT+H*!.
0V
= w~
s/,
Sv
In equation (3)
dQ ndp I odv,
we may subslltutc the above values successively giving
s? t
because ifc s ^ / "r
op Sv
And also
..
^
Replacing o and by their values in terms of X and K,
ZKUNKK'S EQUATIONS 53
In these equations a is the coefficient of dilatation, or  j / is
equal to 7', uncl
v r
A . Y/i .   .
A A \5/)/ii /I A \w/ p
If this devivtiUon of Zcunur's equations is borne in mind, the
irealnu'nl of thcrmotlynamics Ijy many Ocrmun writers may be
readily recognized to be only a variant on that developed by
Clausius and Kelvin.
CHAPTER V.
PERFECT GASES.
THE characteristic equation for a perfect gas is derived from
a combination of the laws of Boyle and GayLussac, which
may be stated as follows:
Boyle's Law. When u given weight of a perfect gas is com
pressed (or expanded) at a constant temperature the product
of the pressure and the volume is a constant. This law is ncnrly
true at ordinary temperatures and pressures for .such gases ns
oxygen, hydrogen, and nitrogen. Guse.s which arc readily
liquefied by pressure at ordinary temperatures, such as ammonia
and carbonic acid, show a notable deviation from this law. The
law may be expressed by the equation
#"" M (S 6 )
in which ^ and v l arc the initial pressure and volume; p is any
pressure and v is the corresponding volume.
GayLussac's Law. It was found by GayLussac that any
volume of gas at freezingpoint increases about 0.003665 of lt
volume for each degree rise of temperature. Gases which arts
easily liquefied deviate Irorn this law fis well ixs from Boyle's
law. In the deduction of this law temperatures were measured
on or referred to the airihcrmomclcr, and the law therefore
asserts that the expansibility or the coefficient of dilatation of
perfect gases is the same as that of air. GayLttssac's law may
be expressed by the equation
v v c (i + a/) (57)
in which v is the original volume at freezingpoint, is the
coefficient of dilatation or the increase of volume for one degree
rise of temperature, and v is tho volume corresponding to the
temperature / measured from freezingpoint.
54
CIIA.KACTKUISTIC KQUATIQN
55
Characteristic Equation. From equation (57) we muy
calculate any special volume, such as v lt getting
v l  v (i  a/).
Assuming lhal /, in equation (56') is the normal pressure of
[he (ionosphere // , uml Kub.slUuting the vulue jual found for v,,
we have for ihe combination of Ihe laws of Boyle uml (luy
Luasac
pv
f /) ^
 (5 s )
If it he assumed that a KIW conirucls a purl (if its volume ut
freexingpoint for each degree of tempuniture below free/an^
then the ulj.solule xern of the irll)ermomi'U.'r will be degrees
below freezing, and
may be replaced Ijy T, Llio absolute icmpcrnlurc b) r the air
thermometer.
The usual form of the characteristic equation for perfect
gases may be derived from equation (58) by fuibstltuting T ,
the absolute temperature of freezingpoint, for  , giving
RT (59)
where n. is a constant representing the quantity
For solution of examples it la more convenient to write equa
tion (59) i" the form
*
PROPERTY OF
' r 1
i.j!
'JJCT GA.SKS
j
Absolute Temperature. Recent investigations of the prop
erties of hydrogen by Professor Cullender* indicate that the
absolute zero is 273.! C. below freezingpoint. This docs
not differ much from taking a 0.003665 as given by Rcgmuilt,
for which the reciprocal is 272.8. In this work we shall tako
for the absolute temperature
T / + 273 centigrade scale.
T _ / ) 459. 5 Fahrenheit scale.
These figures are convenient and sufficiently exact.
Relation of French and English Units. For the purpose of
conversion of units. from the metric system (or vice versa) the
following values may be used;
one metre 303? inches,
one kilogram 2.2046 pounds.
Specific Pressure.  The normal pressure of the atmosphere
is assumed lo be equivalent to ihnt of a column of mercury
760 mm. high at frccx.ingpoint. Now Kcgmiult t gives far
the weight of a Hire, or one cubic decimetre, of mercury 13.5959
kilograms; consequently the specific pressure of the atmosphere
under normal conditions is
l>v " 10,333 kilograms per square metre.
Using the conversion units given above for reducing (life
specific pressure to the English system of units gives
/> 2116.32 pounds per square foot,
which corresponds lo
14.697 pounds per square inch,
or to
29. gat inches of mercury.
It is customary and sufficient lo use for the pressure of the
atmosphere 14.7 pounds to the square inch.
* Phil. Mag,, Jan., 1903.
f MSnwires do 1'Instttnl da France, vol. xxl.
SI'KCIl'lC VOLUMKS
57
Specific Volumes of Gases, I'rom rm*m (Iclcrminiilioiw of
(Icnttilit's of KIISC.X by Lidue, Mnrlcy, untl Kiili'igh il appears tlitil
[he most probable values of UK specific volume of the ionimuna
ses ii rr
VOI.UMKS JN iTHir MKTUKS Ul ()NK ICII.tH 1KAM,
AimospliLrit air ....... ....
Oxygen ....
}iy<\niKvn
1 1 . ? 33
: Tin correspond! UK (juanlilies fur Kn^lih unit* an ^iveii in
^ tin ne.xt (able.
VOI.UMKS IN rnnr I\:KT <H ONI:
Aimctsphrrir air . ........
i j . 31;
u.7i
it.ar
178. a
To iht'si may In addi'd tin valw for uirlion tlioxitlt 1 , 0.506
culm mi'lri: per kiltigrnm r S.io tubir feel per pound; but
us llic cHiic/il umfM'ratiirc for ibis .siiUsunn 1 is alfoul 31 L\, or
88 I 1 '., rnlculiiliontt by Llic i'([uiilions fnr J^IIHCK un Htililu lo bo
iilTwU'fl by InrKi crrcirs.
Value of R t Tht ccnihtaiu K wliirh uppnirs in tbc usual
form of tbc thanuifrisiu nimliim for ti giiH iTpnHrniH thu
expression
Tlu values for /^ rurri'siiontliiiK in ihe French nncl the Kn^lUh
of unilK may lie uilrulaled HH f
l'renrh units,
a 73
Knglisli unilK, A!  uL..
Vfduc of R fnr other ^itscs may bt calc'iiliiicil in a Jikr nmiincr.
s g PERFECT GASES
Solution of Problems, Many problems involving the proper
tics of air or other gases may be solved by the characteristic
equation
J>v = RT t
or by the equivalent equation
T T
which for general use is the more convenient.
Jn the first of these two equations (he specific pressure and
volume lo be used for English measures arc pounds per square
foot, and the volume in cubic feet of one pound.
For example, let it be required to find the volume of 3 jwundt
of air at 60 pounds gftugeprcssurc and at 100 F. Assuming a
barometric pressure of 14.7 pounds per square inch,
V tea
S.V3S (450.5 'I TOO)
(1,17 + 60) i.(4
2.774 cubic feet
Is the volume of i pound of air under the given conditions, and
3 pounds will have a volume of
3 X 2.774 8.322 cubic feet.
The second equation 1ms the advantage that any units may
be used, and that ll need not be restricted to one unit of weight.
For example, Jet the volume of n given weight of gas, at 100* C,
and at atmospheric pressure, be 2 cubic yards; required lh.es
volume at 200 C. and at 10 atmospheres. Here
i X 2
373
10 V
473
v & 47.1 X j.
*
Specific Heat at Constant Pressure. The specific hcnl far
true gases is very nearly constant, and may be considered to be
APPLICATION OF LAWS OF TIIKKMOUYNAMICS 51)
.so for thermodynumic equations. Ucgniiull gives for llu: mean
values for specific heal al constant pressure the following results:
Atmospheric: air o^.ns
Nitrogen o.a. % tH
Oxygen 0.2175
Hydrogen .^po
Ratio of the Specific Heats.  My a Nuri;il experiment on
the adiabalie expansion of air, Ronigen* delermined for the
ratio of the" specific heats of air, al constant pressure, anil al
constant volume,
' n .
This value u^rcen well wilh a compulalion to fftllow, whirh
depends on the tippllciiium of the laws n[ llurmodynanii(s lo a
jierfecl gas, and also wilh a delerminiilion from ihr theory of
SLs by fxivrf llml llu* miio ftir uir should be i.^ojt. If Ihc
value for lliis nitio be auvpU'd the rcmiiintk'r of the work
in (his chftpter fciIlnwH uilJumi ftny refcrcna (o Ilic law of
thermodynamics.
Application of tho Laws of Tliormodyimmlcs. The prrrcd
in^ slutcmenlH concerninij; the Mpefific IICIUM iif [Krfrci KIIHCA
and their ratio would be alisfaclory were it delinilely delinnined
by experiment, llwl the Hjiecific heal al con.slanl volume is IIH
nearly constant na in the wptrilk' lutil ut conslnnl preswire.
None of the experimental delerminalions (not iven ihm by July ^:)
din be considered as wtlbfiictory us Llu ML* for tlie speciCu heal
ill conRlftnt prt'ssucc; roji.sertii'jnly iJicrt is romnVlrrnbU' !m>nr
lancu lo be attached to the application of the laws of thirmn
dynamics lo the (.'linrui'irrhtic equitlion for a jierfect HHH, and,
moreover, this applicalinn furnislus one of ibe nuwl witUfuciory
dclcrminuiions of the ralio of the specllic heals.
'd Annalcn, \\,
t W. Mag,. July, iH<jr,.
J f'roc. Kyal Hoe., vol. xll, ).
6o
I'KUI'KCT
It is convenient at this place to make the application of the
laws of thermodynamics by aid of equation (55), page 49.
* '
c,, c v <=> '1/V s . (63)
From the equation
we have
pv
Bt
KT,
Bf
.'. c,,
AR
This equation shows conclusively that if tin charactcmlic
equation is accepted the differences of the specific heals must be
considered to be constant, and if one U treated as constant so
also must the other. Conversely, the assumption of conalnnt
specific hcaLs lor any subsUUHT is in cflVrl the a.sHumplIon of
the characteristic equation for a perfect gas.
The solution of equation (64) for (he ruiio of the specific
heal3 gives
 son 1 .JO/).
torn X 0.77H
. ''vv . t, JU.UL
426.9 X 273 X 0.2375
For those who have not read Chapter IV, the following deriva
tion of equation (64) may be interesting, In Fig. 26 let ah repre
sent the change of volume at constant pressure clue
to the addition of heal ^A/wliercA/i.s Ibc increase
of temperature ; and let cb represent the change at
v pressure due to the addition of hciu <yV; if ac U
an isothermal, the liUler change of lernpcralure will
be equal to (he former, but the heat applied will be leas on account
of the external work /jAi (approximlcly). Consequently, '
PIG. 16.
C e
ISOTHERMAL LINK 6l
the last transformation making use of the partial derivative
Bv R
5 ^ " ]>'
Thermal Capacities. The values of the several thermal
capacities for a perfect gas were derived on page 12 and may ho
written
} f lL t f c \ , ., L t, .... , \ tr } f } )
' ' n t f /' 'i'> .. I'/' ''' ' \ UI V
M
t
/7
I
?
*r,
the transformatioiifl in equations (66) and (67) bring made by
aid of the rhorftcterlMllu equation.
General Equations. To deduce the general equations for
gases from equations (i), (a), and (3)1 It la only nrrcHwiry to
replace the letters /, ni, n, and a by their values Jusl obtained,


v
Isothermal Lino. The eqimlinn Ui iht iKothcrmul line for
n. gas is obiainw) by nmklng T connlnni In the chnrncicrlaile
efjijaUon, HO that
/n R'l\  /),
or
^' " ^1*1   (73)
This equation will he recognised as the expression of Boyle 'a
tow. It isj of course, the equation lo an equilateral hyperbola.
PKUFKCT GASES
To obtain the external work during an isothermal expansion
; may substitute for p in the expression
we may
W ".
from the equation to the isothermal line just stated, using for
limits the final and Initial volumes, v t and v v
If the problem in any case culls for the external work of one
unit of weight of a uns, then v l and v a must be the initial and
final specific volumes; but in many cases the initial and final
volumes arc given without any reference to a weight, and tt h
then sufficient to find the external work for the given expansion
from the initial to the fina! volume without considering whether
or not they are specific volumes.
The pressures must always he specific pressures! in ihc Englfeh
system the pressures must he expressed in pounds on the square
foot before using them in the equation for external work, or, for
that matter, in any thcrmoclynamic equation. '
For example, the specific volume of air at frcexinxpolnt and
at 14,7 pounds pressure per square inch is about 12,4 cubic fcetf
at the same temperature and at ay..) pounds pur square inch the
specific volume is 6.2 cubic feet. The external work during
an isothermal expansion of one pound of nir from 6,3 lo 13.4
cubic feet is
p lVl
 29.4 X 144 X 6.2 IOR. 18,190 footpounds.
For example, the external work of Isothermal expansion from
3 cubic feet and 60 pounds pressure by the gauge to a volume
of 7 cubic feet is
W (60 4 14.7) W X 3 log,^ *. 37,3,10 footpounds.
o
ISOKNKUCilC LINK
In both problems ihc pressure per stjimru inch is multiplied
by i.j.i to reduce it to the square fool, In the 1'ii'sl problem tbe
pressures are absolute, thul is, they are measurud from /em
pressure; in ihe second problem the pressure by the gauge is
60 pounds above the pressure of llie atmosphere, which is here
assumed to be 1*1.7 pounds per squart incli, and is added to
give the. absolute pressure. In eareful experimental work ihe
pressure of thu ulinospheiv is measured by a barometer and is
added to the gaugepressure.
Jsoenergic Line. The isothermal line for u per fir t gas i
also tlu: (.soenrrgu: line, a fail tlmt may be prom) as follow*:
The heat applied during an isothermal expansion may be ml
by making T u constant in equation (70) and then
thus:
i'
V rr. 1 1 1
' /'') l>
or, .sulxslUulinK
r l
from equation (d,\
^ , ( . 
V
(75)
A comparison of ecimtion (75) with eqmxilon (;.) ahow
tlmt the heiit applied during un isoLhennid expunsion Is ctpilv
alcnt lo the. exlernul work, or \ve niuy say itml nil llu* luul applied
is chunRud into exlernul work, m> thill ihe intrinsic iiurgy IK nni
dmttgc'd. This ccincluslon i Imscd on the assumption ihnt
the j>roj)crllcs (ire nceuralely reprenented by ihe HwruriiTmlii:
equation and that the spec I lie heals tire toiiHlunt. As both
nssiimpiiona tire approximnle so alwo is the amrlusion, IIH will
appear in the discusHion of How through a porous plug.
An imcrt'sliiitf corollary of lite (h'rufisian jusl given h that
an infinite moihermal expansion jjlvis IUI infmlie tunoimi of
work. Tliua tbc nrea rondiined between the
axis OV (1'ig. 27), the ordinale 6, and tbe
iaolhcrmal line act extended without limit Is
log,
to,
\,
1'EKFKCT OASES
This may also be seen from UK consideration thai if heat h
continually applied, and all changed inio work, there will be a
limitless supply of work.
Adiabatic Lines. During an fidialmlic change for exam
pie, the expansion of a gas in n nonconducting cylinder heat
is not communicated to, nor abstracted from, the g as  conse
quently dQ in equations (70), (71), and (73) becomes zero.
From equation (72)
^ dO r <//; T f
" P '* v" '
r f iy ( LL.
C a V h '
The ratio ? of the specific heal* may bu represented by *, and
the above equation may be \vrllicn
const.
' &6.)
(77)
This is the adiabatic equation for a perfect gas which is most
frequently used. If adiabnllc equations involving other vnrfa~
bles, such as v, and 7',, arc desired, they may be derived from
equation (76) by aid of the characterise equation, which far
this purpose may be written
flV
* EH)
T
so that
and
L
I
T.v.* 1
* \ v [
MHABATIC LINKS
Or equations (78) nnd (70) may be dalueed directly from
equation (70) UK equations (76) nnd (77) were from equiuion
In like manner we mny deduce from equation (71)
T}>'  V,/', " (80)
or we may derive it from equation (76).
To find (he external work the equation
W f* ptv
may be used after fUihsO'iufiiiK for /> from equation (77)
In Fig. 28 the nrca between the xi OT', ,.
the ordimuc /', and iho ncllatmlU 1 line an ex
tended without limit, becomes
V,
fl
I'd!. 10.
nnd not infinity, ns IR the. case with ihe isolhermiLl line,
Here, aa with (he cnlcuiatton of external work during itso
thermal expansion, specific volumes xhould be used when the
problem involves (i unit of weight; but work may be calculated
for .any given initial and final volumes without considering
whether they are specific volumes or not. The pressures n re
al ways pounds on Ilia square font for Ihe KnglWi system.
For example, the external work uf ndlalHiUc cxpunitlon from
3 cubic feel and o"o ]ioundfl pressure by the KIUI^C tn the volume
of 7 cubic feet Is
W
M'7._XMfl X
231140 foolpounds,
66
PKRFKCT GASKS
which Is considerably less than the work for tliu torres
isothermal expansion.
Attention should be called to the fuel thai ealcuhLllonx Uj
method are subject to a considerable error from the. 1 foci
the denominator of the coefficient contains llu: urm tc
(00.405; if It bo admitted that (he 1 Jnst figure Is umcrirflft to
oxlont of two iinllSj the error of calculation IncmmcM half a
cent.
Intrinsic Energy. Since external wnrlc during n
expansion is done at the expense of tin intrinsu oniTgy, I lie
obialnable by n fnfinJie expansion ninnot IK ^r<sttf<
intrinsic energy. Jf it be ndmitted tliat sneh tin
changes all of the intrinsic energy into external \vrk we
1m ve
IK
which gives a ready way of culcu luting
practice we nlwys deal wJlh difTcri.'nn'.s r>f intrijisic
that oven If there be a residual Intrinsic energy after (in
adlabatlc cxpnnslon the error of our niclluKl will be
from nn equation having ilie form
Sponntiat Equation. The expiinsitins aiul
of ulrand other gases (n practice arc Hildoni exut'ily
fuliabailci more commonly nn acluul optTiuiini IM
between the two. It Is convenient ami usually
represent such expansions by an cxpcineiHwl t<Utiiitin
In which has a value iK'lwcen unity anrl i..oc;. Tlir
Integration for external work is (lit! same as for that of <i<
oxtmnslon, and the amount of external work in
between that for adiabntic and lluit for isotlurmul
ENTROPY
Change of temperature during such an expansion may be
calculated by the equations
(85)
IH
which may be deduced from equation (S.f) by nid of (he char
acteristic equation _
as equation (79) is deduced from equation (76).
If it is desired to find the exponent of an equation representing
a curve passing through two points, as a t and a 2 p
(Fig. 29), we may proceed by taking logarithms
of both sides of the equation
glxm n logtt, Mog /, = log v 3 + log 2 ,
so that locf jfr. log />
log v a  log v,
y'or example, the exponent of an equation to a curve passing
through the points
Pi = 747, v, = 3, and 3 = 30, v 2 = 7,
is __ ogJ4.7 log 30 _
log 7 log 3 ltl04 '
II .should be noted that as approaches unity the probable
error of calculation of external work is liable to be very large.
Entropy. For any reversible process
consequently from equations (70), (71), and (72) we have
jj. ( " , / \^ v
<P < c v  f (c p c,) .
y v
,
I c p ;
p v
68
I'KKFKCT ifASKS
and, integrating between limit 1 *,
<f> 3  </),  c, lo^rf I (r jp  c
' i
<f> 3  </>,  0, lutf, .*
which give ready means of ciUmhimK fhun K cs of cniroi
These cqutitions give the vnirnpy dian^s pn pound, and fire
be muliipliod by the weifilu in pounds u, K i vc the change
the acliml conditions.
For example, the change of intrupy in pjissiji K / rom lhc pc
sure of 74.7 pounds iiUsoIult per s.pmrt inch and the volu
of 3 cubic feet to lhc prtHsure uf A o pounds ubsoluie and I
volume of 7 cubic feet is
Since the prcnsurcs form (he numiTiiinr and denominator
a fraction, there is nu nm.'wity i rlcc (hem to the aqu
foot. In this problem the pressures am] volumes arc taken
random; they correspond in a umpi'niluiv of i.,0F rit
initial condition. As has nlruidv been suid, there is sold
occasion in practice Tor usin^ UK imropy f n K , !S .
Comparison of the AlrThermomoter with the Absolute 8ci
In connection with (ho iscKlymunic liiu it was shown llmE '
intrinsic energy fe a f um1 j nn llf 1)t . (( , 11?mll(Rl on , T
conclusion is deduced from llu HmrarKnstir vt[Wl \i on O n
assumption that the scale of the air thmno.mU, coincides
inc^hcrmodynnmic scule, and it alTords a delicate method
esung the (ruth of the characteristic equation, and of compat
the two scales.
COMPARISON CU' 1 T11K AIR TllKKMOMKTKU 69
Tin most complete experiments for this purpose were made
liy Jimli and Lord Kelvin, who forml nir slowly through a porous
pluf; in a lube in such u manner llitu no beui was ininsmillecl
Ui r from the jtir during tin process. Also Ihe velocity both
lii'fiirt' untl beyond tlu plutf was so small that tin work due lo
ihe elmnjtc of velocity could be disn^ardnl. AH the work Unit
would be developed in free expansion from the higher Lo iho
lower pressure was used in overcoming the resistance of friction
in die plug* unit so itinverli'd into lieut, and as noiK of this bent
csuiped.il was relainrtl by (he air itself, the plu^ remaining at a
umstHiU leniperalure. ll iherrfore uppeurrt llwl llie imrinsk:
ent'ry remained tin siime. ami thai a ilmn^e of temperature
iminuU'il a dfviiiliiui fiin the ii^siimjilions of tin iluory of
PIT ft 1 1 1 leases.
In Ihe disniHsion i>f rrsullM \j(\\vn by Joule and Lord Kelvin*
in iH.s. lln'.v K Itvl ' t"t l ' u ' nUwilulr lempiratnrc of fiei'/in^poinl
JT^.'j C 1 , As the rrrtiili nf Inter exjurimentst llicy Hinlecl that
iht KKilinw for a ttilfereme of pressure uf 100 inches of mercury
wits reprehemeil cm llu lenliKracle wulc by
From tliesc exptrinuMUH mid from other t'onHidimlionH con
cerning the innMnni volume liyctroKcn ihernuimelcr, I'rofcsBor
Cidlendiir IIRH clflvrniinrd llml the nuwl prnbiiblf value for the
aliM.lulc lenipiTiilnre of fnx2lnf{ point !H yjjp.i C'., an nlrcotly
Kivrii, iind nlvt' a liible <tf currc'ellnns (n the hydrogen liter
nuimtHT lo nbtiiin icniprntlurcH nn I be abaolule scale. Aa
llu* corretiion at any temperalure between aoo and f 150"
C 1 . it not mcirr tbitn tAd "f n rle^ree thi IH inicrwllng mainly
in phyhldMi, The rnrreclitmt for the nlr*ibcrmomclcr itl con
hlimt pressure nrc Mimewhul larger, but approach ^ of a
only at 300" C.
* /'Ay/. Train, vol. t'xllv, . J^q.
t IMI. vu). till, p. 570.
70
PERFECT GASES
Deviation from Boyle's Law. Karly experiments on
permanent gases (as they were then known) indicated lhat
there were small deviations evident lo a physicist, but not af
Importance to engineers; but now that air is compressed let
pressures as high as 2500 pounds per square inch, it becomes
necessary to take account of such deviations in engineering
practice.
Perhaps the best conception of ibis subject, and of the four
recognized slates of fluids, can bo hud from a considernlion &/
Andrews' * experiments, which for ilu 1 present purpose arc coo
vcjiicntly represented by his isolliermul curves, which arc* repro
duced in Fig. 20,a, together with the curves for uir. The latter
arc approximate hyperbola: referred to the proper axes, that
for xoro pressure being nearly the whole height of the diagram
below the figure as it is drawn. At .)H.t C., the isothermal for
carbonic acid shows a marked deviation from the hyperbola, a*
may bo seen by comparison with the curves for air, or better
from the /net that a rectangular hyperbola through J* will pug
through Q. On the other hand, the isothermal for 13.! resem
bles that for steam, which is commonly known MS a ftnlu rated
vapor whose pressure is constant at constant
temperature; the hori/ontal part of this
represents a mixture of liquid and
which at the Icfl runs into the liquid
and as liquid carbonic acid has considerable
compressibility, this curve becomes n
line with an appreciable inclination to
axis of zero volume. At the right, the
thermal shows a decided break and alt
away as the volume becomes larger
that of the saturated vapor. The isolhernml
Pin.
for 2i.5 shows similar
the passages from one condition lo another are more gradual
The dotted curve k drawn through (he [joints of saturation ind
liquefaction, and its crest corresponds lo the critical temperown?.
* Phil, Trans., t%(*>. pnrt !i, p. 573 , nml ifyd, jmri II, p. ,, 3( .
IWNHITV AT MKlIt I'KKSKUKK
Tin Isnihmnnl fur $i.i in iluirly alum the critical Irmprni
lurr ami iliH% nnt ihdiialr a liijurfiu titui.
The M'vrrul Mnli^ "f a lluiit imi IK rnumiTiiUtl us
i, IJijiiit).
.j. SiiuirAtrd viijHtr, iniluilinit mixture*. nf liquid und
j. SuNrhfutrrl vnir * luinifiiTunl hy u lurm'P vulumi limn
uilui';U(il wiir fur 11 ((ivni tcnuHruHin 1 itiut proKsuri.
,, t'tiin; near ilu* iriilml U'mnTaluri' llu ilrvlnllunH from
llmIrS Uw rr very liir^c, l lu^litT (tinprrfiturc (he
iU'iiiifiuni iliminKh ami lirnuni uniiniiiriaiil.
Critical Tmu){milur<'i, Tin fulluwin^ Inltlr nf i rilkal
Irnt)HTiUtirr'> ami uf Utility (HIJIIH nl niniotplurli prcvuirr h
Ukfii in  ',u i friim t'rrMnn'?! "'I'hrnry *>f Unit," ny.*.\,
t'Ml
.' I'
Air
Sulphur tlin
KlIltT .
7H,
Wnicr
I f HI {n 4
h Fri^aure. If ihr ihtul mcilu&h (Klwn on
fur llir .iiluUMii sif prntilrm* InvnlvliiK ihr proprrllei
air <ij<l(Yl with vrry hifjh prcvturc, rrrr nmotintin^
In UVH nr ihrrr f irni wrr li(iljt' (u U inturml, uwlitg lu I he
[r\int!im from tn>lr\ Uw. In Hmr iawn, ihU crrnr may lie
if,flnrnl in rtiginrrrinK priuiir; In %nmr cairi ihr rrrnr may lie
jut luticfi in A prai lie . tl f ; i, .1^ will tic indii .Uol in ihr 'U',ii;n uf
ni'r t (tmjirrf./wjr'ii iiul tti nlhrr t.t'sr^i allnwjincr^ liiii'>( lit" Jiimtr
frnm ihr r^srrimrnuit infurnuilnn (urnNhnl hy Arnui^l, ami
which may Isr fuiifi'l in UiwMi <vitd llnrnMrln 'H Tithlr,,
PKKKKCT OASKS
Rontgen's Experiments. J)irtvl cx>mmeiH8 to determine
K may be made as follows. Suppose thai u vessel is filled wfrh
air at a pressure /> while the pressure of I he atmosphere i fa
Let a communication be opened with the atmosphere suftlcfoat
to suddenly equalize the pressure; ihcn let it be closed, .am) lei
the pressure p. 4 be observed after the air lias again attained lllfc
temperature of the atmosphere. If the first operation is suffi
ciently rapid it may be assumed to be adiabalic, nnd we
use equation (77), from which
.leg
IJI ..
^11
The second operation is al cimsliini volume;
the specific volume is the same at Iho final stale aa after '&t
adiabalic expansion of the first operation, llui the Initial ODrtl
final temperatures arc the same; ammiicn(ly
Ing
which substituted in equation (91) jjlves
"" 1() g /!
Th^ same experiment may be made by rarefying th
the vessel, in which case the sign of the second term
Rbntgcn* employed this method, using a vessel contaJnrla
70 litres, and measuring the pressure wilh a gauge made m
the same principle as the aneroid barometer. Instead of cuwtm*
ing the pressure p a al the instant of closing the slopcock to bo
that ef the atmosphere, he measured it with (he same infliruaumt.
A mean of ten experiments on air gave
* 1.4053.
* Paggttubrfi's Annalen, vol. cxlvlli, ji. 580.
KXAMPLKS 73
EXAMPLES. ^
1. Find the weight of . cubic metres of hydrogen ill 30 C.,
iind under the pressure of Hoo mm. of mercury. Ans. 0.3*11 kg.
2. Kind the volume of 3 pounds of nilrngim al a pressure of
.15 pounds lo the square inch by ihe gauge lln( l ^ So I 1 ', Ans.
i r.05.
3. Kind UK temperature al which one kilogram of air will
occupy one cubit metre when at u pressure of 20,000 kilograms
per square metre, Ans. ,ioC.
1 Oxygen and hydrogen lire In he sin red in limits 10 inches
in diameter iind 35 jiu'hes long. Al :i maximum lemperalnrc
of noJ ; ., the pressure nuisl nol exceed 250 pounds gauge.
\Vhiii weight of oxygen can he slnwl in one lank? Whal of
hydrogen? Ans. Oxygen 2.21 pounds. Hydrogen 0.138 pound.
5. A balloon of 12,000 cubic feel capacity, weighing with ear,
ocaipanl, i'lc., 005 pounds, is inflated with 0500 cubic feet
hydrogen ul 60 I'., the barometer reading 30 inches, Kind
UK weight of the hydrogen and ihc pull on ihe anchor rope;
find also (he nmounl ihiil ihe halloon muni be Ilghlcncd to rciich
u height where the Imromeler reads 20 indies, and Uic tempera
ture is 10 below x.ero Fahrenheit. Ans. Weight hydrogen
50..) pounds; pull on rope 12 pounds; balloon lightened 7.5
pounds.
6, A gasreceiver holds 1,1 ounces of nitrogen ul 20 C., and
under a pressure of 39,6 inches of mercury. How many will it
hold at 32 !*., and iu the normal pressure of 760 mm.? Ana,
15.18 ounces.
7. A gafrrccciver having the volume of 3 cubic feel contains
half a pound of oxygen al 70 K Whtil is the pressure? Ana.
29.6 pounds per square inch.
8. Two cubic feel of air expand al 50 K. from a pressure
of 80 pounds lo a pressure of Go pounds by the gauge. Whal
is the external work? Ans. 6f)< foolpounds.
9. Whal would have been the external work had Ihe air
expanded ntliabalically? AIIB. 4450 foolpounds.
74
PERFECT GASES
10. Find the external work of 2 pounds of air which expand
adiabatically until the volume is doubled, the initial
being 100 pounds absolute and the initial temperature
Ans. 36,100 foolpounds.
n. Find the external work of one kilogram of hydrogen,
which, starting wfilh the pressure of 4 atmospheres and with iht*
temperature of 500 C, expands adiabatically till the tcmporfr
ture becomes 30 C. Ans. 489,000 m.kg.
12. Find the exponent for an exponential curve
through the points p = 30, v = 1.9, and p t 15, v t 9.6,
Ans. 0.4279.
13. Find the exponent for a curve to pass through the potftbl
p = 40, v = 2, and pi  12, VL 6. Ans. 1.0959.
14. In examples 12 and 13 let p be the pressure in pounds Oft
the square inch and v the volume; in cubic feet. Find the oxtomtl
work of expansion in each case. Ans. 21,900 and 12,010 foot
pounds.
15. Find the intrinsic energy of one pound of nitrogen undfif
the standard pressure of one atmosphere and at frcczlngpalNt
of water. Ans. 66,500 footpounds.
16. A cubic foot of air at ,492.7 F. exerts 14.7 pounds gaog&
pressure per square inch. How much do its internal energy ami
J its entropy exceed those of the same air under standard cofltll*
tions? Ans. 5052 footpounds; .00912 units of entropy.
17. Find the increase in entropy of 2 pounds of a perfect
during isothermal expansion at 100 F. from an initial
of 84.3 pounds gauge and a volume of 20 cubic feet to a
volume of 40 cubic feet. Ans. 0.453. '
18. A kilogram of oxygen at the pressure of 6 almas)
and at iooC. expands isolhcrmnlly till it doubles Ha
Find the change of entropy. Ans. 0.0434.
19. Twenty pounds of air arc heated at a constant
of 200 pounds absolute per square inch until the volume
from ao cubic feet to 40 cubic feet. Find Ihc initial and
temperatures, the change in internal energy and the incronw in
entropy. How much heat is added? Ans. 80 and
EXAMPLES
75
increase of intrinsic energy 1,420,000 footpounds; increase in
entropy 3.29; heat 2570 JI.T.U.
20. Suppose a hotair engine, in which the maximum pressure
is 100 pounds absolute, and the maximum temperature is 600 F.,
to work on n Carnot cycle. lci the initial volume be 2 cubic
feel, let the volume after isothermal expansion be 5 cubic feel,
nnd the volume after adiabalic expansion be 8 cubic feet. Find
the horsepower if the engine is doublcacling and makus 30
revolutions per minute. Ans. 8.3 horsepower.
CHAPTER VI.
SATURATED VAPOR.
FOB engineering purposes steam is generated in a boiler which
is partially filled with water, and arranged to receive heal from
the fire in the furnace. The ebullition Is usually energetic, artel
more or less water is mingled with (he steam; but if there is il
fair allowance of steam space over the water, and if proper
arrangements are provided for with drawing the steam, It will
be found when tested to contain a small amount of water, usu
ally between hah" a per cent and a per cent and a half. Sleaitt
which contains a considerable percentage of water is passed
through a separator which removes almost all the water. Such.
steam is considered to be approximately dry.
If the steam is quite free from water it is said to be dry aim
saturated; steam from a boiler with a large steam space and
which is making steam very slowly is nearly if not quite dry.
Steam which is withdrawn from the boiler may be healed Lo a
higher temperature than that found in the boiler, and is then aakl
to be superheated.
Our knowledge of the properties of saturated steam and other
vapors is due mainly to the experiments of Rcgnault,* who
determined the relations of the temperature and pressure, Ih0
total heat of vaporization, and the heat of the liquid for many
volatile liquids. Since his time, Rowland's determination of
the mechanical equivalent of heat, gave a more exact determi
nation of the specific heat of water at low temperatures, and
recently Dr. Barnes has given a very precise determination of
that property for water. Again, certain work by Knoblauch,
Linde, and Klebe, has given us a good knowledge of the properties
* Mimotres de FInstiiut de France, etc., tome xxv!.
76
I'KESSUKK OK SATURATKIJ VAPORS
77
of superheated slcum which can be extended to give the specific
volume of saturated steam over a considerable range of temper
ature. AL llic time when llic first edition of this work was pre
pared it appeared desirable to compute tables of the properties
of saturated vapor, taking advantage of Rowland's work,
and eliminating some uncertainties due to the way in which
Kegmuill used his empirical equations in compiUulmg tables.
As all this involved changes of sufficient magnitude to influence
engineering compulations, it seemed necessary to quote the
original diiia at length und to give computations in detail. This
hurndtK'lum to the chapter on saturated vapors was found to be
somewhat confusing lo students reading it for the first time, and
since the main points are now commonly accepted, this work is
given only in the introduction lo the "Tables of the Properties of
Saturated Steam," the reason for printing it being lhal it in not
given elsewhere, as the earlier editions have passer] out of prim.
Recent correction of the absolute temperature of the freezing
point of water by Callcndttr and the elder mlnnllon of the specific
heat of water by Barnes make it neccssnry to recompute the
"Tables of lluf Properties of Snluratecl Steam " which tire
intended to uccompuny this book, and opportunity is taken to
introduce further data in (hose tallies, and in addition a table
has been prepared which will be found to greatly facilitate calcu
lations of adiabatic changes of steam and water,
Pressure of Saturated Vapors. Regnaull expressed the
results of his experiments on the temperature and pressure of
saturated vapors in the form oC the following empirical equation,
log p a + 6ft" H eft" ..... (94)
where p is the presftiire, M is the temperature minus the temper
ature t a of the lowest limit of the range of temperature to which
the equation applies, i.e.;
The constants for the above equation as applied to saturated
steam have boon recomputed and reduced to the laliiudc of .15,
and arc as follow;
mm. of mercury,
' *
Ion c
log n
C, For atcnm from 100 to aao C. rxprrwing the pressure In
mm. of mercury,
 S
log A o.
ti I
B L . For steam from 33 to S\A I 4 ', In KIUIUH [rr Kjunrc Inch,
<i 3,1
log b*>
log c H 8. 13*01 10
log a q.twfliSiais ~ 10
log 0.0038134
II a f 31
lt For steam from aia to 438 K. in toumU (*cr
inch,
. 7^3076
\og
\og i ooauIS^l
ft at I JJ
Pressure of Other Vapors. Regnault clclerminctl olio the
pressure of a large number of snlurnted vapors al various tem
peratures, and deduced equations for each in the form of equa
tion (94) The equations and the constant* w determined by
him for the commoner vapors arc given in the following table;
.
lop,
a
6
'
Chloroform
Carton l)isul>lmlc . .
f'nrlxw Itlrncliloridc .
n  t>i\ n ' cfi n
ll /III* fff^
a  Iit\ cfi
5 335381)3
5.. ion (if) j
ia.otj633.it
3.9531281
y. 13751 Ho
0.0668673
0.3857180
IOKI
log/!
M
Umlii.
T.W?o8557
O.OHS^S
r.WMH1
T.rjq77fn8
T.CJtjyJilJO
T.(>1W).R5
1.006877
T.(>RG8i7(i
T. 0011907
l.ycj,j97Ho
/ 1 ao
/ f 30
/ 30
1 [ 30
( 1 ao
~ 20
 20
1 20
 20
 20
1 i5oC.
J iaoC.
t 164 C.
1 1 4 0C.
1 i8B C.
Cnrlxm hiflulphldc . .
Cfirbon tcirnclilorldc .
Xcuncr* suites ilml there is a slight error in Rcgnault's cal
culalion of the conslnnla for tvccton, und gives instead
log f> ii  Ad"  c/9";
ii~ 5,3085119;
loj(/i(\" lo. 531 376(1 0.00361,18 (j
logc/J" 0.96.15333 0.0315501 /.
Differential CoefAclant 'f.
(it
equation (94) we have
mm the general form of
(95)
>/ being the modulus of the common system of logarithms.
Differentiating,
7?,  7T '' lf) K " "! TT c lo K ^ ^"!
put M M
or, reducing to common logarithms,
ptli
l'rcnclt Units.
B. For o to 100 C., mm. of mercury,
log /I  8.8512739  10;
\ OK B <=> 6. 69305  r ;
log (v,  9.996725828  :o;
log /3, => o. 006861 c.
C. For 100 to 220 C., mm. of mercury,
log /I  8.5495r5 8 ~ T I
log B  63493'  I0 
log tv, = 9 997'H i a 9<i  ii
log /?,= 0.0076418.
English Units.
B,. For 32 to 212 F., promts on Ihe square inch,
log A = 8.5960005 10;
logB  6. .37?8  ioj
log B = 9.91)81^1015  loj
log /?, 0.003813.1.
C,. For 212 lo 438 F., pounds on tho sciuiro Incli,
logA = 8.2943,13,1  10;
log B = 0,09403 to;
log a 9.9g856i83[  10;
log ft 0.004245.}
It is to be remarked that ~ may be found approximately
fjt
by dividing a small difference oC pressure by the corresponding
difference of temperature; that Is, by calculating rr^. With tt
t\t
table for even degrees of temperature we may calculate the
value approx : matcly for a given temperature by dividing the
difference of the pressures corresponding to the next higher and
ihc next lower degrees by two.
The following table of constants for the several vapors nnmctl
were calculated by Zcuiwr from the preceding equations lot
temperature and pressure of the same vapors;
Ft'KKKNTtAr. COEFFICIENT  1  ' f/>
,1 on 'form
(,'nrlion lilt.   .
(jirlidii iclrncliliulcio
If* ( W
 i.nsoo.it o.ooiQHi / 1 a 0003701 0500515'
.
wo.oojsHso I  j.oGfiji 3,10.01.3 1
I.VW77H~O. oo3ii7 ' I a.
1H07K o,oooaH8o/ t ..
Standard Temperature.  H is ruslumary to refer all calcu
hilions for RuScs to llxu Klundnrtt conditions of the pressure of
llic atmosphere (760 nun. of mercury) mid Lo the freexingpoinl
of wiiler. formerly llw frce/in^*[)oiiu wus taken ivs (lie slamiurd
tc'inijcmturr for water ml sleitm 't.s even n\v i( is the initial point
lor tables of (he properties of suluriticrl wipors, lUit the invest!
gut ion of the nieclianical cquivaluni of heaL by Rowland rcsiillcrl
In Ji rlblerminiillon of the specilic hnil of water with much greater
delicacy limn is ]HtHsil)lu by Regnault's method of mixtures, and
showed thai freezingpoint is nol well adapted for the standard
temperature for water. It has been the habil of physicists
for many years Lo lulu: 15 C. as the standard temperature,
und this corresponds substantially with Ga R, at which the
Knglfeh units of measiiru arc standard. Professor CnUendar
rcconimcncU 20 C. as the standard iC'inpei'alurc which would
make a variation of about in 1 in the value of thu mechanical
equivalent of heat and in the specific heat of water.
Mechanical Equivalent of Heat. The most authoritative
determination of the mechanical equivalent of heat appears to he
that by Rowland,* from which the work required to raise the
temperature of one pound of water from 62 to 03 F. is
778 footpounds.
This is equivalent to
427 metre kilograms
in the metric system. Since his experiments were made this
important physical constant has been investigated by several
* * Prae. Am. AatJ.. vol. xv(N. S. vil), i8;t>.
made after a recomparison of his thermometers. The conclu
sion appears to be that his results may be a little small, but thO
differences are not important, find it is not certain that the con
clusion is valid. There seems, therefore, no sufficient reason for
changing the accepted values given above.
Heat of the Liquid. The most reliable determination of the
specific heat of water is that by Dr. Barnes,* who used an electrical
method devised by Professor Callcndar and himself, and who
extended the method to and below freezingpoint by carefully
cooling water without the formation of ice, to 5 C. TMs
method gives relative results with great refinement, and gives nl0
a good confirmation of Rowland's determination of the mechan
ical equivalent of heal. Dr. Barnes reports values of the specific
heat of water up to 95 C. In the following table his results nrO
quoted from o to 55 C.; from 55 to 95 his results have been
slightly increased to join with results determined by recomput
ing Rcgnuult's experiments on the heat of the liquid for wator
(which experiments range from noC. to i8oC.) by allowing
for the true specific heat at low temperature from Dr. Barnes's
experiments. The maximum effect of modifying Dr. Barnes's
results is to increase the heat of the liquid at 95 by onetenth of
one per cent.
SPECIFIC HEAT OF WATER.
Temperature.
Temperature.
Temperature.
1 !.* lulllfJOH
Specific
Heal.
Heat.
Hfltl.
C.
C.
F.
C.
F.
O
32
I .0094
45
H3
0,99760
90
194
.007CS
5
41
1.00530
50
133
0.99800
aoA
.00855
JO
5
1.00230
55
131
0.99850
100
213
.OIOIO
15
59
1.00030
60
140
0.99940
130
248
.Ol69O
20
25
3
35
68
86
95
0.99895
o . 99806
099759
099735
?o
g
149
158
I6 7
176
1.00040
1.00150
1.00275
1,00415
I4O
1 6O
i So
2OO
984
320
356
39 a
,03330
,03B5&
03175
.04100
40
104
099735
" s
IS
100557
230
428
.04760
* Physical Review, vol. xv, p. 71, 1903,
HEAT OF THE LIQUID
83
Heat of the Liquid. The heat required to raise one unit of
weight of any liquid from freezingpoint to a given temperature
is called the heat of the liquid at that temperature; and also at the
corresponding pressure. Since the specific heal for water varies
we may obtain the heat of the liquid by integration as indicated
by the equation
In order to use this equation it would he necessary lo obtain
an empirical equation connecting the specific heal with the
temperature; such an equation has not been proposed and would
probably be complex. Another method is to draw a curve with
temperatures as absussie and specific heats as orclinutcs find inte
grate graphically. The fact that the specific heal is nearly
equal to unity at all temperatures and that consequently the beat
of the liquid for (he Centigrade thermometer is not very different
from the temperature, suggests the following method:
Let c =*> r I ft
when k Is the difference between the specific heat and unity at
nny temperature, k being positive or negative as ihe case may be.
Thm t ....... (97)
winch may be obtained by plotting vuluca of k as cmliimtca and
integrating graphically, which will have the advantage that the
required curve may be drawn to a large scale and give correspond
ingly accurate results. The values for the heal of the liquid for
water in the " Tables of the Properties of Saturated Steam " were
obtained in this way.
The following table gives equations for the hcula of the liquids
of other substances than water, determined by RcgnauU, t
IIF.AT OP TITK LIQUID.
Alcohol .............
Klhcr
Chloroform
Carbon bisulphide
Carbon UilrnchlorHlc
Accton
9 o. 54754 H
I o. 000003306 ('
q 0.5390:^ ) 0.0003959 fl
1 ~ 0.23335 ( I o.oooowy (J
'} "" '35 a 3 ' *l 0.0000815 P
j 0.19798 H O.OOOOOOOP
fl " o.S "43 'I o. 0003965 t 1
1 lit' S 1 11*1 Illl mUL IVM HIM "' !<>... ... .....  ......
cliff erenimviim; for exiimple, the HiteduV IUMI fr *iUuhul U
c  0.5.175.1 I o.oojj.ufi/ \
Total Heat. This term in defined n* tl % lwl rwat\ to
rtiisc a unit of weight of water from fretv.irtK (H>int lo a given.
temperature, nmi lo entirely evaporate it MI I'*" 1 icmporatura,
The experiments made by Rtgnnull wcrr in ll rr verse onlotj
that is, slenm wns Ucl from n \ioHcp into llw tflUmmelir and
there condcnswl. Knowing the Initial nml final wrtghu of
the calorimeter, the temperature of ihc nitnm. nnil the initial
and final temperatures of the water in llu iJilnrimrlcr,
able, after applying the mceswiry corriTtiunH. id
lovn\ hciUs for the acvernl ixptrimtnis,
The results from these experiments art rrprrmUi by the
following equations:
For the metric system,
.//  606.5 ~l' 0.305 / ...... (98)
For the English .system,
H 1091.7 I 0.305 (/ jj) ... (99)
An investigation of the original c*sr>crimrniwl results,
allowing for the true specific heM of the water In iht* ralorlmcler,
showed that the probable crroVs of the mt'lhcxl of cktcrmlntng
the total heat were larger than the deviations of llir true ftcclfc
hctits from unity, the value aaaumcd by Rcgnauli; and, further,
SL appeared thai his equation represents our l>wrt knowlrclgp of
tlie total heat of steam There appears lo lie mi mwm far
changing this equation till new experimcnial vnlun shnll lie
supplied. The deviation of individual experimental resulu
from corresponding compuialiona by ihc equation b \\kc\y lo be
one in five hundred. There i further some uncertainly whether
the method of drawing steam from the holler tllcl no! Involve
some error due lo entrained moisture. The bent check upon
Rcgnault's results is a comparison with Knoulnuth*a work on
superheated steam.
Re#naull gives the equations following for other liquids;
Kllicr 77
Chloroform .?/"
Cnrbon bisulphide //
Cnrbon icirnchlurldu 11
fjl + 045/  o. 00055556 ('
67 10.1375*
I o. i.\(>o\ t 0.0004133 /'
52 I o.i,)6aj;( 0. 000172 / l
Accton 11 => i.jo. 5 i 0.36644 (  o. 000516 f*
Heat of Vaporization. If the heat of the liquid be sub
tracted from the louil heal, Ihe remainder is culled the heat of
vaporization, and is represented by r, so that
r II q (100)
Specific Volume of Liquids. The coefficient of expansion of
mosi liquids is large as compared with thai of solids, bin it is
small as compared wilh thai of gases or vapors. Again, the
specific volume of a vapor is large compared with that of the
liquid from which il is formed. Consequently the error of neg
lecting ihc increase of volume of a liquid with ihc rise of temper
ature is small in equations relating lo the thermodynamics of a
Riituralccl vapor, or of a mixture of a liquid and its vapor when
a considerable pan by weight of the mixture is vapor. It is
therefore customary to consider ihc specific volume of a liquid
o lo be constant.
The following table gives ihc .specific gravities and specific
volumes of liquids:
SPECIFIC OUAVITIKS AND SPKCIl'IC VOlAJMKR ()!' LIQUIDS.
Alcohol .....
Kihcr .......
Chloroform . . . .
Carbon hlaulphklc ,
iclrnchlorldo
Sulphur dioxide .
Aininonift
Wnlcr
Specific
Ornvliy
Specific Volume.
coniiinred
with Wftlov
nl < C.
Cubic Meirei.
Cubic Keel.
0,80631;
o oat a<O
^
o. 736
o 001350
15 = 7
0.000055
1.3922
o 00077,1
l .6iao
0.00613
0,81
0,0013^
i.. 1336
O.OOOf)Sl
O.OIU
0.636.1
0.001571
0.0353
i
o.oor
0.01603
Experiments were made by Him* to determine me volumes
of liquid at high temperatures compared with I he volume at
freezingpoint, by a method which was essentially to use them
for the expansive substance of a thermometer. The results arc
given in the following equations:
SPECIFIC VOLUMES OF HOT LIQUIDS.
Loja Hi Kntiit
6.0361445 
.).. 1781868 
i..l5 B 3'Hfl "
Water,
100 C. 10 200 C.
(Vol. at 4 = unity.)
v  i I 0.00010867875 /
H 0.0000030073653 ('
) 0.0000000387304331'
0.0000000000066457031 /'
Alcohol,
30 C. to 160 C.
(Vol. at o = unity.)
v i 1 0.00073893365 t
\ o. 00001055335 /'
0.000000093480843 r
1 0.000000000.10.113567 /'
a.yfrfjoji?
0.6065370
Ether,
30 C. to 130 C.
(Vol. at o = unity.)
v ~ i + 0.0013480050 i
o. 00000003.1.190756 J 1
1 0.00000000033773063 ('
7 l3Q(jHl9 n
4.8164866 
0.5385371 
Carbon Bisulphide,
30 C. to loo'C.
(Vol. at o = unity.)
v I + 0.0011680559 (
+ 0.000001(1480598 J 7
o.ocxxxMooo8inoo6a t*
7.0671)6,16
07849494 
Carbon TetrnchloHdc,
30 C. to 160 C.
(Vol. at o  unity.)
v => i + 0.0010671883 1
+ 0.000003565 1378^
O.OOOOOOOt4Q<}938l 1*
\ o. 000000000085183318 /'
4.553076.1 
3. 17.1630' 
Ifl
Quality or Dryness Factor. AH the properties of HaluralCtd
steam, such as pressure, volume and heat ot vaporisation, dq>cod
on the temperature only, and are dcicrminablc cilltcr by direct
experiment or by computation, and arc commonly taken from
tables calculated for the purpose.
Many of the problems met in engineering deal with mixtures of
liquid and vapor, such as water and steam. In such problem*
it is convenient to represent the proportions of water and steam
by a variable known as the quality or the dry ness factor;
* Antiales tie CMmle et de Physique, 1867.
factor, .V', is defined as thai portion of a pound of the mixture
which is steam; the remnant, i x, is consequently water.
Specific Volume of Wet Steam. Let the specific volume of
the saturated vapor bo .t and that of the liquid be <r; then the
change of volume is s a = n (m passing from the liquid to
tfic vaporous slate. If a pound of a homogeneous mixture of
water and steam is ;v part .slcam, then the specific volume may
be represented by
 (i .v)
xu +
(101)
where u is Ihc increase of volume due lo vaporization.
Internal and External Latent Heat. The heat of vaporiza
tion overcomes external pressure, and changes the slalc from
liquid lo vapor at constant temperature and pressure. The
external work is
p (s  o) _ pu t
nnd Ihc corresponding amount of heal, or the external latent
heal, is
Ap (s <r) = Apu.
The heat required to do the disgrcgation work, or the internal
latent heat, is
p r Apu (102)
General Equation. In order to apply the general ihermo
dynamic method to a mixture of a liquid and ils vapor, it is
customary lo write a differential equation involving the tern'
peraturc /, the quality x, the specific heals of water and slcam c
and h, and the heat of vaporisation r\ these three last properties
arc assumed lo be functions of the temperature only.
The principal result of the application of the general method
lo such an equation in a formula for calculating the specific
volume s, as will appear later. Following the general method, a
special derivation of the formula for s will be given which may
be preferred by some readers.
When a mixture of liquid and ils vapor receives heat there is
in general " n incrLilSU in mu n.iuji_iaimi, ui int. jjutuvm .v wi
vapor and in the portion i x of liquid, 'and there is n vaporiett*
tion of part of the liquid. Taking c for llic specific heat of the
liquid and h for the specific heat of the vapor, while r is the heal
of vaporization, we shall have for an infinitesimal change,
dQ = lixdt H c (r x) dl + rdx
Application of the First Law. The first law of thermo
dynamics is applied to equation (103) by combining it with
equation (16), so that
dQ = A(dE \ pdv) = Iixdl + c (i x) dl j rdx\
.'. dE = j [hx + c (i *)] di + r ~ dx pdv.
Now v is a function of both / and x t as is evident from equation
(101), in which w is a function of l\ consequently,
) $ v ,, , 8v ,
dv = r dt h 5 dx*
ot ox
But bemg expressed in terms of / and * gives
Sx S/
Bearing in mind that all the functions but * and v arc functions
of t only, the differentiation gives
A dt
Bt
awl
so thai the above equation reduces to
(104)
Application of the Second Law.  The second law ol thermo
dynamics makes
'T
for a reversible process, so that the general equation (103) may
be reduced to
]Jut
r
Si ?'
First and Second Laws Combined. The combination oJ
Uons (io. ( ) and (105) gives
TAT
Special Method. 1 he preceding equation may be obtained
by a special method making use of the
diagram abed in Fig. 30 which repre
sents Gamut's cycle for a mixture at 6
a 1 ___^ liquid and its vapor, Liu; change o[
3 temperature A T being very small. I<cl
a represent the volume of one pound of
JSL water at the temperature T, and fr (he
Km. jo. volume of one pound of steiun nl I he MOM
temperature and pressure. The lint* till
therefore represents the vaporization of one pound of water &l
constant temperature, involving the application of the hcsttl of
vaporization r, and the increase of volume
u M s cr
where s and <r arc the specific volumes of steam ami water,
the second law of thermodynamics the efficiency of this cycle
be
T (r~ Ar) AT
'T "" 7' '
so that the heat changed into work will be
rAT
T
But by the first law of thermodynamics this heat Is equivalent
to the external work, which in this case Is approximately equal
to the increase of volume u multiplied by the change of pressure
Api consequently,
or, at the limit as Ar approaches zero,
Specific Volume and Density. The most important result of
the application of the methods of thermodynamics to the prop
erties of saturated vapor is expressed by equation (106), which
gives a method of calculating the specific volume; thus,
s =
AT
(107)
dl
The numerical value of <r for water for French units is o.ooi,
and for English units is ~ = 0.016, nearly. The density, or
weight of a unit of volume, is of course the reciprocal of the
specific volume.
It is of interest lo consider the degree of accuracy that may be
expected from this method of calculating the density of saturated
vapor. The value of r depends on TI and 17, the total heat and the
heat of the liquid ; the latter is now well known, but the total heat
is probably in doubt lo the extent of sis and may be more. The
absolute temperature T appears to be better known and may be
subject to an error of no more than rtfon or suW; and the mechan
ical equivalent of heat is perhaps as well determined as the
absolute temperature. The least satisfactory factor in the
expression is the differential coefficient , which is derived by
fit
differentiating one of the empirical equations on pages 78 and 79.
It is true that the resulting equations on pages 79 and 80 afford a
ready means of computing values of ihc coefficient with great
apparent accuracy, but some idea of the essential vagueness of
the method may be obtained by comparing computations of the
specific volume of saturated steam at 212 C., a point for which
either equation B t or equation C, will give the pressure as 14.6967
pounds per square inch. The specific volume by aid of equation
(107), using equation B, for determining the differential coefficient,
is 26.62, while the differential coefficient from equation C l gives
26.71; the discrepancy is about nta; or if the mean 26.66 betaken
as the probable value, cither computed value is subject lo an
error of v^u.
Experimental Determinations of Specific Volume. Hy far tho
bcsl direct determinations of Uu spi'cilk volume* I SULIU rated
slcam arc those reported by KnnbUuuh, Limit, and Klvbe, as
expressed by their characteristic equation for Mij>erlienlecl
given on page no. These experiments di'lermlfled the
surcs for various temperatures at cansuiiu volume, amt the
results were so treated as to give the volume nl Mtlurallnn by
cxtcrpolation with great certainly. Tin following U a com
parison of specific volume determined by ihem mul volume* com
puted by equation (107).
SPECIFIC VOLUMBS OF SATURATKD STKAM.
Hv Knoblauch, fjmlf, aiul Kiel*.
Volmno On. M.
Tampon
alum.
loo
Kxporl
nieittnl.
Com
1.665
i . i i 3
1. 674
1.420
110
i, til
1.112
"5
1 20
"5
1037
0.8933
0.7707
i.oa?
o.88a6
0.7617
Tamper
alure.
'30
'35
MS
'50
Volimia t"n. M.
[tutetl,
0.5843
0.50C>1
O..I466
0.3.170
"S747
o . 50 j i
o. ,1105
o . 3880
iftl)
170
.I4U
Nature of the Specific Heats. In the application of ilia gon*
cral thermodynamic method on page 88 the term h I* Intro
duced to represent the specific heat of siUumtcd steam, and iheru
is some interest in the determination of the true nature af thit
property, which clearly cannot be a specific heat at rontrtaat
pressure, nor a specific heat at constant volumo.aincc both prauutv
and volume change with the temperature. The RpedCic heal of
the liquid c properly is affected by the same consideration, but
as the increase of volume is small and is neglected in ilicrmo
dynamic discussions, the importance of the consideration h much
less. The specific heat h of saturated vapor in the amount of
heat necessary to raise the temperature of one pound of the
vapor one degree, under the condition that the pressure
increase with the temperature, according to the law for saturated
vapor.
Equation (105) gives a ready way of calculating the specific
heat for a vapor, for from it
. dr r
Now r may be readily expressed as a function of I, and then
dr
by differentiation  may be determined. For steam
r = 11 q = 606.5 + 0.305 / ~ fo 1 G (t /,)],
in which /, is the temperature at the beginning of the range, as
given by the table on page So, within which I may fall. There
fore
dt
c.
and
A = 0.305 
For other vapors the equations, deduced from the empirical
equations for q and H on pages 83 and 85, are somewhat more
complicated, but they involve no especial difficulty.
The following table gives the values of h for steam at several
absolute pressures:
Pressures, Ibs, per sq. in.,
Temperatures, t F. . .
Sj>ecific heal, h
SPECIFIC HEAT OF STF.AM.
zoo
,1 2 76
0.82
162.3
i . 30
20.9
0,93
200 300
381.7 417.4
0.70 0.63
The negative sign shows that heat must be abstracted from
saturated steam when the temperature and pressure are increased,
otherwise it will become superheated. On the other hand,
steam, when it suddenly expands with a loss of temperature and
pressure, suffers condensation, and the heat thus liberated sup
plies that required by the uncondensed portion.
riirn ^ VITIIIWI mis (.oiuiuaion i* HWIMHIM ^HIMUIH ineatn lit
a cylinder with glass aides, whrriuM4i ihr itair MiiuralccI steam
suffered partial amdenwilUin, n* indiuiial hy the formation oU
cloud of mist. The reverse of thin r** rimml <*ho\vct thai
docs not condense with sudden romprrwiun. *huwn by
Ether has ft positive value for A. A* ihr ihmiry indicate, &
cloud ia formed during sudden t'tirnprrwUin, 1ml mil during iqd?
den expansion.
The table of valuea of h for Mrnm ihntv^ .1 nnhiljlc dccrcasa
for higher temperatures, which InditAirt (mint n
which h ia zero and above which A K jKndivr, tiui the
lure of that point cannot be determined fmm our
knowledge. For chloroform tin* (mini of Invrninn
lated by Cazin t lo be i33..8 ( atitl dctrrmlnttl rxrimrntallyby
him to be between 125 and ut>. The db&reiwwiy i% nuv^ly
due lo the imperfection of the npimraliiv uwrl. which ulMtliuiod
finite changes of considerable mngnlluclr for the
small changes required by ihc theory.
Isothermal Lines. Since the prauurr of aiuniiei vajxir JH (i
function of ihc temperature only, the luuhrrtna) lint I H mixture
of a liquid and its vapor ia a line of comtmnt pnrviurc, parallel lo
the axis of volumes, Steam expanding from the boiler into the
cylinder of an engine follows aucli u line; ihm K Ihr tca(n*Une
of an automatic cutoff engine with ample port* is nearly parallel
to the atmospheric line.
The heat required for an increase of volume ni m.imm press
ure s
Q
in which r is the heat required to vnporto one pound of liquid,
and x, and .r, arc the initial and final qualities, so ilul *, *i
is the weight of liquid vaporized.
The external work done during an isothermal expansion is
W _ p (v t  V J M ^ H (, Vl ^ , Vl ) . , . . (109)
* Bulletin do la Soclelt In,!, fa Afujfo^ c*n.W t
t Compiet nndia do 1'Acatttmte ties Stfenw, U.
Intrinsic Energy, Of the heal required to raise a pound of
any liquid from freezingpoint Lo a given temperature and to
completely vaporize it at thai temperature, a part q is required
to increase the temperature, another part p is required to change
the state or do disgrcgation work, and a third part A pn is required
to do the external work of vaporisation. Consequently for com
plete vaporisation we may have,
Q A (S [ /  W)q I p + A pit = H.
For partial vaporization the heat required to do the disgrega
lion work will be xp, and the heat required to do the external
work will be Apxu. Therefore the heat required Lo raise a pound
of a liquid from freezingpoint to a given temperature and to
vaporize & part of it will be
Q = q  xp I Apxn  A(E + W)
where E is the increase of intrinsic energy from freezingpoint.
It is customary to consider that
L.
A
I <?)
(no)
represents the intrinsic energy of one unit of weight of a mixture
of a liquid and its vapor.
Isoenergic or Isodynamlc Lines. If a change of fi mixture
of a liquid and its vapor takes place at constant intrinsic energy,
the value of /iwill be the same at the initial and final conditions,
find
which equation, with the formula;
enable us to compute the initial and final volumes. If desired,
intermediate volume corresponding to intermediate temperature
can be computed in the same way, and a curve can be drawn
in the usual way with pressures and volumes for the coordinates.
For example^ if a mixture of iV steam and T^T water oxpfinds
isocncrgically from too pounds nlm.Uiir
Ihc final condition will be
15 lnimN absolute,
'9395.
The initial and final specific
art
The converse problem requiring llir prt^urr KiriTHK.mling lo
a given volume cannot be solved clirrdly. "Hir only method
of solving such a problem la tit nnHumr irllilr timit prcMuro
and find the corresponding volume; lluii. if nttrwiry, nuumo
a new final pressure larger or smaller % may IK rrf(ulrcd t and
solve for the volume again; nml so on until ihr ilwirnl degree
of accuracy is obtained,
This method does not give an explicit rcuniinn connrcifng Iho
pressures and volumes, but it will be found n it inl ilmt curve,
drawn by the process given above cn be rrprmminl fairly well
by an exponential equation, for which the* cxKmrni ran be
determined by the method on page 66.
Having given or determined the initial and Anal volumes, tho
exponential equation may bo dcLermlnccl, and ihm ihc external
work may be calculated by the equation
W
> I
Jlt&i,
i
For exompte t the exponent for the equation.
expansion of the above problem is
n . log Pi " log fa ^ JpjLooj;
log v, log Vi log 34.54 
and the external work of expansion IB
s
I.O.!
1.041
Since there is no change in the intrinsic energy during an
isocnergic expansion, the external work is equivalent to the heat
applied. Thus in the example jusl solved the heat applied is
equal to
IOO,OOO T 778 = I2(J TJ.T.U.
There is litlle occasion for the use of the method just given,
which is fortunate, as it is not convenient.
Entropy of the Liquid. Suppose that a unit of weight of a
liquid is intimately mingled with its vapor, so that its tempera
ture is always the same as that of the vapor; then if the pressure
of the vapor is increased the liquid will be heated, and if the
vapor expands the liquid will be cooled. So far as the unit of
weight of the liquid under consideration is concerned, the pro
cesses are reversible, for it will always be at the temperature of
the substance from which it receives or to which it imparts heat,
i.e., it is always at the temperature of its vapor.
The change of entropy of the liquid can therefore be calculated
by equation (37),
which may here be written
_ f & _ f *
J T "J T
("3)
On page 83 it is suggested that the specific heat of water for
temperature Centigrade may be expressed as follows:
c = i 4 k
where k is a small corrective term that may be positive or negative
as the case may be. Using this correction, equation (113) may
be written
T
(114)
Tne nrst term ciin
second term, which is small, nm be. delermined graphically,
that the expression Tor entropy of water bmimes
/
(V
I A
''ft /
The columns of entropy of water in Clio tables wort determined
in this manner.
In iihc discussion of cncropy on page 31 it wan pointed out
that there is no natural zero of entropy rnrrcHpowling Ui the nbo
lute zero of temperature. It is customary to treat llit freesing.
point of water as the xcro of entropy both for ihut \\t\uvl and
for other volatile liquids; some liquids ihcrefnrc huvt* lu'gnitve
entropies at temperatures below frccx/mgpoinl of water in ihfi
appropriate tables of chctv properties.
For a liquid like ether which has the heat of the litjiltd repre
sented by an empirical equation,
q *<* 0.52901 /  0.0003059 / a ,
the specific heat is first obtained by differentiation, giving
c * 0.52901 ( 0,0005918 /.
Then the increase of entropy above that for the frcc%ingpoim of
water may be obtained by aid of equation (113), which gives for
ether with the French system of units,
i/S73
.52901  0,OOOS9l8
373)
0.0005918 r//);
' ^=00005918 (T 1  373) + 0.3670
.. 0= 0.0005918 /h 0.3670 log,
273
.... ( M 6)
For temperatures below the freezingpoint of water, equation
(116) gives negative numerical results.
Other liquids for which equations for the heat of the liquid
arc given on page 83, may be treated in a similar method.
Entropy due to Vaporization. When a unit of weight of a
liquid is vaporized r thermal units, equal to the heat of vaporiza
tion, must be applied at constant temperature. Treating such
a vaporization as a reversible process, Ihc change of entropy may
be calculated by the equation
Y
',** T
This properly is given in the " Tallies for Saturated Steam,"
but not in general for other liquids.
Entropy of a Mixture of a Liquid and its Vapor. The increase
in entropy due to heating a unit of weight of a liquid from freez
ingpoint to the temperature; t and then vaporizing x portion of
it is
01^
M T ,
where is the entropy of the liquid, r is the heat of vaporization,
and T is the absolute temperature. For steam ^ may be taken
from the tables; for other vapors it must usually be calculated.
For any other state determined by .%'i and ^ we shall have, for
the increase of entropy above that of liquid at freezingpoint,
The change of entropy in passing from one stale to another
13
'i  .  (u?)
When the condition of the mixture of a liquid and its vapor
is given by the pressure and value of x, then a table giving the
properties at each {wind may be conveniently used for this work.
gives
,
When ihc initial atnlc, Oclrrminnl by *. anil /, .if /> U
and the fmal temperature * or the fin.1 urc , ihc Ami
vMuo *, may be found by cquMlun (i
volumes may be ciilculniwl ty lw
Tablca of Ihc propcriicH of wnumlwl v ft j* i.mmcmly give (he
specific volume 5, but
1 .1  1 cr.
The value of o for wmcr fe o.otfi, uml fr thtr lwiiWi will bo
found on page 85.
*V fl**itt^c, one pound of dry Mcnm
pressure will have the values
/ * 337.fi K, r,  884.0, C, 
tuntK
IE the final prcasurc is 15 pounds n
(,  ai3.o I 1 '., r a 965.1,
whence
have
.
788.3
o
673,7
,v
The initial and final volumes nre
,
I
Problcma Jn which the initial condlllun ami ihc final tem
perature or pressure arc given may be galval elircrlly by uifl 01
llic ])rt;ccding equations. Those giving the; final volume instead
millions. An equation to an adiabalic curve in terms of p and v
cannot be given, but such a curve for any particular case may
be construct c'd point by point.
Clatisius and Runkine independently and at about the same
time deduced equations identical with equations (117) and
(118), but by methods each of which differed from that given
here.
Rankine called the function
the lltcrmodynantic function ; Clausius called it entropy.
In the discussion of the specific heat // of a saturated vapor, it
appeared Unit thu expansion of dry saUmiled steam in a non
conducting cylinder would be accompanied by partial conden
sation. The same fact may be brought out more clearly by the
above problem.
On the other hand, A is positive for ether, and partial conden
sation lakes place during compression in a nonconducting
cylinder.
For example, let the initial condition for ether be
/, 10 C ., r 12
i  93 I2 >
and let the final conditions 'be
/. <=> 120 C., ?a 72.26,
0.0191,
0.2045;
tfocn
and
 ~
283
72.26.V. .
'  * I
393
Equation (it8) applies to all possible mixtures of a liquid and
Us vapor, including the case of x t  o or the case of liquid with
out vapor, but at the pressure corresponding to the temperature
according to the law of saturated vapor. When applied to hot
\vatcr, this equation shows that an expansion in a nonconduct
ing cylinder is accompanied by a partial vaporization.
IO2
SATURATED VAPOR
There is some initial stale of the mixiuri 1 such that the
of x shall be the same (it llu bL'KinninK uml ui [lie end, though ft
may vary at intermediate suites. To find Unit value make *,
x l in equation (nB) and solve 1 for .v,, which
The value of A', for steam to fullil ilu conditions
with the initial nnd final temperatures cliomn, 1ml In any
will not be much diflerem from tint Imlf, It may therefore
generally slated that a mixture of steam uml water,
expanded Jn A nonconducting cylinder, will .show
dcnsation if more thnn half is Klram, and pariwl
more limn half water. If tht mixlurt* in nenrly half walor
half steam, the change must he invi'HtlKutwl to drtvrmlnc
evaporation or condensation will occur; but In nny tw& th
action will be small.
External Work during Adlabatlc Kxpftnalon. Since no
is transmitted during nn admhuttt fx[)iinsio/i, (til of ihe
energy lost is changed into external work, ao that, by
t E,
For example, the external work of one pound of dry
expanding adiabaticully from too pounds let 15 pounds
is
W  778 (297.9  181.8 I i X Hoa.8 . 0.894 X
W  120.2 X 778  93,500 fuotimimcla.
Attention should be called to (he unavoidable defect
method of calculation of cxlcrnnl work during ndlnlmllc
sion, in that it depends on taking ihr fliffercnce o
which arc of Ihc same order of magnitude. For example, ifes
above calculation appears to give four places of significant %*ff^.
while, as n mailer of fact, the lotal heal II from which p is derived
is affected by a probable error of ^ or perhaps more. Both
Ihc quantities
have a numerical value somewhere near 1000, and an error of
 is nearly equivalent to two thermal units, so that the probable
500
error of the above calculation is nearly two per cent. For a
wider range 1 of temperature [he error is less, and for a narrower
range it is of course larger. This mutter should be borne in
mind in considering the use of approximate methods of calcula
tions; for example, the teinpcniUt re entropy diagram to be dis
cussed later.
The adiabatic curve cannot be well represented by an expo
nenlial equation; for if an exponent be determined for such a
curve passing through points representing the initial and final
stales, it will be found that the exponent will vary widely with
different ranges of pressure, and still more with different initial
values of x\ and that, further, the intermediate points will not be
well represented by such an exponential curve even though it
passes through the initial and final points.
This fact was first pointed out by Zcuner, who found that the
most Important, clement in determining n was x lt the initial con
dition of the mixture. Tie gives the following empirical formula
for determining , which gives a fair approximation for ordinary
ranges of temperature:
n 1.035 "I* o.ioovv
There docs not appear to be any good reason for using an
exponential equation in this connection, for all problems can be
solved by the method given, and the action of a lagged slcam
enginc cylinder is far from being adiabatic. An adiabalic line
drawn on an indicatordiagram is instructive, since it shows
to the eye Ihc difference between the expansion in an actual
engine and that of an ideal nonconducting cylinder; but it can
be iiHcingcnuy uruwn umj  ..... ...... " " ^
general purposes ilic hyperbola w I he litsl airw fur comparison
with ihc expansion curve of an indicator ilm^um, for the reason
that it is the conventional curve, ami if nwir enough to the curve
of the diagrams from good engines in nllciw n pruciiuit engineer
to guess at the probable behavior of nn engine, from the diagnm
alone. It cannot in any sense be considered us the theoretical
If the entropies of
curve.
TemperatureEntropy Diagram.
liquid and the entropies of vaporisation ftir mwm arc plotted with
temperature for ordinates we gel ft iilrtKm Ukc #u.\ vry com^
mimly ulMtnluie Icmperatura
nrr inkrn in ttrnwlng thodli*
gram in ureter 10 rmphulio
rht role \i\nyn\ by nbaoluto .
irmiwrRiurpH in ihc dcier*
minntion cif the efficiency of
Curnnl 's rye Ic. It would seom
brlicr lu inkc the (empcroluro
by (he ccnilgrnilc or i ho Fnh*
rcnhrii ihcTmomcier, us they
art 1 ilie basb of
too
1
Via. ion.
and the temperatureentropy diagram is* ihc equivalent of such a
table.
Now the entropy of a mixture con lain tng x [mrl stenm is
so that the entropy of a mixture containing x purl of steam can
be determined by dividing the line such d$ (which represent*
the entropy of vaporization) In ihe proper rntlo.
dc
It is convenient to divide the several lines like ab and th Into
tenths and hundred tha, and then, If an adinbnile expansion te
represented by a vertical line like be, the entropy at c may be
determined by inspection of the diagram. Conversely, by noting
the temperature at which a given line of constant entropy crosses
a line of given quality we may determine the temperature to
which it is necessary to expand to attain that quality, a determina
tion which cannot be made dircclly by ihc equation.
When a temperatureentropy diagram is used as a substitute
fora "Table of the Properties of Saturated Steam," it is custom
ary to draw the lines of constant quality or clryness factor, and
other lines like constant volume lines and lines of constant heal
contents or values of the expression
AT I q>
the use of which will appear in (lie discuss/on of s teamengines
nnd steamturbines.
To gel a aeries of constant volume lines we muy compute the
volume for each quality x t .1,, .v, ,z t x .3, etc., by the
equation
and since the volume increases proportionally to the increase in
x, we may readily determine the points on thai line for which
the volume shall be whole units, such as 2 cubic feet, 3 cubic feet,
etc. Points for which the volumes are equal may now be con
nected by fair curves, so thai for any temperature and entropy the
volume may readily be estimated.
Curves of equal heat contents can be constructed in a similar
way.
If desired, a curve of temperatures and pressures can be drawn
so that many problems can be solved approximately by aid of the
compound diagram.
At the back of this book a temperatureentropy diagram will
be found which givca the properties of saturated and superheated
steam. It is provided with a scale of temperatures at either
side, and a scale of entropies at the bottom, while there is a scale
of pressure at the right.
To solve a problem like that on page 100, I.e., to find the quality
after fin adiabatic expansion from 100 pounds iihsnluto to \t
pounds absolute, and the specific volume (it the Initial and final
stales, proceed as follows:
From the curve of temperatures and pressure*, select the ten*
pcralurc line which corresponds to roo pound* niul note whew It
cuts the saturation curve, because it is assumed thai the steam Is
initially dry. The diagram gives the entropy an approximately
1.61. Note the temperature line which cuts the tampcrauifr
pressure curve at 15 pounds, and estimate the value of x from Id
intersection with the entropy line i.Gij by thia method the valutf
of x is found to be about 0.89. In likr manner the volume may
be estimated to be about 23.4 cubic feel.
TemperatureEntropy Table. Now that the compulation of
isocntropic changes has ceased to be llu' divenion of students
of theoretical investigations and has hcconu* ihc necessity of
engineers who arc engaged in such nuUiera as the? design of
steamturbines, the somewhat Inconvenient mi'ihodn which were
incapable of inverse solutions, have become somewhat burden
some. A remedy has been sought in the use of temperature
entropy diagrams just described. Such a diaicrum to be really
useful in practice must be drawn on so large n gcnlc M (a be very
inconvenient, and even then is liable to Inck accuracy. To meet
this condition of affairs a temperatureentropy table linn been com*
putcd and added to the "Tables of the Properties of Sfllu
Steam." In this table each degree Fahrenheit from 1 8o e to
is entered together with the corresponding pressure.
have been computed and entered in the proper columns Hut
following quantities, namely, quality .v, /teat contents AT <f f, and
specific volume v, for each hundredth of a unit of entropy.
In the use of this table it is recommended to take the nearest
degree of temperature .corresponding to the absolute* iircuun
if pressures are given. Following the Una across (he table select
that column of entropy which corresponds moat nearly with ibo
initial condition; the corresponding initial volume may be read
directly. Follow down the entropy column to the lower temper
" TEMPKRATUREENTROrV TABLE
107
alurc and then find the value of x and the specific volume. The
external work for udiabaiic expansion may now readily be found
' by aid of equation (120), page 102. As will appear later, the
problems that arise in practice usually require ihc heal contents
and not the intrinsic energy, so that property has been chosen
in making up the table.
For example, the nearest temperature to 100 pounds per square
inch is 328 F.; the entropy column 1.59 gives for x, 0.995, which
indicates half of one per cent of moisture in the steam. The corre
sponding volume is ,139 cubic feet. The nearest temperature to
15 pounds absolute is 213 K, and at 1.59 entropy the quality
is 0.888 and the specific volume corresponding is 23.2 cubic
feet.
Jf greater accuracy is desired we must resort to interpolation.
Usually it will be sufficient to interpolate between the lines for
temperature in a given column of entropy, because the quantity
that must be determined accurately is usually the difference
x t r t } g l  (.v/ 2 + ft)
and this difference for two given temperatures 1^ and / 3 is very
nearly the same if taken out of two adjacent entropy columns.
A similar result will be found for the difference
if computed for values of x found in adjacent columns.
Another way of looking at this matter is that one hundredth
of a unit of entropy al 330 pounds corresponds to one per cent
of moisture.
Evidently this table can be used to solve problems in which
the final volumes arc given, or, as will appear later, to determine
intermediate pressures for steam turbines.
io8
HATl'RATKlt VAl'OK
I. WftUr HI loo I', H fed in ei Uiiltr in whkh ih
130 pounds absolute per square inch. Haw much
be supplied to evaporate each jmuml ? .An*. 1 1 18 A
a, One mund wet si rain HI 150 jKnimH mb^iU
cubic feet. What er rent nf mokture Is prrMrtit
"quality" of the Bieam? Ann. 17. t jwr *(tii f
1.3, A Kturul nf sU'iim rul wnirr ut i n**
.() Rlcnm, Wluit is i he inrfiMir nf rnirupy *Uw
33 K? Ann, i,i,j.i,
.(. A kilogram cif i hlnn>rirm ai ICM" t*. i*
the mcrcaxc of cntrcipj nUivt* ilmt of du li
k 5. The initifil rcmifUicm tf n mUtun
/  3^o e R, v * o,H. Whm K the linal i
cx[mnsitm in ji j a I". ? Anv 0,7.1,
/ 6. Tlie inillnl rcindlilim f >i mUiurr ;
3000 mm., .v  o.tj. I'tnilittriimilliinAArirr AH*
aion ( ^3^ mm, Ana. 0.8,18.
7. A cubic fool nf i mislure of
under the pmuurc of to jxiuiulft by ihr
after It vxpnmU BdUlmilcally lil! iht* timnurv
pounds by the gauge; HMI the eslprnal wnr k f
3,68 cubic feel and goto faaipnumU.
8. Three pnundx nf a mixture of
pounds it! wo Ink 1 prrwtire occupy 4,^
heat muni be added in dauMe tin? volume
and what U the chana? f Inirfnalc
g. Find the intrinsic
5 (Kiumls of n mixture o( wniw and icnm which
Htcom, the prncturc l"inK i^e pound* Hlw^
nwgXi ,3,710,000; lira* t amenta, 509$ n.r.t*.;
feel.
r.o.
TKMPICRATUREENTROI'Y TAHLE
109
io. Three pounds of water arc heated from 60 F. and evapor
ated under 135.3 pounds gauge pressure. Find the heal added,
and the changes in volume, and intrinsic energy. Ans. Kent
added, 3490 B.T.U.; increase in volume, 8.99 cubic feet; intrinsic
energy, 2,520,000. / * ,'*
( , ii. A pound of steam at 337.? F, and 100 pounds gauge
' pressure occupies 3 cubic feel. Find its intrinsic energy and its
entropy above 32 F. Ans. Intrinsic energy, 718,000; entropy,
12. Two pipes deliver water into a third. One supplies 300
gallons per minute at 70 F.; the other, 90 gallons per minute at
200 F. What is the temperature of the water after the two
streams unite? Ans. 100 F,
13. A lest of an engine with the cutoff at 0.106 of the stroke,
and the release at 0.98 of the stroke, and with 4.5 per cent clear
ance, gave for the pressure at cutoff 62.2 pounds by the indicator,
and at release 0.2 pounds; the mixture in the cylinder at cutoft
was 0,465 steam, uncl at release 0.921 steam. Find (i) condition
of the mixture in. the cylinder at release on the assumption of
acliabatic expansion to release; (2) condition of mixture on the
assumption of hyperbolic expansion, or that pv w p^^ (3) tho
exponent of an exponential curve passing through points of cut
off and release; (4) exponent of a curve passing through the initial
and final points on the assumption of adiabatic expansion; (g)
the piston displacement wtis 0.7 cubic feet, find the external work
under exponential curve passing Ihrough the points of cutofT and
release; also under the adlaba'llc curve. Ans. (i) 0.472; (2)
0.524; (3) " 0.6802; (4)  1.0589; (5) 3093 and 2120 foot
pounds.
CHAPTER VII.
SUPKUUKATEl) VAPORS.
A CRY and saturated vapor, not in contact with the
from which it is formed, may be healed to a temperature greater
than that corresponding to the given pressure for the fittttie
vapor when saturated; such a vapor is said lo be superheated,
When far removed from the temperature of saturation, such ft
vapor follows the laws of perfect gases very nearly, but near (ta
temperature of saturation the departure from those laws t Ion
great to allow of calculations by them for engineering purpoMfc
All the characteristic equations that have been proposed,
have been derived from the equation
pv = RT t
which is very nearly true (or the socalled perfect gasca ut mod
crate temperatures and pressures; it is, however, well knm
that the equation docs not give satisfactory results al very
pressures or very low temperatures. To adapt this equation
represent superheated slcam, a corrective term is added to I
righthand side, which may most conveniently be assumed
be a function of the temperature and pressure, so that
tions by it may be made to join on to I hose for saturated
The most satisfactory characteristic equation of this sort
that given by Knoblauch,* Linde, and Klcbc,
pv  BT  p (r h rt/0
\T/
>D
in it the pressure is in kilograms per square metro, v IB !n
cubic metres, and T is the absolute temperature by
* Mitteilungen fiber J'orseliuttttsarbcilcn, crlc., Heft 21, R. 33,
no
SUPKKHEATED VAI'ORS Jri
centigrade Ihcrmomclcr. The constants have ihc following
values:
B <= 47.10, a = 0.000002, C *= 0.031, D ~ 0.0052.
In the English system of units, ihc pressures being in pounds
per square fool, the volumes in cubic feel per pound, and the
temperatures cm ihc Fahrmhcil scale, we have
/v85.85 7 l ~/.(io.ooopo 97 6/o 0.0833
The following equation may be used with ihc pressure in
pounds per square inch ;
/wo. 5962 Tp (i + .ooMjfr)( T Ja322!229_ 0.0833) . (r2 3 )
The labor of calculation is principally in reducing the cor
rective term, and especially in the compulation of ihc factor
containing llic temperature. A table on page 112 gives values
of this factor for each five degrees from 100 to 600 F.; the
maximum error in the calculation of volume by aid of the table
is about o.< of one per ceni at 336 pounds pressure and 428 F.;
that ia at the upper limit of our table for saturated steam. At
150 pounds and 358 K, which is about the middle range
of our table for saturated steam, the error is not more lhan 0.2
of one per cent, which is not greater than the probable error of
the equation ilself under those conditions. At lower pressures
and al higher temperatures the error tends to diminish.
The following simple equation is proposed by Tumlirx*
v 8T C>
where /> is the pressure in kilograms per square metre, v Ihc
specific volume in cubic metres, and T the absolute temperature
ccnUgradc, The constants have the values
B 47.10 C 0,016,
based on the experiments of Knoblauch, Lindc, and Klcbc.
* Math. Natitrw. Kl. Wlen., 1899, HH S. 1058.
112
SUPKRHKATBU VAPORS
In the English system with the pressure in pounds per square
foot and the volumes in cubic feel, for ubsoluie temperatures
Fahrenheit,
pv 85.85 7'  0.356 J (135)
This equation has a maximum error of o.S of one per cent a$
compared with equation (121).
TA1ILK I.
... . ., , 150,100,000
Vnluva of llic forlnr   o.ofljj.
Fnhr.
Abi.
Vnlub
of
Factor.
300
659S
0.441
305
6645
0.429
3IO
669.5
0.417
"5
671 5
0.405
6795
0395
335
6845
035
330
680.5
0375
a .15
604 5
0365
340
609.5
03S6
245
70.L5
0317
350
7095
0338
355
7115
0330
360
7'95
0.330
365
7315
0.313
370
730 5
0.301
a ?5
7345
0.996
380
7395
0.388
585
7445
0.381
300
7J9 5
0.374
395
7515
0.367
T a nip oral ura.
Value
Tom
Fat.r.
Abi.
Pftcicr,
Fahr.
300
75') 5
0.360
400
,15
761.5
0353
405
310
760.5
0.347
410
3 '5
7745
0.340
415
330
335
7795
7.!S
0.334
0.338
4 jn
330
7895
0.333
Lin
335
7945
0.3 id
135
340
7005
0.31 t
40
3IS
804.5
0.305
415
350
809.5
0.300
45
355
8145
o. 105
155
360
8i9.5
O. [1)0
460
365
8 j.i. 5
0185
465
370
820.5
o. iSo
470
375
834.5
0.175
475
3o
839.5
0.171
480
35
8.145
o.i 66
485
390
849,5
o. 163
395
85.1.5
0158
195
85'). 5
Hfti/5
811,. 5
45
HHo.c
()0 . 5
()<.*) . 5
014.5
a..jt
951
Value
Focior.
o 15.1
o 1. 10
0.145
o. i.i
o. 131
o, i J7
o. i j.i
Q. no
a. 117
a. 1 1,1
o, no
o. 107
0.1 0.
o. 101
o.ooK
0.005
O.OQ3
fl.(XJO
505
510
5'5
5)0
5)5
535
550
555
560
S6S
575
SOS
Al*.
OMS
070. S
0995
IOJ45
1010. s
10J..JJ
1031
Specific Heat, Two investigations have been mndc of
specific heat of superheated slwim nt conslnni pressure, on
Professor Knoblauch* and T)r. Jakob nml the other by _
lessor Thomas and Mr. Short; f the results of the hitler's inm
tigalion have been communicated *for use in this
anticipation of the publication of the completed report.
* MtoollHHxen liber Punch wwarbelien t Itcfi 36. p. tot).
t Thosb by Mr. Short, Cornell Unlvenliy
SPECIFIC HEAT II3
Professor Knoblauch's report gives the results of the inves
tigations made under his direction in the form of a table giving
specific heats at various temperatures and pressures and in a
diagram, which can be found in the original memoir, and lie
also gives a table of mean specific heals from the temperature of
saturation to various temperatures at several pressures. This
lallcr lablc is given here in both the metric syslcm and in ihc
English syslcm of units.
SPECIFIC HKAT OF SUPKRHKATKD STEAM.
Knoblauch ami Jnkab
The construction of this lal)lc is readily understood from the
following example: Required the heat needed to superheat a
kilogram of steam at 4 kilograms per square centimetre from
saturation to 300 C. The saturation temperature (to ihe nearest
degree) is 143 C.; so that the steam at 300 is superheated 157,
and for this la required the heal
157 X 0,493 77,3 calorics.
The experiments of Professor Knoblauch were made at 2, 4,
6, and 8 kilograms per square centimetre; the remainder of the
(able was obtained from the diagram which was extended by aid
of crosscurves to the extent indicated. Within the limits of
the experimental work the table may be used with confidence.
Interpolated results arc probably less reliable limn those
obtained directly by Professor Thomas.
114
SUPERHEATED VAPORS
The following table gives the mean specific heat of super
heated steam as measured on a facsimile of Professor Thomas's
original diagram without cxtcrpolation.
SPECIFIC HEAT OF SUPERHEATED STEAM
Thomas and Short.
1'rewure Lb. pet S(, In. (Absolute.)
Superheat Falir.
6
15
30
00
100
200
400
20
o.53<>
0517
0.558
0.571
oSO.1
o.6ai
o. 6.19
5
0.533
0533
0513
oSSS
0575
0.600
0.631
100
0.503
0.<;i3
0.534
S37
0557
o.ijSi
0599
150
0.486
0.406
0.508
0.533
05M
0.567
0.585
200
0.471
0.480
0.404
0.500
'5M
o55 f >
oSM
250
0.456
o.i66
0.481
0.406
0.533
0.5,16
0.564
30
0.442
Q.153
0.468
0.484
0.511
0537
oSSi
Here again the arrangement of the table can be made evident
by an example: Required the heat needed to superheat steam
100 degrees at 200 pounds per square inch absolute. The mean
specific heat from saturation is 0,581, so that the heat required
is 58.1 thermal units.
Total Heat. In the solution of problems that arise in engi
neering it is convenient to use the total amount of heat required
to raise one pound of water from freezing point to the tempera
ture of saturated steam at the given pressure and to vaporixo
it and to superheat it at that pressure to the given temperature.
This total heat may be represented by the expression
I
+ r + c,
where t is the superheated temperature of the superheated
steam, /, is the temperature of saturated steam at ihc given
pressure p, and q and r arc the corresponding heat of the liquid
and heat of vaporization. The mean specific heat Cj, may
usually be selected from one of the given tables without inter
ENTROPY 115
polation, as a small variation does not have a very large
effect.
The total heat or heat .contents of superheated steam in the
temperatureentropy table were obtained by the following
method. From Professor Thomas's diagram giving mean
specific heats, curves of specific heats at various temperatures
and at a given pressure were obtained, and the curves thus
obtained were faired after a comparison with curves constructed
with Professor Knoblauch's specific heats at those temperatures.
These curves were then integrated graphically and the results
checked by comparison with his mean specific heats.
Entropy. By the entropy of superheated steam is meant
the increase of entropy due to heating water from freezingpoint
to the temperature of saturated steam at the given pressure, to
the vaporization and to the superheating at that pressure. This
operation may be represented as follows:
/
J
cpdl
T, T
in which T is the absolute temperature of the superheated steam,
and T t is the temperature of the saturated steam at the given
f
pressure; and may be taken from the " Tables of Saturated
* i
Steam." The last term was obtained for the temperature
entropy table by graphical integration of curves plotted
with values of ^ derived from the curves of specific heats at
various temperatures just described under the previous section.
If the temperature entropy table is not at hand, the last lerm
of the above expression may be obtained approximately by divid
ing the heal of superheating, by the mean absolute temperature
of superheating.
This may be expressed as follows:
c (/  O .
1 (' + O + 4595
n <5 SUPERHEATED VAPORS
where t is the temperature of the superheated steam, /, is the
temperature of saturated steam at the given pressure, and c is
the mean specific heat of superheated steam.
If this method is considered to be too crude, the computation
can be broken into two or more parts. Thus if / ( is an inter
mediate temperature, the increase of entropy due to superheat
ing may be computed as follows:
(' ~ O
F I' (I
! U
Ci + t) H <f595
+ O I 4595
where cj is the mean specific heal between t, and t lt and c,," is
the specific heat between /, and /. This method may evidently
be extended to take in two intermediate temperatures and give
three terms.
Adiabatic Expansion. The treatment of superheated steam
in ihis chapter resembles thai for salimucd steam in tlmt it docs
not yield an explicit equation for the adiabatic line. If ihc
steam were strongly superheated (hiring the whole operation it
is probable that the adiabatic line would be well represented
by an exponential equation, and for such case a mean value of
the exponent could be determined that would suffice for engi
neering work. But even with strongly superheated steam at
the initial condition the final condition is likely to show moisture
in the steam after adiabalic expansion, or, for that matter, after
expansion of the steam in the cylinder of an engine or in a steam
turbine.
Problems involving adiabatic expansion of steam which is
initially superheated can be solved by an extension of the method
for saturated steam, and this method applies with equal facility
to problems in which the steam becomes moist during the expan
sion. The mast ready method of solution is by aid of the tempera
turccnlropy table, which may be entered at the proper pressure
(or the corresponding temperature of saturated steam) and the
proper superheated temperature, it being in practice sufficient to
take the line for the nearest tabular pressure and the column
PROPKRTIKS UK SULPHUR DIOXIDK 3l?
)owing the nearest degree of superheating. Following clown
ic column for entropy to the final pressure, the properties for
ic final condition will be found; these will be the heat con
nls, specific volume, and either llu: temperature of superheated
cam or the quality .v, depending tm whether the steam remains
ipcrhcalcd during the exptm.Nion or btronu'H moist.
If the external work of adinhalic expansion of steam initially
ipcrhcalcd is desired, it can be had by Diking the difference of
e intrinsic energies, The Jinil rquivnlwil of imrinsiV energy
moist steam is
x (r
I q xr I q Apxu t
id of this expression the qiwnlity AT I q may be lulun from
c (cmpcmturcenlropy inhle, nnd tlic quimiity Aji.vu ran
: determined by did of the nU'iim Kibk. .hi like innnner tbe
:at contents of superheated slenm
r/ I r I
ilch is computed nnd set down in the temperatureentropy
blc may be miirtc in yield the hcul equlvnlcni of the intrinsic
crgy by subirncling I he Jiwil equivalent of tbe cxlcnial work
vaporising and superheiiling thu atcum
icre v is the aiwclfic volume ttf the* superheated Hiram. Tills
jthod In subject to some crilirisni, espcrially when thu steam
not highly superheated, because mime hem will be required
do the dlsgrcgallon work of auperhcaling. Fortunately the .,
?acr part of problcmn ftrlning in t'ligmecring involve the heat **;
nlcnts, so that this question is avoided, j x /'' 1
Properties of Sulphur Dioxide.  One of the most inlcreHiintf "'
d imporiant appJIcutionH f (Jit* theory f fliiptrhenUfl vn^Ktrs
found in the approximate calfiiliilion of [troperiien of eerluin
atilc liquids which arc uaetl in rcfrlKcrailngmachlnw, iintl for
Ich we have not suflicienl txprrimrnial tlain loconalruct inhlia
Ihc manner explained in the chapter on saturated vaporn.
n g SUPKRHEATED VAPOUS
For example, Rcgnault made experiments on the pressures
of saturated sulphur dioxide and ammonia, but did not de
termine the heal of the liquid nor the total heal. He did,
however, determine some of the properties of these substances
in the gaseous or superheated condition, from which it is pos
sible to! construct the characteristic equations for the super
heated vapors. These equations can then be used to make
approximate calculations of the saturated vapors, for .such equa
tions arc assumed to be applicable down to the saturated con
dition. Of course such calculations arc subject, to a considerable
unknown error, since the experimental data are barely sufficient
to establish the equations for the superheated vapors.
The specific heat of gaseous sulphur dioxide is given by
Rcgnaull* as 0.15438, and the coefficient of dilatation as
0.0039028. The theoretical specific gravity compared with air,
calculated from the chemical composition, is given by Lundoll
and Bdrnsicin f as 2.21295. Gmclin t gives (he following
experimental determinations: by Thomson, 2.222; by Bcrxclius,
2.24.7. The figure 2.23 will be assumed in this work, which
gives for the specific volume at frecx.ingpoinl and at atmospheric
pressure
v = '333* ^ a ^,7 cu bi c metres,
The corresponding pressure and temperature arc 10,333 n&d
273 C.
At this stage it is necessary to assign a probable form for the
characteristic equation, and for that purpose the form
pnTcf ./.... (125)
proposed by Xcuner has commonly been used, and it is con
venient to admit that it may take the form
 Cf
(jafi)
* M&moires tie I'lnst'tlttt da France, tonic xxl,
t PliysHtalischeclieinlsclie Tabellan.
f Wall'a irnnstnifan, p. a8o.
PROPERTIES OF SULPHUR DIOXIDE
The value of the arbitrary constant a may be determined
from the coefficient of dilatation as follows. The coefficient
of dilatation is the ratio of the increase of volume at constant
pressure, for one degree increase of temperature, to the original
volume; so that the preceding equation applied at o C. and at
i C. gives r
A
i>i ^o = c p a ^
If A PnVn
The value of a obtained by substituting known values in the
above equation is 0.212. Now as a appears in both the first and
the last terms of the righthand side of equation (126), a con
siderable change in a has but little effect on the compulations
by aid of that equation. As will appear later an assumption
of a value 0.22 for a will make equation (126) agree well with
certain experiments on the compressibility of sulphur dioxide,
and it will consequently be chosen. If now we reverse the process
by which a was calculated from the coefficient of dilatation,
the latter constant will appear to have a computed value of
0.004, which is but little different from the experimental value.
To compute C we have
0.15438 X 426.9 X 0.22 = 14.5,
and the coefficient of p a is
14.5 X 273 10333 X 0.347 .
ij2 ' "* O 'y a  u ~ = 48 nearly;
I0 333 '
so that the equation becomes
pv ~ 14.5 T 48 p'* 2 ( 12 ?)
Regnault found for the pressures
Pi ~ 697.83 mm. of mercury,
p s = 1341.58 mm. of mercury,
and at 7.7 C. the ratio
J\ tj
~ = 1.02088.
120
SUPERHEATED VAPORS
Reducing the given pressures to kilograms on the square
metre, and the temperature lo the absolute scale, and applying
to equation (127), we obtain 1.016 instead of the experimental
value for the above ratio,
Rcgnaull gives for the pressure of saturated sulphur dioxide
in mm. of mercury, the equation
log/) w a /in" cfP\
a  5,6663700;
log 6 0.4793425;
logc * 9,1659563 10;
Jopr 9.9972989 10;
Jog /? * 0.98720002 10;
w  < H 28 C,
Applying equation (95), page 76, (o this case,
log R  9.9972989;
log jfl M 9.98729002;
log A 8,63521.16;
logJ3' 7.9945332;
H / I 28 C.
The specific volume of saturated sulphur dioxide may be
calculated by inserting in equation (137) for the superheated
vapor the pressures calculated by aid of the above equation.
The results at several temperatures are as follows:
o H 30 C.
30
0,8293
0.2256 0.0825
AmlrdcfT * gives for the specific gravity of fluid sulphur dioxide
3,4336; consequently the specific volume of the liquid is
ff eon O.OOO7'
* Ann. Chain, i'ltarnt., 1859.
PROPERTIES OF SULPHUR DIOX1OK
The value of r, the heat of vnporiailion, may now be rn
lated at the given temperatures by equation (106), W 80,
I V<lP
r Aul ti
131
I .10 C.
In which u ** s <r.
The results arc
t  30 C. o
r 106.9 w.Go 005'J
Within the limits of error of our method of uiKuluiitm, iht
value of r may be found by the equation
; esa (j8  O.47 / (ijH)
The specific heat of the liquid in derivid by ihr fuUnwitiu
device. First assume that llu entropy of the Mipirltntlrd vnHir
may be calculated by the equation
tl& c I (c  r ) ^
11 V ' '' ^
given on page 67 for perfect gases. This may be irnntformcfl
into / ( }i K . j '/'
CV 1 "" Ji^ y ^ ^
But if we jnlroducc into the equation for n ptrfeci
pv *> RT t
the value of R from the cquailon
Cp *" Cp J ' !1 /I A
the characteristic equation may lake the form
f tf " i
Comparison of this equation with equation (laft)
replacing the term in equation (tag) by the Arbitrary
n
factor a, so that it may read
r
The expression for Ihc entropy of n liquid find ils vapor is
t fa//
L *i
if the vapor is dry. When differentiated this yields
~ H or
I
If it be assumed that equations (130) and (131) may both be
applied al saturation we have
/ Frf\ , , dr r . . .
( I [ . n . * EJU .1 ~ ~* . IT10)
JJ ( p till dl T ' (1 V>
If it be admitted further that the differential coefficient f can
/
be computed by the equation on page 120, the above equation
affords a means of estimating the specific heat of the liquid. At
o C., this method gives for the specific heat
c 0.4.
In English units we have for superheated sulphur dioxide
pv 26.4 T  184 p*** (133)
the pressures being in pounds on the square foot, the volumes
in cubic feet, and the temperatures in Fahrenheit degrees
absolute.
For pressures in pounds on the square inch at temperatures
on the Fahrenheit scale,
log p  a 6a" c$ n \
a 3.9527847;
log b  0,4792425;
log c  9.1659562 10;
log a 9.9984994 to;
log (3 9.99293890 10;
n = t + i8.4F.
For the heat of vaporization
r =i?(> 0,27 (/ 32)
and for the specific heat of the
(134)
c 0.4.
In applying these equations to the calculation of a table of
the properties of saturated sulphur dioxide the pressures corre
sponding to the temperatures are calculated as usual. Then
the heat of the liquid is calculated by aid of the constant specific
heat. The heat of vaporization is calculated by aid of equation
(134). Next the specific volume is calculated by inserting the
given temperature and the corresponding pressure for the sat
urated vapor in the characteristic equation (133). Having
the specific volume of the vapor and that of the liquid, the heat
equivalent (Apu} of the external work is readily found. Finally,
the entropy of the liquid is calculated by the equation
0= clog, ....... (135)
*
If the reader should object that this method is tortuous and
full of doubtful approximations and assumptions, he must bear
in mind that any method that can give approximations is better
than none, and that all the computations for rcfrigerating
machines, that use volatile fluids, depend on results so obtained.
And further, much of the waste and disappointment of earlier
refrigcra tingmachines could have been avoided if tables as good
as those computed by this method were then available.
Properties of Ammonia. The specific heat of gaseous
ammonia, determined by Rcgnault, is 0.50836. The theoretical
specific gravity compared with air, calculated from the chemical
composition, is given by Landolt and Bernstein as 0.58890.
Gmclin gives the following experimental determinations: by
Thomson, 0.5931 ; by Biot and Arago, 0.5967. For this work
the figure 0.597 will be assumed, which gives for the specific
volume at freezing point and at atmospheric pressure
1.30 cubic metres.
The coefficient of dilatation has not been determined, and con
sequently cannot be used to determine the vftluc of a in equation
(126). It, however, appears that consistent results arc obtained
if a is assumed to be \. The coefficient of T then becomes
0.50836 X 4a69 X
and the coefficient of /* is
5fr.3.><. a Lz
10333
so that the equation becomes
pv  54.3 T
*
543>
'* w 1 42 ;
142 />'
The coefficient of dilatation, calculated by the same process
as was used in determining a for sulphur dioxide, is 0.00404,
which may be compared with that for sulphur dioxide.
Rcgnault found for the pressures
Pi 703.50 mm, of mercury,
Pi 14353 mm  of mercury,
and at 8.i C. the ratio
i
fc2i.i.ox88,
PPt
while equation (136) gives under the same conditions 1.0200.
For saturated ammonia Rcgnault gives the equation
log a bct n c{F\
a  11.504333;
lOg b 0.8721769;
log c 9.9777087 10;
log a 9.9996014 10;
log /? 999397 2 9 *J
n  i + 22 C.;
by aid of which the pressures in mm. of mercury may be calculated
for temperatures on the centigrade scale. The differential
coefficient may be calculated by aid of the equation
log ,4 = 8.1635170 ro;
log B 8.4822485 10;
log ft = 9.9996014 10;
/ + 22 C.
The specific volume of saturated, ammonia calculated by
equation (136) at several temperatures arc
I  30 C. o + 30 C.
5 0.9982 0.2961 0.1167
AndrdcfT gives for the specific gravity of liquid ammonia at
o C. 0.6364, so that the specific volume of the liquid is
tr = 0.0016.
The values of r at the several given temperatures, calculated
by equation (128), arc
/ 3.C. o + 3oC.
f 3 2 S7 3*5 2775
which may be represented by the equation
r = 300 0.8 L
The specific heat of the liquidj calculated by aid of equation
(132), is
c = i.i.
In English units the properties of superheated or gaseous
ammonia may be represented by the equation
pv 99 T 710 *,
in which the pressures arc taken in pounds on the square foot
and volumes in cubic feet, while T represents the absolute
temperature in Fahrenheit degrees.
The pressure in pounds on [lie square inch may be calculated
by the equation
log p a ~~ ba n c/?";
a  9.7907380;
log 1) 0.8721769 ro;
log c 9.9777087 10;
log 9.9997786 10;
log /? 9.9966516 10;
 / J 7.6 I'.
The heal of vaporization may be calculated by the equation
r 546  0.8 (* 32),
and the specific licat of the liquid is
C E" I.I,
EXAMPLES.
1. What is the weight of one cubic foot of superheated steam
at 500 K, and at 60 pounds pressure absolute? Knoblauch's
equation. Ans. 0,106 pounds.
2. Superheated steam at 50 pounds absolute has half the
density of saturated steam at the same pressure. What is the
temperature? Tumlini'a equation. Ans. 930 F.
3. What is the volume of 5 pounds of steam at 129.3 pounds
gauge pressure and at 359.$ F.? Ans. 15.8.
4. At 129.3 pounds gauge pressure a pounds of steam occupy
7 cubic feet. Find its temperature. Assume value of T for
entering Table I, page 112, and solve by trial. Ans. 424 F.
5. A cubic foot of steam at 140 pounds absolute weighs 0.30
pounds. What is its temperature? Ans. 374?.
6. Two pounds of steam and water at 129,3 pounds pressure
above the atmosphere occupy 6 cubic feet. Heat is added and
(he pressure kept constant till the volume Is 8.5 cubic feet. Find
the final condition, and the external work done in expanding.
Ans. Temperature 68iF.; work 51800.
7. Saturated steam at 150 pounds gauge, containing 2 per cent
of water, passes through a superheater on its way to an engine.
Its final temperature is 400 F. Find the increase in volume
and the heat added per pound.
8. Let the initial temperature of superheated steam be 380 F.
at the pressure of 150 pounds absolute. Find the condition
after an adiabatic expansion to 20 pounds absolute. Determine
also the inilial and final volumes. Ans. (i) 0.895; (2) 3.09
cubic feet; (3) 17.8 cubic feet.
y. In examples, page 109, suppose that the steam at cutoff
were superheated 10 F. above the temperature of saturated
steam at the given pressure, and solve the example. Ans.
(i) 0.887; (2) 87 superheating; (3) same as before; (4) =
I.I37J (5) I 97 2 anci X 95 footpounds.
CHAPTER VIII.
THE STEAMKNOINE.
THE steamengine is still the most important heatengine,
though Its supremacy is threatened on one hand by the steam
turbine and on the other by the gascnginc. When of large size
and properly designed and managed its economy is excellent and
con be excelled only by the largest and best gasengines,
and in many cases these engines (even with the advantage of
a more favorable range of temperature) depend for their com
merclal success on the utilization of byproducts.
It can be controlled, regulated, and reversed easily and posi
tivelyproperties which are not possessed in like degree by
other heatengines. It Is interesting to know that the theory
of thermodynamics was developed mainly to account for the
action and to provide methods of designing steamengines;
though neither object is entirely accomplished, on account of
the fact that the enginecylinder must be made of some metal to
be hard and strong enough to endure service, for all metals arc
good conductors of heat, and seriously aftcct the action of a con
densable fluid like, steam.
Carnot's Cycle for a steamengine is repre
sented by Fig. 31, in which ttb and cil arc
isothermal lines, representing the application
and rejection of heat at constant temperature
and at constant pressure, be and da arc
adiabatic lines, representing change of tem
perature and pressure, without transmission
of heat through the walls of the cylinder.
The diagram representing Carnot's cycle has an external resem
blance to the indicatordiagram from some actual engines,
but it differs in essential particulars.
128
In the condition represented by the point a 'the cylinder con
tains a mixture of water and steam at the temperature /, and
the pressure ,. If connection is made with a. source of heat
at the temperature t lt and heat is added, some of the water will
be vaporised and the volume will increase at constant pressure
as represented by ab. If thermal communication is now inter
rupted, adiabatic expansion may take place as represented by be
till the temperature is reduced to / 2 , the temperature of the
refrigerator, with which thermal communication may now be
established. If the piston is forced toward the closed end of
the cylinder some of the steam in it will be condensed, and the
volume will be reduced at constant pressure as represented by
cd. The cycle is completed by an. adiabatic compression rep
resented by da.
If the absolute temperature of the source of heat is 7\, and
if that of the refrigerator is T^ then the efficiency is
whatever may be the working fluid.
For example^ if the pressure of the steam during isothermal
expansion is 100 pounds above the atmosphere, and if the pressure
during isothermal compression is equal to that of the atmos
phere, then the temperatures of the source of heat and of the
refrigerator arc 33?.6 F, and 212 F., or 797.1 and 671.5 abso
lute, so that the efficiency is
.797.1  671.5 ^
7971 3/
The following table gives the efficiencies worked out in a
similar way, for various steam pressures, both for t a equal to
21 2 F., corresponding to atmospheric pressure, and for / S1
equal to u6F., corresponding to an absolute pressure of 1.5
pounds to the square inch:
THE STEAMENGINE
EFFICIENCY OF CARNOT'S CYCLE FOR STEAMENGINES.
Initial Pressure
by the Gauge,
above the
Atmosphere.
Almcuplieric
PreiBUre.
iS bounds
ALaohilo.
15
0.053
o. i8t)
.10
60
IOO
15
o.o8,
0.12.1
0.157
0./H6
0.310
0.278
0.303
200
O.307
0.320
300
0.33
0.3I7
The column lor atmospheric pressure may be used as a
standard of comparison for noncondensing engines, and the
column for 1.5 pounds absolute may be used for condensing
engines.
It is interesting to consider the condition of the fluid in the
cylinder at the different points of the diagram for Garnet's
cycle. Thus if the fluid at the condition represented by b in
Fig. 31 is made up of x b part steam and i x fc part water, ihcn
from equation (118) the condition at the point c is given by
$
(137)
In like manner the condition of the mixture at the point d is
.... (138)
It is interesting to note that if x b is larger than onehalf, that
is, if there is more steam than water in the cylinder at b, then
the adiabatic expansion is accompanied by condensation. Again,
if x a is less than onehalf, then the adiabatic compression is also
accompanied by condensation. Very commonly it is assumed
that #6 is unity, so that there is dry saturated steam in the cylin
der at b\ and that x a is zero, so that there is water only in the
EFFICIENCY OF CAUNOT'S CYCLE
I'M
nag
ylinder at o; but there is no necessity for such assumptions,
nd they in no way alTcct the efficiency.
The temperatureentropy diagram (or Ounol's cycle for a
teamengine is shown by Fig. 32, on which arc drawn also the
ncs for entropy of the liquid
id, and the entropy of sfilur
tcd vapor be t os well ns the
ncs which represent the value
f #, the dryncss factor. This
iagram represents lo the eye
ic vaporization during the m
iotlicrmal expansion ab, the
artia! condensation during
ic adiabalic expansion bc t
ic isothermal condensation along cd, and the condensation
uring the adiabalic compression rffl. In the diagram thcwork
ig substance is shown as water at and as dry steam at b\
ic cITicicncy would clearly be the same for a cycle a' b' c' d' t
hich contains a varying mixture o( water and steam under aU
Midi I ions.
If the cylinder contains M pounds of steam and water, the
oat absorbed by the working substance during Isothermal
xpansion Is
Q t Mr, (x t  .v w ) ...... (139)
id the heat rejected during isothermal compression Is
<?,  Mr t (;v fl  xj) t
i that the heat changed inlo work during the cycle is
<?!<>, M(r, fa  x a )  r a fa  a? d )j
But from equations (137) and (138)
THE STEAMENGINE
and the expression for the heat changed into work becomes
This equation is deduced because it is convenient lor making
comparisons of various other volatile liquids and their vapors,
with steam, for use in heatengines. It is of course apparent
lhftl ^ g.  Q a ^ LTZa.
e "" Q, "" 7\ J
from equations (139) and (MO), a conclusion which is known
independently, and indeed is necessary in the development of
the theory of the adiabalic expansion of steam.
In the discussion thus far it has been assumed that the work
ing fluid is steam, or a mixture of steam and water. But a
mixture of any volatile liquid and its vapor will give similar
results, and the equations deduced can be applied directly. The
principal difference will be due to the properties of the vapor
considered, especially its specific pressures and specific volumes
for the temperatures of the source of heat and the refrigerator.
For example, the efficiency of Cavnol'a cycle for n fluid
working between the temperatures 160 C. and 40 C. is
160 + 273
0.277,
The properties of steam and of chloroform at these tempera
lures arc
Pressure, mm. mercury
Volume, cubic moircn .
Hcdt of vnporlxiuioii, r
Entropy of liquid, . .
Sioom. Chloroform.
10 C. 160 C. no' C. i(5o s C.
. 5.1. yi 1651..! 369.36 873I 3
1971 0.3035 Q..I.M9 00343
. 57 8 7 '1913 6 3i3 553
o. 136.) o. .1633 o. 03196 o. 1 1041
For simplicity, we may assume that one kilogram of the fluid
is used in the cylinder for Garnet's cycle, and that Xt is unity
while x a is zero, so that from equation (io)
7' T"
n _ /}_..  i  * n .
EFFICIENCY OF CAKNOT'S CYCLIC
= 137 calorics,
'33
 a x 0>
and for steam
(?,<?>
while for chloroform
(2,  Q, 5053 X 0,377 "' 14 calorics.
After acliabalic expansion the qualities of the fluid will be,
from equation (137), for stenm
* 
0>79S
and for chloroform
63.13 \ 100 I 273
The specific volumes nflcr mllaluilic cxpunmon nru,
qucntly, for steam
v e  Jf,tf, I <r 0,795 (19.74 o.ooj) I o.ooi 15.7,
and for chloroform
v, = ;v e , + o 0,969 (0.1(449 " 0000655) H 0.000655 "" 0.431
These values for v e junL rulculntcd arc Ihc volumes in the
cylinder at the extreme diBplucemcnl of the pinion, on the
assumption that one kilogram of Ihc working fluid is vuporlml
during isothermal cxpnnalon. A bcllcr idea of the relative
advantages of the two fluids will he nhinlnc'd hy fincJin^ the
heat changed into work for crich culilc metre of maximum pialon
displaccmcnt, or for a cylinder having the volume of one cubic
metre. This is obtained hy dividing Q t  Q r the heat chnngccl
into work for each kilogram by TV. Vor Bicam llic result is
(Qt  0>) 4  V * 137 + 15.7 M, 8.73,
and for chloroform it la
(Qt ~ Oa> * % *"" i.\ * 0.413 ^ 34 1
from which it appears thnt for the snmc volume chloroform
can produce more than three and a half limca AH much power.
134
THE STEAMENGINE
Even if we consider that the difference of pressure lor chloro.
form,
87342  3693 = 83649 mm.,
is nearly twice thai for steam, which has only
4651.4  54.9 ra 459 6 5 mm 
difference of pressure, tlic advantage appears to be in favor of
chloroform. If, however, the difference of pressures given for
chloroform is allowable also for steam, giving
8364.9 I 5(i.<> 8419.8 mm.
for the superior pressure, then the initial temperature for steam
becomes i84.9 C., an <l lnc efficiency becomes
184.9 ~ 4
1849 + 273
0.318,
instead of 0.277. On the whole, steam Is the more desirable
fluid, even if we do not consider the inflammable and poisonous
nature of chloroform. Similar calculations will show that on
the whole steam is at least as well adapted for use in heatengines
as any other saturated fluid; in practice, the cheapness and
incombustibility of steam indicate that it is the preferable fluid
for such uses.
Nonconducting Engine. Rankine Cycle, The conditions
required for alternate isothermal expansion and adlabatlc expan
sion cannot be fulfilled for Carnot's cycle with alcam any more
than they could be for air. The diagram for the cycle with
steam, however, is well adapted to production of power; the
contrary is the case with air, as has already been shown.
In practice steam from a boiler is admitted to the cylinder of
the steamengine during that part of the cycle which corre
sponds to the isothermal expansion of Carnot's cycle, thus trans
ferring the isothermal expansion to the boiler, where steam is
formed under constant pressure. Jn like manner the isothermal
compression is replaced by an exhaust at constant pressure,
during which steam may be condensed in a separate condenser,
Fie.
oled by cold water. The cylinder is commonly made of cast
m, and is always some kind of metal; there is consequently
nsiderablc interference due to the conductivity of the walls of
e cylinder, and the expansion and compression are never
liabutic. There is an advantage, however, in discussing first
L engine with a cylinder made of some nonconducting material,
though no such material proper for making cylinders is now
town.
The diagram representing the operations in a nonconducting
Under for a steamengine (sometimes called the Rankinc cycle)
n be represented by Fig. 33. ab represents
c admission of dry saturated steam from
c boiler; be is an adiabatic expansion to the
:haust pressure; cd represents the exhaust;
id da is an adiabatic compression to the
itial pressure. It is assumed that the small
3lumc, represented by a, between the piston and the head of
ic cylinder is filled with dry steam, and that the steam remains
amogcneous during exhaust so that the quality is the same at
as at c. These conditions are consistent and necessary,
nee the change of condition due to adiabatic expansion (or
>mpression) depends only on the initial condition and the
litial and final pressures; so that an adiabatic expansion from
to d would give the same quality at d as that found at c after
3iabalic expansion from b, and conversely adiabatic compres
on from d to a gives dry steam at a as rcquirefl.
The cycle represented by Fig. 33 differs most notably from
arnot's cycle (Fig. 32) in that ab represents admission of steam
rid cd represents exhaust of steam, as rms already been pointed
ut. It also differs in that the compression da gives dry steam
istcad of wet steam. The compression line da is therefore
:ccpcr than for Carnot's cycle, and the area of the figure is
ightly larger on this account. This curious fact docs not
idicatc that the cycle has a higher efficiency; on the contrary,
ic efficiency is less, and the cycle is irreversible.
If the pressure during admission (equal to the pressure in
136
THE 8TKAMKNGINE
Ihc boiler) is > and if ihc pressure during exhaust is p v then
the heat required to raise ihu water resulting from the conden
sation of the exhauststeam is
ft ~ fti
where g, is the heat of ihc liquid at the pressure p lt and ft is the
heal of the liquid al ihc pressure /> a . The heat of vaporization
at llic pressure p l is r,, so that Ihc heal required lo raise the feed
water from the temperature of the exhaust lo the temperature
in the boiler and evaporate il Into dry steam is
Q, < r, I ft  ft (141)
and this is the quantity of heat supplied to the cylinder per
pound of slcam.
The slcam exhausted from the cylinder has the quality x v
calculated by aid ol the equation
and the heal that must be withdrawn when it is condensed is
0, */, (142)
this is the heat rejected from the engine. The heat changed
inio work per pound of slcam in
n n wa I n a x r . . . . daO
ri u an r I q. i/ a .ijr, .... \it\ji
The cfTicicncy of the cycle is
0,
(H4)
If values are assigned to fa and p 9 and the proper numerical
calculations arc made, il will appear that the efficiency for a
nonconducting engine Is always less than the efficiency lor
Carnol's cycle between the corresponding temperatures.
U should be remarked thai the efficiency is nol affected by
Ihc clearance or space between the piston and the head of the
cylinder and the space in the Blcam passages of the cylinder,
provided that the clearance is filled with dry saturated steam as
indicated in Fig. 3* Thh is ^.Unl fn.m lh, fn,t llml i urn.
..presenting the clearance, or volume ul , UK .U. 'MM"'' "
Lion (M4) Or, again, we may .miUlcr tlml UK anim m
the cylinder at ihc beginning nf the stroke, (,u.y.n K lr vl
umc represented by , oxpamia during llu wlluUiu mnum
and is compressed again during I'umpnwinn. HI> Ihnl nr
operation is equivalent lo and couniL'rlmlnnr ihi oilirr. nnil
so docs not affect Ihc efficiency of I lie eydi'.
Use of (he TemperatureEntropy Dlngrnm. Tin Kiuikinr
cycle is drawn with a varying quiinlily nf HIHIIII in HIP iylimlir,
beginning at a, Fig. 33, wilh the uam nuiKlu in llu tlmntmr
and finishing at ft, wilh ihut wiiKlU pliw llu wriKlu ilmwn fn.m
llic boiler; consequently ft proper uinrnUiirr cjnr..jy
which represents ihc changes of oni ]>untl of ilu
stance, cannot be drawn.
We may, however, use ihc umpmituri' (nlntpy
(like Fig. 30, page ro,(, or the plfitc in tJir ent\ of ihr
solving problems connected wilh lhal iyclf inntcAd of niin(icir
(143) and (I,M)
In the first place we have by cquu T.
tion (96), page 83, "
C ,
q j all,
" te
and by equation (113), page 97, (
fat
J
for a volatile liquid. From ihc Inner
.
we have
all
therefore
From this last equation it la evident lhal the lien I of Ihr liquid 91
for water represented by ihc poinl a in Mg. 3.1, ii nimurnl by
i 3 8
THE HTEAMENGINE
the area Otnao. In like manner the heat of the liquid q l cor
responding to the point d t is represented by tlie area Owrfn.
Again, the heat added during the vaporization represented by
*
ab, is r lt while the increase of entropy is ^ . Therefore the heat
* i
pf vaporisation can be represented by the area oabp. In like
manner the partial vaporization X 3 r 3 can be represented by the
area ndcp. Therefore the heat changed into work for the cycle
in Fig. 33, which has been represented by
'i + ffi  (Vs + ? 3 )>
tan equally well be represented by the area
abed == area Oinao + area oabp
(area Omdn  area ndop}.
It will consequently be sufficient to measure the area abed
by any means, for example, by aid of a planimcler, in order to
determine the heat changed into work during the operation of the
nonconducting engine working on the Rankine cycle. If the plan
imetcr determines the area in square inches, the scale of the draw
ing for Fig. 34 should be one inch per degree, and one inch per
unit of entropy, or, if other and more convenient scales are to be
used, proper reductions must be made to allow for those scales.
IL must be firmly fixed in mind that the use of a diagram like
Fig. 34 is justified because it has been proved that the area
abed (drawn to the proper scale) is numerically equal to Ihc
heat changed into work as computed by equation (143), and
that the diagram does not represent the operations of the cycle,
This is entirely different from the case of the diagram, Fig. 33,
which correctly represents the operations of Carnol's cycle.
The illustration of the use of the temperatureentropy diagram
for this purpose is chosen for convenience with dry saturated
steam at b, Fig. 34. It is evident that it could (with equal
propriety) be applied to an engine supplied with moist steam if
r l is replaced by #,*," in equation (143) and if b is located at the
proper place between a and b.
'The actual measurement of areas by 'a planimeter is seldom
if ever applied, but the diagram is used effectively in the dis
cussion of certain problems of nonrcvcrsible flow of steam in
nozzles and turbines, with allowance for friction.
It further suggests an approximation that may sometimes be
useful, especially if the change of pressure (and temperature)^
small. Thus the area abed may be approximately rcprescntod
by the expression
I ' 1
so that in place of equation (143) we may have
_ j _. .. i
(us)
for (he heat changed into work by Rankinc's cycle.
This approximation depends on treating <ib us a straight line,
ami this assumption is more correct as the difference of temper
ature is less; that is for those cases in which equation (143)
deals with the difference of quantities of about the. same magni
tude, and may consequently be affected by a large relative error.
TemperatureEntropy Table. The lempcralurccntropy table
which has been described on page 106 was computed for solu
tion of problems of this nature, more especially in turbine
design, and enables us to determine the heal changed into work
directly with sufficient accuracy for engineering work, without
interpolation; it also gives the quality x and the specific volume.
Incomplete Cycle. The cycle for a nonconducting engine
may be incomplete because the expansion is not carried far
enough to reduce the pressure to that
of the backpressure line, as is shown
in Fig. 35. Such an incomplete cycle
has less efficiency than a complete cycle,
but in practice the advantage of using
a smaller cylinder and of reducing fric
tion is sufficient compensation for the 10 ' 3S '
small loss of efficiency due to a moderate drop at the end of
the stroke, as shown in Fig. 35.
THE STKAMKNGINE
The discussion of the incomplete cycle is simplified by
ing that there is no clearance and no compression as is in
by Fig. 35. It will he shown later tlmt the efficiency will
same with a clearance, provided the compression is comp]
The most ready way of finding the efficiency for this
to determine Ihc work of the cycle. Thus ihc work.
admission is /
where w t is the increase of volume due to vaporization of a
of steam, and a is the specific volume of water. The work
expansion is
E h /$, (p, I 7,  x c p e  &),
where </, and p, arc the heat of the liquid and the hcatccf!
of Ihc internal work during vaporization at the press
while q and p e arc corresponding quantities for the prcssu
x e is to be calculated by the equation
T
The work clone by the piston on the steam during cxl
Pi (AY", I <r).
The total work of the cycle is obtained by adding t>
during admission and expansion and subtracting th
during exhaust, giving
The last term is small, and may be neglected. Adcll
subtracting Ap&u, and multiplying by A, .we get for It
equivalent of the work of the cycle
 Q,
q l
which is equal to the difference hclwccn the heal supplied tint!
the hctit rejected as indicated, The hcul supplied is
as was deduced for the complete cycle; the cost of making the
steam remains the .same, whether or not H i.i uncd tlVicirnlly.
Finally, the efficiency of the cycle is
=
r _
I
If ^ fl is made equal to />j in Iho prtrerlinK t'fUiiliM, it will
reduced to the same form as uijimlinn (i..()i IHTKUM* lln*
sion in such case becomes complete.
SteamConsumption of Nonconducting Engine. A
power is 33000 footpounds per mmuie or 60 X .13000 fimi
per hour. But the hu changed inlo work ptr pound <if
by a nonconducting engine with complete expansion h, liy
equation (143),
'i + ffi " ( h  V'
so that the steam required per horsepower per hour is
778 (r, Hry,  j, v,)
j the steam )>cr horacpowcr per hour for nn
with incomplete expansion, hy aid of expression (1,16),
_ _ ^P_J*<_ 13995L _
778 (/, i 4Ai  r ^  "^^w; r v,  ST) '
The value of .r a or .v, is to he calculated hy tho Rcncral equtttton
The denominator in cither of the above cxprnufonn fur the
steam per horsepower per hour in of course the work done im
pound of steam, and the parenthesis without the
HE STEAMENGINE
equivalent 778 is cqiml to Q l  Q y If then we multiply and
divide by
that is, by the heat brought from the boiler by one pound of
steam, we shall Imvc in either case for the steam consumption
in pounds per hour
60 X 33000 X 0. 60 X 33000
.. ... ... .M.U^.. i .1 TBI i* n3 ' ............. " v ..i *
(M9)
where
Q.Q,
is the efficiency for the cycle.
Actual SteamEngine. The indicatordiagram from nn aclual
steamengine differs from the cycle for a nonconducting engine
in two ways; (here are losses of pressure between the boiler and
the cylinder and between ihc cylinder and the condenser, due
to ihc resistance to Ihe (low of steam through pipes, valves, and
passages; and there is considerable interference of Ihc mcial of
Ihc cylinder with the action of Ihc steam in the cylinder. The
losses of pressure may be minimized for a slowmoving engine
by making the valves and passages direct and large. The
interference of the walls of the cylinder cannot be prevented,
but may be ameliorated by using superheated steam or by sLcnm
jackcting.
When steam enters the cylinder of an engine, some of it is
condensed on the walls which were cooled by contixct whh
exhauststeam, thereby healing them up nearly lo the tempera
ture of the steam, After cutoff the pressure of the steam is
reduced by expansion and some of the water on the walls of
the cylinder vaporix.es. At release the pressure falls rapidly
to the backpressure, and the water remaining on the walls is
nearly if not all vaporized. It is at once evident that so much
of the heal as remains in the walls until release and is thrown
out during exhaust is a direct loss; and again, the hunt which
is restored during expansion docs work with less efficiency,
ccause it 19 reevaporated at less than the temperature in the
oiler or in the cylinder during admission. A complete state
lent of the action of the. walls of the cylinder of an engine,
nth quantitative results from tests on engines, was first given
>y Him, His analysis of engine tests, showing the interchanges
i heat between the walls of the cylinder and the steam, will be
fiven later. It is sufficient to know now that a failure to con
ider the action of the walls of the cylinder leads to gross errors,
,nd thai an attempt to base the design of an engine on the theory
f a steamengine with a nonconducting cylinder can lead only
o confusion and disappointment.
The most apparent effect of the influence of the walls of the
cylinder on the indicatordiagram is to change the expansion
im! the compression lines; the former exhibits this change moat
Nearly. In the first place the fluid in the cylinder at cutoff
:onsists of from twenty to fifty per cent hot water, which is found
nainly adhering to the walls of the cylinder. Even if there
,vcrc no action of (he walls during expansion the curve would be"
nuch less steep than the adiabatic line for dry saturated steam.
But the rctjvaporalion during expansion still further changes the
:urvc, so that it is usually less steep than the rectangular
iypcrbola.
It may be mentioned that the fluctuations of temperature
in the walls of a steamengine cylinder caused by the conden
sation and rce'vaporation of water do not extend far from the sur
face, but that at a very moderate depth the temperature remains
constant so long as the engine runs under constant conditions.
The performance of EV steamengine is commonly stated in
pounds of steam per horsepower per hour. For example, a
small Corliss engine, developing 16.35 horsepower when
running at 61,5 revolutions per minute under 77.4 pounds
boilerpressure, used 548 pounds of steam in an hour. The
steam consumption was
548 4 16.35 = 335
pounds per horsepower, per hour.
144
THE STEAMKNGINB
This method was considered sufficient in the curlier history
of the steamengine, and mny now be used for comparing simple
condensing or noncondensing engines which use saturated
steam ami do not 1m ve u steiimjaeket, for the total heat of steam,
and consequently the cost of making steam from water ill a given
temperature increases but slowly with the pressure.
The performance of steamengines may bu more exactly
slated in British thermal units per horsepower per minute.
This method, or some method equivalent to it, is essential in
making comparisons lo discover the advantages of superheat
ing, steamjacketing, and compounding. For example, the
engine just referred to used steam cunluiumg two per cent of
moisture, so that .\\ at the steampressure of 771 pounds was
0.98. The barometer showed the pressure of the atmosphere
to be 14.7 pounds, and ihis was tilso the buckpressure during
exhaust. If it be assumed thai the feedwater was or could
be heated lo the corresponding temperature of araF,, the
' heat required lo evaporate U against 77,4 pounds above the
atmosphere or 0,2,1 pounds absolute was
^ ,_ ?i ~ ^ 0.98 X 888.0 H ao.3.1  180.3 982.0 n.T.u.
The thermal unlta per horsepower per minute were
6o
Efficiency of the Actual Engine. When the thermal units
per horsepower per minute are known or can be readily cal
culated, the efficiency of the actual steamengine may be found by
the following method : A horsepower corresponds Vo the develop
ment of 33000 foolpounds per minute, which nrc equivalent to
33000 * 778  42.42
thermal unite. This quantity is proportional lo Q {  Q v and
ihc thermal unils consumed per horacpower per minute, are
proportional .o Q,, so that the efficiency is
~Q { *** D.T.U. per II.P. per mln. '
For example, the Corliss engine mentioned above luul n
efficiency of
42.42 * 5.18 0.077.
This same method may evidently he applied to any heat
engine for which the consumption in thermal untU per horar
power per hour can be applied.
From the tests reported in Chapter XIJ1 il upprnrs llml ihr
engine in the laboratory of the Massachusetts Institute of T It
nology on one occasion used 13.73 pound* of Misun prr hurst
power per hour, of which 10.86 pounds were supplied In ihr
cylinders and 2.87 pounds were condensed in tlviim jiirkctn im ihr
cylinders. The steam in the supplypipi* luul liu prewar r itf
157.7 pounds absolute, and contained i.a per crnl of m<ii*>itirr.
The heat supplied to the cylinders per minute in tin hiram
admitted was
10.86 (x l r 1 I <7 t  (7,) t Go
10.86 (0.988 X 858.6 I
191 JI.T.U.;
j, being the heat of the liquid nl the lempernlure of the
pressure of 4.5 pounds absolute.
The stctim condensed in the HlcnmjnekHfi wn wlihclrnwn
at the temperature due to the pressure find could Jmvc \wcn
returned to the boiler at that temperature; raniiecUrnily ihu
heal required to vaporize it was r v and the hcnt furnkhcd by
the steam in the jackets waa
2.87 X o.g8 X 858.6 t oo ,(o/ n.T.l/.
The heat consumed by the engine waa
191  (o.6 M a p n.T.u.
per horsepower per minute, and the efficiency WAS
e ( a.,ja * 333 0,183.
146
THE STEAMENGINE
The efficiency of Carnot's cycle for the range of temperatures
corresponding to 157.7 anc ^ 45 pounds absolute, namely, 821.^
and 6i7.2 absolute, is
'/',  7 ' a 821.7 ~ 617.2
821.7
0.248.
The efficiency for a nonconducting engine with complete
expansion, calculated by equation (1*14), is for Ibis case
0.821 X 1004.1
* I
858.6 13339 ~ 120 
where *a is calculated by the equation
0.227
'
(
1004,1 \82i.y
0,2282
) * 0.821.
/
During the lest in question Ihe terminal pressure at luccntl of
ihe cxjMinslon in Vhc lowpressure cylinder was 6 pounds tvbso*
hite, which gives
.,. 0,5189  0.2475)  0.832,
 /
995.8 \82i7
and the efficiency by equation (148) was
jn^ l _ *>?* "I* +? ~ A (P* " ^^j
r, H ff,  q,
0.812 XooS8138.0 I 126.01 \n (64.5)0.833x63
uj v __ . ....... i *r. ....... ^.^W . . \t .....  * ..... ' " l* ""
3339 I2 
0.222.
The real criterion of ihe perfection of the nclion of an engine
is the ratio of ils actual efficiency to that of a perfect engine.
It for the perfect engine we choose Carnot'a cycle the ratio is
0.736.
0,2485
In
EFFICIENCY OF THE ACTUAL ENGINE
But jf we take for our standard an engine with a cylinder of non
conducting material the ratio for complete expansion is
e_
a"
0.183
0.227
For incomplete expansion the ratio is
e 0,18
= 0.807.
0.222
= 0.824.
To complete the comparison it is interesting to calculate
the steamconsumption for a nonconducting steamengine by
equation (149), both for complete and for incomplete expan
sion. For complete expansion we luivc
_6o_X 33000
778 X 0.227 (858.6 + 3339 126.0)
and for incomplete expansion
60 X^ 33000
= 10.5 pounds,
778 X 0.222 (858.6 + 3339  126.0)
per horsepower per hour.
But if these steamconsumptions arc compared with the
actual steamconsumption of 13.73 pounds per horsepower
per hour, the ratios are
10.5 4 13.73 =0.766 and 10.7 T 13.73 = 0.783,
which are very different from the ratios of the efficiencies. The
discrepancy is due to the fact that more than a fourth of the
steam used by (he actual engine is condensed in the jackets
and returned at full steam temperature to the boiler, while the
nonconducting engine has no jacket, but is assumed to use all
the steam in the cylinder.
From this discussion it appears that there is not a wide margin
for improvement of a welldesigned engine running under favor
able conditions. Improved economy must be sought cither by
increasing the range of temperatures (raising the steampressure
= 10.7 pounds
148
THK STKAMENUINK
or improving Ihc vncuum), or by choosing .some oilier form of
hciilmolor, such us the gasengine.
Attention should be called to the {act that the real criterion ol
Ihc economy of u heatengine is the cosl of producing power by
that engine. The cost may be expressed in thermal uniis per
horsepower per minute, in pounds of steam per horsepower
per hour, in coal per horsepower per hour, or directly in money.
The expression in thermal imils is the most exact, and the best
lor comparing engines of the same eta, such as steamengines.
If the same fuel can be used for different engines, such as slcam
and gasengines, then the cost in pounds of fuel per horsepower
per hour may be most instructive. IHit in any ease the money
cosl must be the final criierion. The reason why it is not more
frequently stated in reports of tests is lhal it is in many cases
somewhat difficult to determine, and because il is alTcclctl by
market prices which arc subject to change.
Al the present time a pressure as high as 150 pounds above
the almosphcrc is used where good economy is expected, It
appears from the luble on page 132, showing the efficiency of
Curnot's cycle for various pressures, that the gain in economy
by increasing sicamprcasurc above 150 pounds is alow. The
same thing is shown even more clearly by the following Iftblc:
KPFKCT OK KAIHINO STKAMPRKRslmK.
I'roliHhla l'erlorinnce,
Itolltr
lireiiura hy
Kffl clenoy,
Cut not 'i Cjtlt,
H.'l'.U. [>
KPIclency.
II. P. per
Ml mils.
150
0.302
0,37'J
156
300
0.330
0.388
M7
JOO
0347
0.306
US
ll.T.U.par
If. P. PM
MlnuU.
160
Slm r
H.P.pif
hour.
io.S
g.fi
In the calculations for this table the steam la supposed to be
dry as it enters the cylinder of the engine, and the back pressure
is supposed to be 1.5 pounds absolute, while the expansion for
the nonconducting engine is assumed to be complete, The
CONUKNSKKS '(9
heatconsumption of the nonconducting engine is obtained l.y
dividing 4212 by the efficiency; thus for 150 pounds
,}2.*2 r 0.272  ' 156.
The heatconsumption of the actual engine I'K assurmd ( be
onefourth greater than that of the noncondiic'ting engine. The
steamconsumption is calculated by the reversal of the method
of calculating the thermal units per howpower per minute
from tlic steam per horsepower j)er hour, and for uimplMiy
all of the steam is assumed to be supplied u> the cylinder. Mill
an engine which shall show such an economy for n given prrwuirr
as that set down in the table must be a triple "f n <imdniple
engine and must be thoroughly Hlcamjackelcd. The adinil
steamconsumption is certain to be a little larger limn ilmi &\vrn
in the table, as steam condensed in a alem jaekrt yirlilh lr
heat than that passed through the cylinder,
It is very doubtful if tlic gain in fluid efficiency due to im rwifnfc
steampressure above 150 or 200 pounds Is not affect by (tie grratrr
friction and the difficulty of maintaining the engine. Miglirr
pressures than 200 pounds arc used only where great power numl
be developed with small weight and apace, as in torpedo bouts*.
Condensers. Two forma of condenuurn re um*d lo rcmdrnM*
ihc steam from a steamengine, known n jetcondensera nmt
surface condensers. The former fire commonly nun I f(tr 1/tnd
engines; they consist of a receptacle having n volume iquiil i
onefourth or onethird of that of the cylinder or cylinders llml
exhaust into it, into which the ateiun passca from the rxlmiml pljK?
and where it meets and la condensed by n spniy of cold wntrr.
If it be assumed that the ateum in the exhnimt pipe In dry
and saturated and that it is condensed from the [irrwurr /> nd
cooled to the temperature / then (he heat yielded per pmimt
of steam is /./
ii ~ i/i,
where H k the total heal of steam nl the pressure /, nnd </ t i^ (he
heat of the liquid ftl the temperature t k , The heal ricquiml by
each pound of condensing or injection water is
150 THE STEAMENGINE
where <j ( is the heal of the liquid at the temperature /, of tl\e
injectionwater as it enters the condenser. Each pound of steam
will require
G* "I"" / / * / \
* r^r~ Oso)
pounds of injectionwater.
For example, steam at 4 pounds absolute lias for Ihe total
heat 1128.6. If the injectionwater enters wilh a temperature
of 60 F., and leaves wilh a temperature of 120 K., then each
pound of steam will require
1 I ?  g t __ i ij8.6 88 j>
o t fa 88.0 28.12
'73
pounds of injectionwater. This calculation is used only lo
aid in dclcrmining the size of the pipes and passages leading
water to and from the condenser, and the dimensions of the air
pump. Anything like refinement is useless and impossible,
as conditions are seldom well known and arc liable lo vary.
From 20 to 30 times the weight of steam used by the engine is
commonly taken for this purpose.
The jetcondensers cannot be used at sea when the boiler
pressure exceeds 40 pounds by the gauge; all modern steamers
are consequently supplied wilh surfacecondensers which consist
of receptacles, which arc commonly rectangular in shape, into
which steam is exhausted, and where it is condensed on horlxonial
brass tubes through which cold seawater is circulated. The
condensed water is drained out through the airpump and Is
returned to the boiler. Thus the feedwater is kept free from
salt and other mineral matter that would be pumped into the
boiler if a jetcondenser were used, and if the feedwater were
drawn from the mingled water and condensed steam from
such a condenser. Much trouble is, however, experienced
from oil used to lubricate the cylinders of the engine, ns it is
likely to be pumped into the boilers with the feedwater, even
though attempts arc made to strain or filler it from the water.
The water withdrawn from a surfacecondenser is likely to
AIRPUMP I5t
have a different temperature from the cooling water when it
[caves the condenser. If its temperature is *,, then we have
instead of equation (15)
c J. n n
C 1 ' ' 7 '/i / \
* ~ J JJ usu
'/*  '/(
for the cooling water per pouiul of steam. The difference is
really immaterial, as it makes little difference in the actual value
3f G for any disc.
Cooling Surface. Kxpcrimenls on the quaintly of cooling
surface required by n surfacecondenser lire few and unsatis
factory, and ft comparison (if condensers of marine engines
shows ft wide diversity of pruclice. Sciilon says that with an
initial temperature of 60, and with 120 for the feedwater, a
:ondcnsalion of 13 pounds of steam per square fool per hour
is considered fair work. A new condenser in good condition
nay condense much more steam per square foot per hour than
,his t but allowance must ha made for fouling and clogging,
specially for vessels tlml mukc long voyages.
Scaton also gives the following table of square feel of cooling
mrfacc per indicated horsepower:
AbiuUilo Termlnul PrtMiirt,
I'OUTUU jiar Ki\\itte Inch.
l f l
nr I. II. I'.
30
1C
134
10
1.50
i tii
8
I . 77
6
r . 10
For ships stationed hi the tropics, allow 20 per cent more;
or ships which occasionally visit the tropics, ullow 10 per cent
(lore; for ships constantly in a cold climate, 10 per cent less
fiay be allowed.
AirPump. The vacuum in ihc condenser is maintained
y the airpump, which pumps out the air which finch its way
here by leakage or otherwise; the condensing water carries
J52
THE STEAMENGINE
a considerable volume of air into the condenser, and the s
of the airpump can be based roughly on the average percent*
of air held in solution in water; the air which finds its way i
a surfacecondenser enters mainly by leakage around the It
pressure pistonrod and elsewhere.
It is customary to base the si/.c of the airpump on the (
placement of the lowpressure piston (or pistons); for exam]
the capacity of a singleacting vertical airpump for a mcrch
steamer, with tripleexpansion engines, may be about ^V of
capacity of the lowpressure cylinder.
With the introduction of steamturbines, the importance
a good vacuum becomes more marked, and the duly of the :
pump, which commonly removes air and also the water of c
densaiion from the condenser, is divided between a dry
pump, which removes air from the condenser, and a wa
pump, which removes the water of condensation. Airpur
arc treated more at length on page 374, in connection with
discussion of compressed air.
Designing Engines. The only question that is prop<
discussed here is the probable form of the indlcatordiagn
which gives immediately (he method of finding the mean cflfcc
pressure, and, consequently, the sixe of the cylinder of the eng
The most reliable way of finding the expected mean effcc
pressure in the design of a new engine is (o measure n Incllca
diagram from an engine of the same or similar type and s
and working under the same conditions.
If (i new engine varies
much from the type on w]
the design is based thai
diagram from the latter cut
be used directly, the follov
method may be used to n.
for moderate changes of Ix
pressure or expansion.
type diagram cither on the original card or redrawn to a 1
scale, may have added to it the axis of ;<cro pressure and
DESIGNING ENGINES
153
ime OV and OP (Fig. 35a). The former is laid off parallel to
he atmospheric line and at a distance to represent the pressure
if the atmosphere, using the scale for measuring pressure on the
liagram. The latter is drawn vertical and at a distance from aj
vhich shall bear the same ratio to the length of the diagram as
he clearance space of the cylinder has to the pistondisplacc
ncnt. The boilerpressure line m;iy be drawn as shown. The
.bsolute pressure may now be measured from OV with the proper
>calc and volume from OP with any convenient scale.
Choosing points b and c at the beginning and end of e.xpanr
ion determine the exponent for an exponential equation by the
nethod on page 66; do the same for the compression curve ef. .
Draw a diagram like Fig. 35 for the new engine, making the
proper allowance for change of boiler pressure or point of cut
)ff, using the probable clearance for determining the position
)f the line of. Allowing for loss of pressure from the boiler to
:he cylinder, and for wiredrawing or loss of pressure in the
calves and passages, locate the points a and b. The back
pressure line de can be drawn from an estimate of the probable
vacuum. The volumes at c and e are determined by the action
)f the valve gear. By aid of the proper exponential equations
ocate a few points on be and ef and sketch in those curves.
Finish the diagram by hand by comparison with the type dia
gram. If necessary draw two such diagrams for the head and
:rank ends of the cylinder. The mean effective pressure can
now be determined by aid of the planimctcr and used in the
:lcsign of the new engine.
Usually the refinements of the method just detailed arc
avoided, and an allowance is made for them in the lump by a
practical factor. The following approximations arc made:
(i) the pressure in the cylinder during admission is assumed
to be the boiler pressure, and during the exhaust the vacuum
in the condenser; (2) the release is taken to be at the end of
the stroke:; (3) both expansion and compression lines are treated
as hyperbola;. The mean effective pressure is then readily
computed as indicated in the following example.
154
THE STEAMENGINE
Problem. Required the dimensions of the cylinder of an
engine to give 200 horsepower; revolutions 100; gauge pressure
So pounds; vacuum 28 inches; cutoff at stroke; release at end
of stroke; compression at T ' ff stroke; clearance 5 per cent.
The absolute boilerpressure is 94.7 pounds, and the absolute
pressure corresponding to 28 inches of mercury is nearly one
pound. It is convenient to lake the piston displacement as
one cubic foot and the stroke as one foot for the purpose of
determining the mean effective pressure. The volume of cut
off is consequently } cubic foot due to the motion of the piston
plus iV cubic foot due to the clearance or 0.35 cubic foot; the
volume at release is 1.05 cubic foot, and at compression is 0.15
cubic foot.
The work during admission (corresponding to ab, Fig. 35a) is
94.7 X 144 Xo35 footpound,
and during expansion is
# ! v 1 log e * = 94.7 X 144 X 0.35 log.
I.Q.S
The work during exhaust done by the piston in expelling the
steam is
r X 144 X (r  0.15),
and the work during compression is
r X 144 X 0.15
0.05
The mean effective pressure in pounds per square inch is
obtained by adding the first two works and subtracting the last
two and then dividing by 144, so that
M.E.P. = 94.7 Xo.25 + 947 Xo.35 log,
V *J
 i X 0.85  i X 0.15 log,  59.1
005
The probable mean effective pressure may be taken as
of this computed pressure, or 53.2 pounds per square inch,
DESIGNING ENGINES
155
Given the diameter and stroke of an engine together with the
mean effective pressure, and revolutions, we may find the horse
power by the formula
I.H.P. 
where p is the mc;tn effective pressure, 1 is the stroke in feet, a is
the area of the circle for the given diameter in square inches, and
ti is the number of revolutions per minute. For our case we
may assume that the .stroke is twice the diameter, whence
2(t
2OO =
2 X 532 X X X loo
12 4
33000
.'. d = 16.8 inches, $ 33.6 inches.
In practice the diamctcr would probably be made i6 inches
and the stroke 33^ inches.
CHAPTER IX.
COMPOUND ENGINES.
A. COMPOUND engine has commonly two cylinders, one of
which is three or four times as large as the other. Steam from
a boiler is admitted to the small cylinder, and after doing work in
that cylinder it is transferred to the large cylinder, from which
it is exhausted, after doing work again, into a condenser or
against the pressure of the atmosphere. If we assume that the
steam from the small cylinder is exhausted into a large receiver,
the backpressure in that cylinder and the pressure during the
admission to the large cylinder will be uniform. If, further, wo
assume that there is no clearance in cither cylinder, that the
backpressure in the small cylinder and the forward pressure in
the large cylinder arc the same, and that the expansion in the
small cylinder reduces the pressure down to the backpressure in
that cylinder, the diagram for the small cylinder will be ABCD,
FID. 36.
Via. 37
Fig. 36, and for the large cylinder DCFG. The volume in the
large cylinder at cutoff is equal to the total volume of the small
cylinder, since the large cylinder takes from the receiver the samo
weight of steam that is exhausted by the small cylinder, and, in
this case, at the same pressure.
The case just discussed is one extreme. The other extreme
occurs when the small cylinder exhausts directly into the largo
156
COMPOUND ENGINES
157
cylinder without an intermediate receiver. In such engines the
pistons must begin and end their strokes together. They may
both acC on the beam of a beam engine, or they may act on one
crank or on two cranks opposite each other.
For such an engine, ABCD, Fig. 37, is the diagram for the
'small cylinder. The steam line and expansion line AB and BC
are like those of a simple engine. When the piston of the small
cylinder begins the return stroke, communication is opened with
the large cylinder, and the steam passes from one to the other,
and expands to the amount of the difference of the volume, it
being assumed that the communication remains open to the end
of the stroke. The backpressure line CD for the small cylinder,
and the admission Line HI for the large cylinder, gradually fall
on account of this expansion. The diagram for the large cylin
der is HJKG, which is turned toward the left for convenience.
To combine the two diagrams, draw the line abed, parallel to
V'OV, and from b lay off bd equal to ca; then d is one point of the
expansion curve of the combined diagram. The point C corre
sponds with //, and E, corresponding with /, is as far to the right
as / is to the left.
For a nonconducting cylinder, the combined diagram for a
compound engine, whether with or without a receiver, is the same
as that for a simple engine which has a cylinder the same sine
as the large cylinder of the compound engine, and which takes
at each stroke the same volume of steam as the small cylinder,
and at the same pressure. The only advantage gained by the
addition of the small cylinder to such an engine is a more even
distribution of work during the stroke, and a smaller initial stress
on the crankpin.
Compound engines may be divided into two classes those
with a receiver and those without a receiver; the latter arc called
"Woolf engines " on the continent of Europe. Engines without
a receive^ must have the pistons begin and end their strokes at
the same time; they may act on the same crank or on cranks 180
apart. The pistons of a receiver compound engine may make
strokes in any order. A form of receiver compound engine with
158
COMPOUND ENGINES
two cylinders, commonly used in marine work, has the cranks i
90 to give handincss and certainly of aclion. Large marh
engines have been made whh one small cylinder and two larj
or lowpressure cylinders, both of which draw sleam from tl
receiver and exhaust to the condenser. Such engines usual
have the cranks al 120, though other arrangements have bc<
made.
Nearly all compound engines have a receiver, or a spa
between the cylinders corresponding to one, and in no case
the receiver of sufficient size to entirely prevent fluctuations
pressure. In the later marine work the receiver has been ma<
small, and frequently the steamchests and connecting pipes ha
been allowed to fulfil that function. This contraction of si
involves greater fluctuations of pressure, but for oilier reasons
appears to be favorable to economy.
Under proper conditions there is a gain from using a cot
pound engine inslcad of a simple engine, which may amoimt
ten per cent or more. This gain is lo be attributed to the divisi
of Ihe change of temperature from that of the steam at admissi
lo that of exhaust inlo two stages, so that there is less flucli
lion of temperature in a cylinder and consequently less inl<
change of heat between the sleam and the walls of the cylind
Compound Engine without Receiver. The indicalord
grams from a compound engine without a receiver arc rep:
scnlcd by Fig. 38. The sleam line and cxpa
sion line of the small cylinder, AB and J?C',
not differ from those of a simple engine, At
the exhaust opens, and the steam sudclcr
expands inlo the space between the cylindi
and the clearance of the large cylinder, and f
pressure falls from C to D. During the rctv
stroke the volume in ihc large cylinder increases more tuple
than thai of the small cylinder decreases, so that the backprc
urc line DE gradually falls, as docs also the admission line \
of the large cylinder, the difference between these two lines be:
due to the resistance to the flow of sleam from one to the otli
Ftii. 38.
COMPOUND ENGINE WITH RECEIVER
159
At E the communication between the two cylinders is closed by
the cutoff of the large cylinder; the steam is then compressed
in the small cylinder and the space between the two cylinders
to F t at which the exhaust of the small cylinder closes; and the
remainder of the diagram FGA is like that of a simple engine.
From /, the point of cutoff of the large cylinder, the remainder
of the diagram IKLMNH is like the same part of the diagram
of a simple engine.
The difference between the lines ED and HI and the " drop "
CD at (he end of the stroke of the small piston indicate waste
or losses of efficiency. The compression EFG and the accom
panying independent expansion IK in the large cylinder show a
loss of power when compared with a diagram like Fig. 37 for an
engine which has no clearance or intermediate space; but com
pression is required to fill waste spaces with steam. The com
pression EP is required to reduce the drop CD, and the compres
sion FG fills the clearance in anticipation of the next supply from
the boiler. Neither compression
is complete in Fig. 38.
Diagrams from a pumping en
gine at Lawrence, Massachusetts,
are shown by Fig. 39. The
rounding of corners due to the
indicator makes it difficult to de
termine the location of points like
Z>, E, P t and / on Fig. 38. The
lowpressure diagram is taken
with a weak spring, and so has an
exaggerated height.
Compound Engine with Receiver. It has already been
pointed out that some receiver space is required if the cranks
of a compound engine are to be placed at right angles. When
the receiver space is small, as on most marine engines, the fluc
tuations of pressure in the receiver are very notable. This is
exhibited by the diagrams in Fig. 40, which were taken from a
yacht engine. An intelligent conception of the causes and meaning
Fie. 39.
FIG. 40.
COMPOUND ENGINES
of such fluctuations can be best obtained by constructing ideal
diagrams for special cases, as explained on page 164.
Triple and Quadruple Expansion
Engines. The same influences which
introduced Ihc compound engines, when
the common steam pressure changed
from forty to eighty pounds to the
square inch, have brought in the succes
sive expansion through three cylinders
(the highpressure, intermediate, and
lowpressure cylinders) now that 150 to 200 pounds pressure arc
employed. Just as three or more cylinders arc combined in
various ways for compound engines, so four, five, or six cylinders
have been arranged in various manners for tripleexpansion
engines; the customary arrangement has three cylinders with the
cranks at r8o.
Quadruple engines with four successive expansions have been
employed with highpressure steam, but with the advisable
pressures for present use the extra complication and friction
make it a doubtful expedient.
Total Expansion. In Figs. 36 and 37, representing the dia
grams for compound engines without clearance and without
drop between the cylinders, the total expansion is the ratio of
the volumes at E and at B\ that is, of the lowpressure piston dis
placement to the displacement developed by the highpressure
piston at cutoff. The same ratio ia called the total or equiva
lent expansion for any compound engine, though it may have
both clearance and drop. Such a conventional total expansion
is commonly given for compound and multipleexpansion engines,
and is a convenience because it is roughly equal to the ratio of
the initial and terminal pressures; that is, of the pressure at
cutoff in the highpressure cylinder and at release in the low
pressure cylinder. It has no real significance, and is not equiva
lent to the expansion in the cylinder of a simple engine, by which
we mean the ratio of the volume at release to that at cutoil, tak
ing account of clearance. And further, since the clearance of
LOWPRESSURE CUTOFF
the high and the lowpressure cylinders are different there can
be no real equivalent expansion.
If the ratio of the cylinders is R and the cutoff of the high
pressure cylinder is at  of the stroke, then the total expansion
is represented by
and
 = R
e
This last equation is useful in determining approximately the
cutoff of the highpressure cylinder.
For example, if the initial pressure is 100 pounds absolute and
.the terminal pressure is to be to pounds absolute, then the total
expansions will be about 10. If the ratio of the cylinders is
3i, ihcn the highpressure cutoff will be about
 = 34 * 10 0.35
of the stroke.
Lowpressure Cutoff. The cutoff of the lowpressure
cylinders in Figs. 36 and 37 is controlled by the ratio of the
cylinders, since the volumes in the lowpressure cylinder at cut
off is in each case made equal to the highpressure piston dis
placement; this is done to avoid a drop. If the cutoff were
lengthened there would be a loss of pressure or drop at the end
of the stroke of the highpressure
piston, as is shown by Fig. 41,
for an engine with a large receiver
and no clearance. Such a drop will
have some effect on the character of
the expansion line C"F of the low
pressure cylinder, both for a noncon
ducting and ^for the actual engine
with or without a clearance. Its
principal effect will, however, be on
the distribution of, work between the cylinders; for it is evident
that if the cutoff of the lowpressure cylinder is shortened the
FIG. 41.
1 62
COMPOUND KNGINKS
pressure at C" will be increased because the same weight of steam
is tnkcn in a smaller volume, The backpressure DC' of the
highpressure cylinder will bo raised and the work will be
diminished; while ihe forward pressure; DC" of the low
pressure cylinder will be raised, increasing ihe work in ihat
cylinder.
Ratio of Cylinders. In designing compound engines, more
especially for marine work, it is deemed important for the smooth
aclion ol the engine that the total work ahull be evenly distributed
upon the several cranks of the engines, and that ihe maximum
pressure on each of the cranks shall be the .same, and shall not
be excessive. In ease two or more pistons art on one crank,
the total work and the resultant pressure on those pistons are
to be considered; but more commonly each piston acts on a
separate crank, and then the work and pressure on the several
pistons arc to be considered.
In practice both the ratio of the cylinders and the total expan
sions are assumed, and then the distribution of work and the
maximum loads on the crankpins arc calculated, allowing for
clearance and compression. Designers of engines usually have
a sufficient number of good examples at hand to enable them
lo assume these data. In default of such data it may be ncccs
aary to assume proportions, to make preliminary calculations,
and lo revise the proportions lil! satisfactory results arc obtained.
For compound engines using 80 pounds slfamprcsaurc the ratio
is i: 3 or i! 4. For tripleexpansion cn(incs the cylinders may
be made lo increase in the ralio r : a or i : air.
Approximate IndicatorDiagrams. The indicatordiagrams
from some compound and multipleexpansion engines arc irreg
ular and apparently erratic, depending on the sequence of. the
cranks, the aclion of the valves, and the relative volumes of iho
cylinders and the receiver spaces. A good idea of the effects and
relations of these several influences can be obtained by making
approximate calculations of pressures at Ihc proper parts of the
diagrams by a method which will now be Illustrated.
For such a calculation it will be assumed Ihat all expansion
DIRECTEXPANSION ENGINE
163
lines are rectangular hyperbola;, and in general that any change
of volume will cause the pressure to change inversely as the
volume. Further, it will be assumed that when communication
is opened between two volumes where the pressures are different,
the resultant pressure may be calculated by adding together the
products of each volume by its pressure, and dividing by the sum
of the volumes. Thus if the pressure in a cylinder having the
volume v c is p et and if the pressure is p r in a receiver where
the volume is v r , then after the valve opens communication from
the cylinder to the receiver the pressure will be
The same method will be used when three volumes are put into
communication.
It will be assumed that there arc no losses of pressure due to
throttling or wiredrawing; thus the steam line for the high
pressure cylinder will be drawn at the full boiler pressure, and
the backpressure line in the lowpressure cylinder will be drawn
to correspond with the vacuum in the condenser. Again, cylin
ders and receiver spaces in communication will be assumed to
have the same pressure.
For sake of simplicity the motions of pistons will be assumed
to be harmonic.
Diagrams constructed in this way "will never be realized in
any engine; the degree of discrepancy will depend on the type
of engine and the speed of rotation. For slowspeed pumping
cngines the discrepancy is small and all irregularities are easily
accounted for. On the other hand the discrepancies arc large
for highspeed marineengines, and for compound locomotives
they almost prevent the recognition of the events of the stroke.
Directexpansion Engine. If (he two pistons of a compound
engine move together or in opposite directions the diagrams
arc like those shown by Fig. 42. Steam is admitted to the high
pressure cylinder from a to b\ cutoff occurs at b, and be repre
sents expansion to the end of the stroke; be being a rectangular
COMPOUND ENGINES
hyperbola referred to the axes OV and OP, from which a, l t
c are laid off to represent absolute pressures and volumes, incl
ing clearance.
At the end of the stroke release from the highpres
cylinder and admission to the lowpressure cylinder arc ussu
la lake place, so that communication is opened from the 1
pressure cylinder through' the receiver space into llio lowp
urc cylinder. As a consequence the pressure falls from c \
and rises from it to h in the lowpressure cylinder. The
O'P' Is drawn at a distance from OP, which corresponds Ic
volume of the receiver space, and the lowpressure diagra
referred to O'P' and O' V as axes.
The communication between the cylinders is maintained
cutoff occurs at / for the lowpressure cylinder. The lim
and hi represent the transfer of steam from the highpro
to the lowpressure cylinder, together with the expansion d 1
the increased size of the large cylinder. After the cutoff
the large cylinder is shut off from the receiver, and the slcn
it expands lo the end of the slrokc. The backpressure
compression lines for that cylinder arc not affected by compc
ing, and arc like those of a simple engine. Meanwhile; the
piston compresses steam Into the receiver, as rcprcscnlc
eft till compression occurs, after which compression inti
clearance space is represented by/. The expansion and
prcssion lines ik and mn arc drawn as hyperbolic referred i
axes O'P' and O' V. The compression line cfh drawn as an \
bola referred to O'V and O'P', whilc/ is referred loOVand
IMRKCTEXl'ANSION KNC.1NK
In Fig. 42 (he two clifigrums urc drawn widi the .111 me* wli'
for volume and pressure, and are placed so us to show to Uie
eye (he relations of the diugrum.s to wicli other. DiiiKrums
taken from such an engine resemble I host 1 of I''ig. ,w. which
have (lie same length, and different vertical Hnilts depending*
on the springs used in (he indicators.
Some engines have only OIK* valve lo gi\v release nnd ami
pression for the highpressure cylinder and dmi.s.*mirt and itu
off for the lowpressure cylinder, tn such nisi llurr is nu
receiver space, find the points tnnd/roimiiJi.
When (he receiver is closed by (he nimprrHsiim uf ilif ItiKh
pressure cylinder it is filled with slcum wilh tin prcs.nrc tvpn
sen ted by /. It is fisaumed dial die jnvssurc in (In nuiivrf
remains unchanged till the rectivii in opened ui tlu end nf iln
stroke. It is evident thai the drouo/ may U rtdiucd li\ ..Imri
cninglhc cutoff of the lowpressure cylinder HO UK in j^ivi inure
compression from e to /nnd con.se(Uenily n I)iK)rr prr^urr n\
/ when the receiver In closed.
Representing the pressure and volume at ihe wvrrnl pnlnln
by p and v willi ftppropriittc .subHcrirt lettcnt, nnd reprrseiU
ing the volume of the receiver by i' f , we liavr ilu* following
equations;
p a m, j) b initial pressure;
PI ** pm**
V f \
n
f
v n
Pa  p k  (
P,  A A/
h
t/,
v ) 4
. Vr );
v ,
The pressures p. and A, can l.c calculated direc ily. Then ilir
equations for p* /> U nd fy farm a set of three .imulu
equations with three unknown quantities, whlrli cnn br
solved. Finally, p v and p t may )* calcululed dirertly
For example, let us find the approximate diagram for a direct,
expansion engine which lias the lowpressure piston displacement
equal to three limes the highpressure piston displacement.
Assume that the receiver space is half (lie smaller piston dis
placement, and that the clearance for each cylinder is onclcnlh
of the corresponding piston displacement. Let the cutoff for
each cylinder be at halfstroke, and the compression at nine
tenths of the stroke; let the admission and release be at the end
of the stroke. Let the initial pressure be 65.3 pounds by ihc
gauge or 80 pounds absolute, and let the backpressure be two
pounds absolute.
If the volume of the highpressure piston displacement be
taken as unity, then the several required volumes arc;
v b = 0.5 + o.i = 0.6
% = V* ~ i.o 4 o.i =
v, = 0.5 I o.i = 0.6
Vf = O.I  O.I = O.2
W, = 0,1
VA v * 3 X o.i 0.3
i.i v/ 3 (0,5 4 o.i) = 1,8
v* v t 3 (i.o  o.i) '
v m 3 (o.i I o.i) 0.6
v,. 0.5
33
The pressures may be calculated as follows:
P = Pb = 80; pt = p, n n 2;
#<r p& b * v c 80 X 0.6 i i.i 43.6;
A.  #v m 4 V B 2 X 0.6 * 0.3 4 ;
A = A* C^c + v 4 v r ) 4 (v a F v, h v r )  p a (i.i + 0,3 + 0.5)
** (0.6 H 1.8 h 0.5) = 0.655 A'!
Pt ~ ^o (^ + V r ) i (V/ + V r )  ^> e (0.6 + 0.5) H (0.3 + 05)
1.57 ^ = i57 X 0.655 A*  103 A*J
Pd  (# fl w + AV + M) * (v c I v + w r )
= (80 X 0.6 h 4 X 0.3 + 0.5 p f ) + (0.6 + 0.3 h 0.5)
= 25.89 40.26^;
A/  25.89 + 0.26 X 1.03 p a ; p tl  35.36;
A  A = 0.655 A/ = 0655 X 35.36  23.2;
Pt = 103 A. = 103 X 35.36 36.5;
^ = ^ + v, 36.5 x 0.2 f o.i 73;
v*  23.2 x t.8 H 3.3 12.6.
DIRECTEXPANSION ENGINK
I6 7
As the pressures and volumes are now known the diagrams
of Fig. 42 may be drawn to scale. Or, if preferred, diagrams
like Fig. 39 may be drawn, making them of the same length and
using convenient vertical scales of pressure. If the engine runs
slowly and has abundant valves and passages the diagrams
thus obtained will be very nearly like those taken from the engine
by indicators. If losses of pressure in valves and passages are
allowed for, a closer approximation can be made.
The mean effective pressures of the diagrams may be readily
obtained by the aid of a phmimcter, and may be used for esti
mating the power of the engine. For this purpose we should
cither use the modified diagrams allowing for losses of pressure,
or we should affect the mean effective pressures by a multiplier
obtained by comparison of the approximate with the actual dia
grams from engines of the same type. For a slowspeed pump
ingengmc the multiplier may be as large as 0.9 or even more;
for highspeed engines it may be as small as 0.6.
The mean effective pressures of the diagrams may be calcu
lated from the volumes and pressures if desired, assuming, of
course, that the several expansion and compression curves are
hyperbolae. The process can be best explained by applying it
to the example already considered. Begin by finding the mean
pressure during the transfer of steam from the highpressure
cylinder to the lowpressure cylinder as represented by de and /*.
The net effective work during the transfer is
pdv =
= 144
f v r )
t ,
 144x354(1.1 +0.3
4120 footpounds
;' , V ' *'
u$ f Vh f v r
0.6 + 1.8 f Q5
for each cubic foot of displacement of the highpressure piston.
This corresponds with our previous assumption of unity for the
displacement of that piston. The increase of volume is
1 1
=0.6+1.810.5
so that the mean pressure miring uiu
4120 HI X 144 " 28  6
P
pounds per square inch, which acts on bolh the high and the
lowpressure pistons.
The clTcctivc work for the small cylinder is obtained by add
ing the works under ab and be and subtracting the works under
tie, ef, and/f. So thai
Wl!  l.M If, (V ~ V.) \ frVt log.^j  f>, (V4  V.)
144 J8o (0.6  o.i) t 80 Xo.fi log.  a8.6 <i.i 0.6)
. . . , U.U V U.S
21.2 (o.G V 0.5) iou ""*"'
"" 114 X 3326 4789 fooli)oniuls.
t x ' a
This is the work for each cubic foot of the highpressure piston
displacement, and the mean effective pressure on the .small piston
is evidently 33.26 pounds per square inch.
In a like manner the work of the large piston is
144 j 38.6 (1.8 0.3) I 33.3 X 1.8 log, 3i
 a (3.3   6 ) ~ a X 0.6 log. i~ .= i, t 4 X
8f>i6 fooljmundg.
Since the ratio of the piston displacements is 3, the work for
each cubic fool of the lowpressure piston displacement is onethird
of the work just calculated; and the mean effective pressure on
the large piston is
61.92 4 3 = 20.64
pounds per square inch.
The proportions given In the example lead to a very uneven
distribution of work; that of the large cylinder being nearly
twice as much as is developed in the small cylinder. The clis
CROSSCOMPOUND ENGINE
169
tribution can be improved by lengthening the cutoff of the
large cylinder, or by changing the proportions of the engine.
As has already been pointed out, the works just calculated
and the corresponding mean effective pressures are in excess
of those that will be actually developed, and must be affected
by multipliers which may vary from 0,6 to o.o, depending on
the type and speed of the engine.
Crosscompound Engine. A twocylinder compound engine
with pistons connected to crunks at right angles with each other
is frequently called a crosscompound engine. Unless a large
receiver is placed between the cylinders the pressure in the space
between the cylinders will vary widely.
Two cases arise in the discussion of (his engine according as
he cutoil of the large cylinder is earlier or later than halfstroke;
n the latter case there ia a species of double admission to the
owprcssuro cylinder, us Is shown in Mg. ,(3. For sake of
iimplicily the release, and also the admission for each cylinder,
s assumed to be at the end of the stroke. If the release is early
he double admission occurs before halfstroke.
The admission and expansion of steam for ihe highpressure
yllndcr arc represented by ab and be. At c release occurs,
mtling the small cylinder In communication with the inlcr
ncdiate receiver, which is then open to the large cylinder. There
5 a drop at cd and a corresponding rise of pressure m on the
arge piston, which is (hen at Imlfatroke; H will be assumed
hat the pressures at {/ and at fire identical. From <l to e the
steam is transferred from the small in the large cylinder, and
the pressure falls because the volume increases; no is the corre
sponding line on ihc lowpressure diagram. The cutoff at o
for Ihc large cylinder interrupts this transfer, and stctim is then
compressed by the small piston into the intermediate receiver
with a rise of pressure as represented by </. The admission lo
the large cylinder, tk, occurs when the small piston is at ihc
middle of its stroke, and causes a drop,/?, in the small cylinder.
From g to h steam is transferred through the receiver from the
small lo the large cylinder. The pressure rises al firsl because
the small piston moves rapidly while the largo one moves slowly
until its crank gels away from the deadpoint; afterwards the
pressure falls. The line kl represents this action on the low
pressure diagram. Al h compression occurs for the small
cylinder, and hi shows the rise of pressure due to compression.
For the large cylinder Ihc line Im represents the supply of steam
from the receiver, with falling pressure which lasts till the double
admission at inn occurs.
The expansion, release, exhaust, and compression in ihc large
cylinder are not affected by compounding.
Strictly, the two parts of the diagram for the lowpressure
cylinder, mnopq and stklm, belong to opposite ends of the cylin
der, one belonging to the head end and one to the crank end.
With harmonic motion the diagrams from the two ends arc
identical, and no confusion need arise from our neglect lo deter
mine which end of the large cylinder we arc dealing with at any
time. Such an analysis for the two ends of the cylinder, taking
account of the irregularity due lo the action of the connecting
rod, would lead to a complexity that would be unprofitable.
A ready way of finding corresponding positions of two pistons
connected to cranks at right angles with each other is by aid
of the diagram of Fig. 44. Let be the centre of ihc crank
shaft and pR v R*q be the path of the crankpin. When one piston
has the displacement py and its crank is at OR V , the other crank
may be 90 ahead at O^nnd the corresponding piston displace
ment will be px. The same construction may be used if the
CKOSSCOMl'OUNJ) KNOINK
crank is 90 behind or if ihe angle KyOR t in other than a
angle. The actual piston position and crank tingles wlun
affected by the ir/cRuluriiy due to the
connecting rod will differ from those found
by this method, but the positions found
by such a diagram will represent the aver
age positions very nearly.
The several pressures may be. found as
follows: HI.. .
fa = fa M initial pressure;
h =, p & backpressure;
j>< t  A,
A  A
A C^ I t'rt t r r )
I v,) + (i>'M'r
 /'* I/'/ (^ I iv) I y
A
(n
The pressures ^ and fa cun be found dirtrlly from il iniliiil
pressure and the hftckprcssure, ami Tiniilly tin IHHI twn rqun
lions give direct calculations for fa and p f HO MJOH us fa uml fa
are found. There remain six eqimiionH ccin[nininf(fix unkmiwn
quantilics, which can be raidlly solved afltr numfrul vnlunt
arc assigned to the known pressures nnrl lo nil ihc wilumm.
The expansion nml compression lines, be and ///, ttir llir hi^h
pressure diagrams arc hyperbola; rrfcrrwl lo l\w tw rM' and
OP; and in like manner the pxjjniwion find comprruilon \\t\r* ttp
and sl t for the lowpressure diagrnm, art hypirlmJffi rrfrrrnl i<.
O'V and 07". The curve //is an hyperbola referred in O' ' um\
O'P', and the curve Im is un hyperbola rcfrrml lo <M" ..nd
OP. The transfer lines tie and o, gh and W, arr nm ], M rr
boltc. They may be plotted point by point by finilinft '
spending intermediate piston positions, p x find p v> by aid of Fig.
44, and then calculating the pressure for these positions by the
equation
The work and mean effective pressure may be calculated in n
manner similar to that given for the directexpansion engine;
but the calculation is tedious, and involves two transfers, de and
no, and gh and kl. The first involves only an expansion, and
presents no special difficulty; the second consists of a compres
sion and an expansion, which can be dealt with most conveniently
by a graphical construction. All things considered, H is better
to plot the diagrams to scale and determine the areas and mean
effective pressures by aid of a planimcter.
Jf the cutoff of the lowpressure is earlier than halfstroke so
as to precede the release of the highpressure cylinder the transfer
represented by de and no, Fig. 43, docs not occur. Instead there
is a compression from d to /and an expansion from / to m. The
number of unknown quantities and the number of equations arc
reduced. On the other hand, a release before the end of the
stroke of the highpressure piston requires an additional unknown
quantity and one more equation.
Triple Engines. The diagrams from triple and other mul
tipleexpansion engines arc likely to show much irregularity, the
form depending on the number and arrange
ment of the cylinders and the sequence of the
cranks. A common arrangement for a triple
engine is to have three pistons acting on
cranks set equidistant around the circle, as
shown by Fig. 45. Two cases arise depending
on the sequence of the cranks, which maybe
in the order, from one end of the engine, of
highpressure, lowpressure, and intermediate, as shown by Fig.
45; or in the order of highpressure, intermediate, and low
pressure.
With the cranks in the order, highpressure, lowpressure, and
Fl '
KNGINES
'73
intermediate, as shown by Fig. 45, the diagrams arc like those
given by Fig. 46. The admission and expansion for the high
pressure cylinder arc represented by ale. When the high
pressure piston is at release, ita crank is at fJT t Fig. 45, and the
intermediate crank is at /, so that the intermediate piston is
near halfstroke. IE the cutolT for that cylinder is later than
100
HMfn
AIA1IM
twrlo I Inn
it (mm
Ihtla (0
fin. 46,
halfstroke, it is In communication with the first receiver when
its crank is at /, and atcarn may poaa through the first receiver
from the highprcsaurc to the intermediate cylinder, and there is
a drop cd t and a corresponding rlao of pressure no in the inter
mediate cylinder. The transfer continues till cutoff for tho
w uiC
position c for the highpressure cylinder. From the position e
the high pressure piston moves to the end of the stroke at/,
causing nn expansion, and Ihcn starts to return, causing the
compression fg. When the highpressure piston is at g the
intermediate cylinder takes stcfim fit the other end, causing the
drop gh and the rise of pressure xl, Then follows a transfer of
slciim from the highpressure to the Intermediate cylinder repre
sented by In and hit. At / the highpressure compression ik
begins, and is carried so far (is to produce a loop at k. After
compression for the highpressure cylinder shuts it from the
first receiver, the steam in that receiver and in the intermediate
cylinder expands as shown by wit. The expansion in the inter
mediate cylinder is represented by pq and the release by qr,
corresponding to a rise of pressure /? in the low pressure cylin
der. rs and fa represent a transfer of steam from the inter
mediate cylinder to the lowpressure cylinder. The remainder
of the backpressure line ol the Inlormcdmlc cylinder and the
upper part of ihc lowpressure diagram for the lowpressure
cylinder correspond to the same parts of the high pressure and
the intermediate cylinders, so that a statement of the actions in
detail does not appear necessary.
The equations for calculating the pressure arc numerous, but
they are not difficult to state, and the solution for a given exam
ple presents no special difficulty. Thus we have
//
* Inlilnl pressure;
'* *"V, ;
/M(TM 1f. 1up) * (v, I Vj>
(v, H up) i (v/l vp);
TO) * (v I v/);
vol. first receiver;
vol. acfjnd receiver;
(Vm + V/i)
J T, i
TRJrLE ENGINES
JIL p,
f>
' /* = J#(v u + f fl) 4 t>if>Ji\ * (f, + ui + V B)
p=* P* (* + Vi) + v n ) s (v w 4 *> + I'D);
Pt =* pf *= backpressure;
The pressures at c and at ? can be calculated immediately
:rom the initial pressure and from the backpressure. Then it
will be recognized that there are four individual equations for
finding p f , p*, p tl and p&. The fourteen remaining equations,
solved as simultaneous equations, give the corresponding four
teen required pressures, some of which are used in calculating
the four pressures which are determined by the four individual
equations. The most ready solution may be made by contin
uous substitution in the four equations which are numbered at the
left hand. Thus for p g in equation II, we may substitute,
A
** J*
In the actual computation the several volumes and the proper
sums of volumes arc to be first determined; consequently the
factors following p d will be numerical factors which may be con
veniently reduced to the lowest terms before introduction in the
equation. This system of substitution will give almost immedi
ately four equations with four unknown quantities which may
readily be solved; after which the determination of individual
pressures will be easy. In handling these equations the letters
representing smaller pressures should be eliminated first, thus
giving values of higher pressure like p d to tenths of a pound;
afterward the lower pressure can be determined to a like degree
of accuracy. A skilled computer may make a complete solu
tion of such a problem in two or three hours, which is not exces
sive for an engineering method.
If the cutoff for the intermediate cylinder occurs before the
release of the highpressure cylinder, then the transfer represented
by tie and op docs not occur. In like manner, if the cutoff for
the lowpressure cylinder occurs before the release for the inter
mediate cylinder, the transfer represented by rs and fa does
not occur. The omission of a transfer of course simplifies the
work of deducing and of solving equations.
In much the same way, equations may bo deduced for cal
culating pressures when the cranks have iho sequence high
pressure, intermediate, and lowpressure. The diagrams take
forms which arc distinctly unlike those for the other sequence of
cranks. In general, Ihc case solved, i.e., highpressure, low
pressure, and intermediate, gives a smoother action for the
engine.
For example, the engines of the U. S. S. Mnehias have the
following dimensions and proportions:
Ultth
Inter*
Djiurieicr of platan, Inches
Piston displacement, cubic feet
Clearance, por com
Cutoff, por conl stroke
Release, per cent stroke
Compression, per conl stroke
Rmlo of piston displacements
, ^
,
Volume first receiver, cubic feel .........
Volume second receiver, cubic fool .........
Ratio of receiver volumes to liIghproMura plslon din
placement .................. Ot g.,
Stroke, Inches ..................
Boilerpressure, absolute, pounds per sq. In ......
Pressure !n condenser, pounds per aq. In .......
aaj
SS3
M
66
03
18
3.33
6,30*
1 80
I.Ow
prMture.
35
7
66
M
18
4.94
If the volume of the highpressure piston displacement is
taken to be unity, then the volumes required in the equations for
.K KNOINES
177
It"
y. i
B
V,
079
7J rf w I .06
1.1O
** I 1 3
OQ
BB I/A "" O.OO
=" 0.31
, n. V fl rt 0.13
Vm ^ 9^
V "^ ^fl ^
y_ 1 .63
W ' 3sa *'^ l i
V M V B
v w * 0.63
.39 ^
i.aG
3.18
1.85
'fa ^ ^H IHI1 ^'35
V, ^ 2.O3
t/ y M 3.6O
ij(. isa T/ ( ** 4'0't
4
. JJl V.3OU1 <il
m *
A
= A =
150 A
= 165
A  A =
25.6
A
= 112
A
= 60.0
A  523
A
= A 
76.5 # ff
= 55
/> = 22.1
A
= p p =
675 A
= p f = 28.3
P&  I8. 5
A
= 67.5
A
= Py = 25.3
P, = Pf =
5
A
= 76.9
A
= 25.1
Ptl J?'
,
A
= A =
735 A
= 29.0
A
 # =
69.3 A
, = p y = 28.2 '
Diagrams with the volumes and pressures corresponding lo
this example are plotted in Fig. 46 with convenient vertical
scales. Actual indicatordiagrams taken from the engine arc
given by Fig. 47. The events of the stroke come at slightly
different piston positions on account of the irregularity due to
the connectingrod, and the drops and other fluctuations of
pressure arc gradual instead of sudden; moreover, there is con
siderable loss of pressure from the boiler to the engine, from one
cylinder to another, and from the lowpressure cylinder to the
condenser. Nevertheless the general forms of the diagrams arc
easily recognized, and all apparent erratic variations arc
accounted for.
Designing Compound Engines. The designer of compound
and multipleexpansion engines should have at hand a well
systematized fund of information concerning the sizes, pro
portions, and powers of such engines, together with actual
indicatordiagrams. He may then, by a more or less direct
method of interpolation or extcrpolation, assign the dimensions
and proportions to a new design, and can, if deemed advisable,
draw or determine a set of probable indicatordiagrams for the
new engines. If the new design differs much from the engines
for which he has information, he may determine approximate
diagrams both for an actual engine from which indicatordia
grams are at hand, and for the new design. He may then
sketch diagrams for the new engine, using the approximate
OKSICiNINCV COMPOUND KNGINKS
1 79
diagrams as a basis and faking n comparison of the approximate
and actual diagrams from the engine already built, as a guide.
It is convenient to prepare and use a table showing the ratios of
actual mean effective pressures and approximate mean effective
pressures. Such a Uilile enables the designer to assign mean
effective pressures to a cylinder of the new engine and to infer
very closely what its horaepiwr will be. It is also very useful
as a check in sketching probable diagrams for a new engine,
which diagrams are not only useful in estimating the power of the
new engine, but in cakulating Kitesses on the members of that
engine.
A rough approximation of Ihc power of nn engine may be
made by calculating the power tin though (ho total or equivalent
expansion took place in (lie lowpressure cylinder, neglecting
clearance and compression. The power thus found is to be
affected by a factor which according to the nine and type of the
engine may vary from 0.6 to o.o for compound engines and from
0.5 to 0.8 for triple engines, Scalon and Kounlhwallo * give the
following table of multipliers for compound marine engines:
MUI/ni'UKRS FOR. FIN I) WO I'LUHIMH.K M.K.I'. COMPOUND
AND TKIl'U: MARINK KNCUNKS.
l)e*;rl>iloii of Knn!n<i.
jackaiad.
Un)oklil.
Throecylinder triple, merchant ahiii
0.6.1 [u o.Tifl
O.6o to 0. 6
Threecylinder triple, gunluiuit And turi win Ixinu
0.6o lo o.f
For example^ lei the boilerpressure be 80 pounds by the gauge,
or 94.7 pounds absolute; let the backpressure be 4 pounds
absolute; and let the total number of expansions be six, so that
the volume of steam exhausted to the condenser is six limes the
* Packet Ilaak of Afarlne Rngiiie6r{ng>,
volume admitted from the boiler. Neglecting the effect of clear
ancc find comi>rcssion, the mean effective pressure is
<M7 X i I 9*1,7 X A log,
4 x i ~ 40.06 . M.E.P.
If the large cylinder is 30 inches in diameter, and the stroke
is 4 feel, the horsepower at 60 revolutions per minute is
,1
7T3O
4
X 40.06 X 3 X 4 X 60 t 33000 * 412 H.P,
If the factor to be used in tin's case is 0.75, then the actual
horsepower will be about
0.75 X 400 300 H.P.
Binary Engines. Another form of compound engines using
two fluids like steam and ether, was proposed bydu Trembly* in
1850, to extend the lower range of temperature of vaporengines.
At thai time the common steampressure was not far from thirty
pounds by the gouge, corresponding to a temperature of 250 F.
If the backpressure of the engine be assumed to be 1.5 pounds
absolute (115 F.), the efficiency for Cafnot's cycle would be
approximately
350 h 460
0.19,
If, however, by the use of a more volatile fluid the result at
lower temperature could be reduced to 65 F., the efficiency
could be increased to
350  6$
250 + 460
0.26.
At the present time when higher steam pressures arc common,
the comparison is less favorable. Thus the temperature of
steam at 150 pounds by the gauge is 365 F., so that with r.$
*Mintiul du Conducted ties Machines & Vaporous combinfes au Martinet
JJhialres, nlao Kanhine Steam Engtnv, p. 44,).
BINARY ENGINES
iflc
pounds absohilc for 115 l r O
for Carnot's cycle is
l)ack pressure the
., 0.30,
365 I 4o
and for a resultant temperature of 65 F., the efficiency would be
*(>< 6s ,
i* M * t O.7O.
365  400
If a like gain of economy could be obtained in prnclirr, it
would represent a saving of 17 percent, which would lie well
worth while. Further discussion of this mutter of rwnoiny will
be given in Chapter Xf, in connection with cxH'riini'ii(n MM
binary engines using steam and .sulphurdioxide.
The practical arrangement of a binary rnginr sulisliliiui fur
the condenser an appliance having somewhat llir winu form n*
a tubular surfacecondenser, the steam being condensed on llir
outside of the tubes and withdrawn in the form of miter of con
densation at the bottom. Through Ihc lubes !H forced the
more volatile fluid, which i ( vaporijscd much as it would be In n
"watertube" boiler. The vapor is then used In a cylinder
differing in no essential from Hint for a slcnm engine, nnd In turn
is condensed in a surfacecondenser which is cooler) with wnirr
at the lowest possible temperature.
An ideal arrangement for a binary engine avoiding llir UHC of
airpumps would appear to be the combination of a compound
noncondensing steamengine with a third cylinder on (he blnnry
system which should have for its working sulmlnncc* a fluid llinl
would give a convenient pressure at aiaF., and ft prnuurr
somewhat above the atmosphere at 60 F. There is no known
fluid that gives both these conditions; thus ether at au I 1 *, give*
a pressure of about 96 pounds absolute, but UK hoillngjKiint n(
atmospheric pressure is 94 F t) consequently it would from
necessity require a vacuum and an airpump unlrwf tin rilirr
couid be entirely freed from air, and leakage inlo tlu vacuum
space entirely prevented. Sulphurdloxldc givcjs n prwisurr of .\\
pounds IIUSOIUIU ILL UU 1'., U UUIL it L.UU turnip a uu
pressure above the atmosphere; but 212 F. would give an incon
venient pressure, and in practice it 1ms been found convenient
to run the steamengine with a vacuum of 22 inches of mercury
or about 4 pounds absolute, which gives a temperature of 155 F.,
at which sulphurdioxide has a pressure of 1 80 pounds per square
inch by the gauge.
The attempt of du Trembly to use ether for the second fluid
in a binary engine did not result favorably, as his fuelcon
sumption was not less than that of good engines of that lime,
which appears to indicate that he could not secure favorable
conditions.
CriAI'TKR X.
TKSTINU STKAMKNtiWKS.
THE principal object of U'Hls of sicamengmcs is Lo determine
the cost of power. Scries of engine tests are made: to
determine ihc elTccl of certain conditions, such as superheating
and steamjackets, on ihc economy of the. engine. Again, tests
may be made to investigate llie mlctrlwngcs of heat between the
slcamand the walls of the cylinder hy ihe aid of llirn's analysis,
and thus find how cerutin conditions produce clTcets thitt are
favorable or unfavorable lo economy,
The two main elements of an engine lest arc, llun, the meas
urement of the power developed nnrl the rh'R'rminalion of Ihc
cost of the power in terms of thermal units, ponndH of steam, or
pounds of coal. Cower fa most commonly measured by aid of
the steamengine indicator, but ihe power delivered by the
engine is sometimes determined by u dynamometer or a Friction
brake; sometimes, when nn indicator cannot be used conven
iently, the dynamic or brake power only is determined. When
the engine drives a dynunioHirirU' Kcnenilor Ihc power applied
to the generator may be determined clmricully, and thus the
power delivered by the engine may he known.
When the cost of power is Riven in terms of coal per horse
power per hour, it is sufficient to weigh Ihc coal for a definite
period of lime. In such case a combined boiler and engine lest
is made, and all the methods and precautions for a careful boiler
test must be observed. The time required for such ti test
depends on the depth of the fire on the grate and the rate of
combustion. For faclory boilera ihe test should be twentyfour
hours long If exact results are desired.
When the coal of power IH staled in terms of slcnm per horse
power per hour, one of two methods may bo followed, When
the engine has a surfacecondenser die steam <
engine is condensed, collected, and weigh<
usually sufficient lor tests under favorable c
intervals} ten or fifteen minutes, give fairly
The cliicf objection to this method is that the
to leak water tit the tube packings. Under fa.
the results of tests by this method and by dcti
water supplied to the boiler tiro substantially t]
on noncondensing and on jetcondensing ci
consumption is determined by weighing or m. t
water supplied to the boiler or boilers that fui
engine, Stenm used for any other purpose
engine, for example, for pumping, heating, ot
nations of the quality of the steam, must b<
allowed for. The most satisfactory way is
weigh such steam; but small quantities, as
quality by a steam calorimeter, may be gaugcx
flow through an orifice, Tests which depend
feedwater should be long enough to minimizi
uncertainly of the amount of water in a boiler
an apparent height of water in a watergauge:
height of the walcrlcvel depends largely on llu
lion and the activity of convection currents.
When the cost of power Js expressed in tl
necessary to measure the steampressure, the ai
in the steam supplied to the cylinder, and the t
condensed steam when il leaves the condenser.
in jackets or rchcatcrs it must be accounte.
But it is customary in all engine tests to ta.
temperatures, so that the cost may usually
thermal units, even when the experimenter is c
in pounds of steam.
For a Kirn's analysis it is necessary to weig
condensing water, and to determine the tempo
sion to and exit from the condenser.
Important engines, with their boilers and otht
TESTING STEAMENGINES jgt
are commonly built under contract to give a certain economy,
and the fulfilment of the terms of a contract is determined by a
test of the engine or of the whole plant. The test of the entire
plant has the advantage that it gives, as one result, the cost of
power directly in coal ; but as the engine is often watched with more
care during a test than in regular service, and as auxiliary duties,
such as heating and banking fires, arc frequently omitted from
such an economy test, the actual cost of power can be more
justly obtained from a record of the engine in regular service,
extending for weeks or months. The tests of engine and boilers,
though made at the same time, need not start and stop at the
same time, though there is a satisfaction in making them
strictly simultaneous. This requires that the tests shall be long
enough to avoid drawing the fires at beginning and end of the
boiler test.
' In anticipation of a test on an engine it must be run for some
time under the conditions of the test, to eliminate the effects of
starting or of changes. Thus engines with steamjackets are
commonly started with steam in the jackets, even if they arc to
run with steam excluded from the jackets. An hour or more
must then be allowed before the effect of using steam in the
jackets will entirely pass away. An engine without steam
jackets, or with steam in the jackets, may come to constant
conditions in a fraction of that lime, but it is usually well to
allow at least an hour before starting the lest.
It is of the first importance that all the conditions of a test
shall remain constant throughout the test. Changes of steam
pressure arc particularly bad, for when the steampressure rises
the temperature of the engine and all parts affected by the steam
must be increased, and the heat required for this purpose is
charged against the performance of the engine; if the steam
pressure falls a contrary effect will be felt. In a series of tests
one element at a time should be changed, so that the effect of
that element may not be confused by other changes, even though
such changes have a relatively small effect. It is, however, of
more importance that steampressure should remain constant
limn that nil tests nl a given pressure should have identically the
same steampressure, because the loUtl heat of steam varies more
slowly than tin temperature.
All the instruments and apparatus used for an engine test
.should be tested and standardized either jusl before or just
after the test; preferably before, tu avoid annoyance when any
Instrument fails during the test and is replaced by another.
Thermometers. Temperatures arc commonly measured by
aid of mercurial thermometers, of which three grades may be
distinguished. For work resembling that done by the physicist
the highest grade should be used, and these must ordinarily be
calibrated, and have their boiling and freezingpoints deter
mined by the expvvimeuUir or Home qualified person; since the
freezing point is liable to change, it should be redder mined when
necessary. For Important data good thermometers must be used,
such as are sold by reliable dealers, but It is preferable that they
should be calibrated or else compared with a thermometer llmt
is known Ui be reliable. For secondary data or for those requir
ing little accuracy common thermometers with the graduation
on the stem may be used, but these also should have their errors
determined and allowed for. Thermometers with detachable
scales should be used only for crude work.
Gauges. Pressures are commonly measured by Bourdon
gauges, and if recently compared with a correct mercury column
Ihcso are sufficient for engineering work. The columns used
by gaugemakers arc sometimes subject lo minor errors, find tire
not usually corrected for temperature. It is important that
such gauges should be frequently rclesled.
Dynamometers. The standard for measurement of power
is lue. frictionbrake. For smooth continuous running it is
essential that the brake and its band shall be cooled by a stream
of water thai docs not come in contact with the rubbing sur
faces. Sometimes the wheel is cooled by a stream of water cir
culating through it, sometimes the band is so cooled, or both may
be. A rubbing surface which is not cooled should be of non
conducting material. If bolh rubbing surfaces arc metallic they
INDICATORS
nust be freely lubricated with oil. An iron wheel running in a
furnished with blocks of wood requires lialu or 110 lubn
:alion.
To avoid the increase of friction on the brakebearings clue
o the lond applied at a .single brakearm, two equal nrrns mny
jc used with two equal tint] opposite forces applied at tlic ends
o form a statical couple.
With cure und good workmanship a frictionbrake, may be
nndc an instrument, of precision .sufficient. for physical inve.sti
;alions, but with ordinary care and workmanship it will give
csiills of sufficient accuracy for cnginei'dn^ work.
An engine which drives an electricgemralnr may readily have
he dynamic or brakepower deicnnimcl from the electric out
mi, provided that the efficiency of the gcncralor is properly
Ictcrmincd.
The only power thai can be measured far a Klwimuirhinc is
he dynamic or brakepower; when connected with nn oleelric
cncmtor this involves no difficulty. For marine propulsion i:
> customary lo dclcrmine lhe power of Hleamturbinea by some
3rm of lorsionmcirc applied to (he shaft that connects the
.irbinc lo the propeller. This instrument measures the angle
f torsion of the shaft while running, and conserjuemly, if the
lodulus of elasticity linn been determined, gives IL positive
clcrmination of ihe, power delivered lo ihu propeller. Under
ivorablc condiiions a torsionmetre may have, .in error of not
lore than one per cent.
Indicators. The most important antl at the same time the
iast satisfactory instrument used In engincUsling is the incli
Uor. Even when well made and in good condition it is liable
) have on error which may iimouni to two per cent when used
t moderate speeds. At high speeds, three hundred revolutions
cr minute and over, it is likely lo have two or three limes ns
inch error. As a rule, nn indicator cannot be used at more
tan four hundred revolutions per minute.
The mechanism for reducing the. motion of the crosshead of
ic engine and transferring h lo the paper drum of an indicator
aitumit ^ I.UIK.I.I in Mvo.^ii .... .iv, uum uuuuu looseness. It
should require only a very short cord leading lo the paper drum
because till the error.s due lo the paper drum tire proportional to
the length of UK cord and may be pruclically eliminated by
making the cord short.
The weighing and recording of the RICH m pressure by the indi
ailorpislon, pencilmotion, and pencil arc affected hy errors
which may be classified us follows:
t. Scale of the spring,
a. Design of ihe pencilmotion.
.V Inertia of moving parts.
<. Friction and backlash.
Good Indicatorsprings, when tested by direct loads out of
the indicator, usually have correct and uniform scales; that is
they collapse under pressure the proper amount for each load
applied. When enclosed in the cylinder of an indicator the
spring ia healed by conduction and radiation to the temperature
of the cylinder, and that temperature is sensibly equal to the
mean temperature in the enginecylinder. But a spring is appre
ciably weaker til high temperatures, so that when thus enclosed
in the indicatorcylinder, It gives results thai are too large; the
error may be two per cent or more.
Oulsidc springindlcalors avoid this difficulty and are lo be
preferred for all important work. They have only one disad
vantage, In thai the moving parls arc heavier, but tins may be
overcome by increasing the area of the piston from half a square
Inch lo one square inch.
The motion of the piston of the indicator in multiplied five
or six times by the pcncilmoiion, which Is usually tin approx
imate parallel motion. Within the proper range of motion
(about two inches) the pencil draws a line which is nearly
straight when the paper drum is at rest, and it gives a nearly
uniform scale provided thai the spring is uniform. The errors
due to the geometric design of this part of the indicator arc
always small.
INDICATOKS
189
When steam is suddenly let into the indicator, as at admission
to the enginecylinder, the indicatorpiston and attached parts
forming the pencilmotion arc set into vibration, with a natural
time of vibration depending on the stiffness of the spring. A
weak spring used for indicating a highspeed engine may throw
the diagram into confusion, because the pencil will give a few
deep undulations which make it impossible to recognize the
events of the stroke of the engine, such as cutoff and release.
A stiffcr spring will give more rapid and less extensive undu
lations, which will be much less troublesome. As a rule, when
the undulations do not confuse the diagram the area of the dia
gram is but little affected by the undulations due to the inertia
of the piston and pencilmotion.
The most troublesome errors of the indicator are due
to friction and backlash. The various joints at the piston
and in the pencilmotion are made as tight as can be without
undue friction, but there is always some looseness and some
friction at those joints. There is also some friction of the piston
in (he cylinder and of the pencil on the paper. Errors from this
source may be one or two per cent, and are liable be excessive
unless the instrument is used with care and skill. A blunt
pencil pressed up hard on the paper will reduce the area of the
diagram five per cent or more; on the other hand, a medium
pencil drawing a faint but legible line will affect the area very
little. Any considerable friction of the piston of the indicator
will destroy the value of the diagram.
Errors of the scale of the spring can be readily determined and
investigated by loading the spring with known weights, when
properly supported, out of the indicator. This method is prob
ably sufficient for outside spring indicators. Those that have
the spring inside the cylinder are tested under steam pressure,
measuring the pressure either by a gauge or a mercury column.
Considerable care and skill arc required to get good results,
especially to avoid excessive friction of the piston as it remains
at rest or moves slowly in the cylinder. It must be borne in
mind that the indicator cylinder heats readily when subjected to
progressively uiguci hiuuiu jHu^uiuh, uui mat u puns with heat
slowly, and that consequently testa made with falling steam
pressures arc not valuable.
Scales. Weighing should be done on scales adapted to the
loud; overloading leads to excessive friction til the knifeedges and
to lack of delicacy. Good commercial platform scales, when
tested with standard weights, arc sufficient for engineering work.
Cool and ashes arc readily weighed in barrows, for which the
tare is determined by weighing empty. Water is weighed in
barrels or tanks. The water can usually be pumped in or
allowed lo run in under a head, so that the barrel or tank can be
filled promptly. Large quickopening valves must be used lo allow
the water to run out quickly. As the receptacle will seldom drain
properly, it is not well lo wail for it lo drain, but to close the
exitvalve and weigh empty wilh whatever small amount of water
may be caught in it. Neither is it well lo try to fill the receptacle
lo a Riven weight, us the jcl of water running in may ixtfeci the
weighing. With large enough scales and lanks the largest
amounts of water used for engine tests may be readily handled,
Measuring Water. When it is not convenient 10 weigh wjiicr
directly, it may be measured in tanks or other receptacles of
known volume. Commonly two are used, so thai one may
(ill while the other is emptied. The volume of a receptacle may
be calculated from ils dimensions, or may be determined by
weighing in waicr enough lo fill It. When desired a receptacle
may be provided with a scale showing the depth of the water,
and so partial volumes can be determined. A closed recep
tacle may be used to measure hot waicr or other fluids.
WaterMeters of good make may be used for measuring water
when other methods are not applicable, provided they arc Icstcd
and rated under the conditions for which they arc used, laldng
account of the amount and temperature of the water measured.
Metres arc most convenient for testing marine engines because
water cannot be weighed at sea on account of the motion of the
ship, and arrangements for measuring water in tanks arc expen
sive and inconvenient. For such tests the metre may be placed
TH ROTTLI NGC A, LO RIMETER
1OT
on a bypass through which the feedwater from the surface
condenser can be made to pass by closing a valve on the direct
line of feedpipe. If necessary the metre can he quickly shut
off and the direct line can be opened. The chief uncertainty in
the use of a metre is due to air in the water; to avoid error from
this source, the metre should be frequently vented to allow air
to escape without being recorded by the metre.
Weirs and Orifices. So far as possible the use of weirs and
orifices for water during engine tests should be avoided, for, in
addition to the uncertainties unavoidably connected with such
hydraulic measurements, difficulties are liable to arise from the
temperature of the water and from the oil in it. A very little oil
is enough to sensibly affect the coefficient for a weir or orifice.
The water flowing from the hot well of a jet condensing engine
is so large in amount that it is usually deemed advisable to
measure it on a weir; the effect of temperature and oil is less
than when the same method is used for measuring condensed
steam from a surfacecondenser.
Priming Gauges. When superheated steam is supplied to an
engine it is sufficient to take the temperature of the steam, in the
steampipe near the engine. When moist steam is used the amount
of moisture must be determined by a separated test. Origi
nally such tests were made by some form of calorimeter, and
that name is now commonly attached to certain devices which
arc not properly heatmeasurers. Three of these will be men
tioned : (r) the throttlingcalorimetcr, which can usually be applied
to all engine tests; (2) the separatingcalorimeter, which can be
applied when the steam is wet; and (3) the Thomas electric calor
imeter, intended for use with steamturbines to determine the
moisture in steam at any stage of the turbine whatever may be
the pressure or quality of the steam.
ThrottllngCalorimeter. A simple form of calorimeter,
devised by the author, is shown by Fig. 48, where A is a
reservoir about 4 inches in diameter and about 12 inches long
to which steam is admitted through a halfinch pipe b, with a
throttlevalve near the reservoir. Steam flows away through an
t\i j m (v K* VU K*~ "" '"^iinuiuiH mu jncssurc, ana at
there in a deep cup for a thermometer lo measure the temper
nlurc. The boilerpressure may be taken
from a gauge on the main steampipe
near the calorimeter. It should not be
taken from a pipe in which there is a
rapid flow of steam as in the pipe 4,
since the velocity of the alcam will affect
the gaugereading, making it less than tho
real pressure. The reservoir is wrapped
with hairMi and lagged with wood to
reduce radiation of heat.
When n Vest is lo be made, tho valve on
the pipe d is opened wide (this valve is
frequently omitted), and the valve nl Ms
opened wide enough lo give a pressure of
five to fifteen pounds in the reservoir.
Readings arc then taken of the bailee
gauge, of llie gauge at/, and of the thermometer at e. It is well to
wall about ten mlnulca after the instrument is Blurted bcloro Ming
readings so that it may be well healed. Let the boilerpressure
be p, and let r and q be iho latent heat and heat of the liquid
corresponding. Let /\ bo the pressure in the calorimeter, r { the
heat of vaporisation, 0, the heat of the liquid, and t { the tempera.
lure a saturated steam at thai pressure, while /, ia the tempera
ture of the superheated steam in the calorimeter. Then
KQ  <"
ser
{\J ISO!
Example, The following arc the data of a lest made with
calorimeter;
Pressure of the atmosphere . . .
Steam pressure by gauge . . .
Pressure In the calorimeter, gauge
Temperature in the calorimeter .
14.8 pounds;
69.8 "
12.0 "
a F.
Specific lieat of superheated steam for the condition of the
st 0.48.
x = 9438 + 212.7 r 048 (268.2  24.3.9)  285.9 M o88 .
892.3 '
Per cent of priming, 1.2.
A little consideration shows that this type of calorimeter
an be used only when the priming is not excessive; otherwise
he throttling will fail to superheat the steam, and in such case
icthing can be told about the condition of the steam cither before
>r after throttling. To find this limit for any pressure /, may be
nade equal to /, in cquation(i52); that is, we may assume that
he steam is just dry and saturated at that limit in the calorimeter.
Drdinnrily the lowest convenient pressure in the calorimeter is
he pressure of the atmosphere, or 14.7 pounds to the square inch.
The table following has been calculated for several pressures in
.he manner indicated. It shows that the limit is higher for higher
pressures, but that the calorimeter can be applied only where
:he priming Is moderate.
When this calorimeter is used to test steam supplied to a
:ondcnsingcngine the limit may be extended by connecting the
exhaust to the condenser. For example, the limit at 100 pounds
absolute, with 3 pounds absolute in the calorimeter, is 0.064
instead of 0.040 with atmospheric pressure in the calorimeter.
LIMITS OF THE THROTTMNGCALORtMETER.
Pressure.
Priming.
Abioltile.
Cauga.
300
=853
0.077
250
2OO
'85! 3
0.070
0.061
175
160.3
0.058
150
'2$
'353
no. 3
0.053
0.046
IOO
75
60.3
0.040
0.032
5 .
353
0.033
In case the calorimeter is used near Us limit thai is, \vhcn
UK superheating is u fiw degrees only it is essential that the
thermometer sluuilil In entirely reliable; otherwise it might
happen ihni the thermometer should show superheating when
(he sU'iun in the calorimeter was saturated or moist. In any
oilier ni.se n nmHidenibk error in the. tcmpiailurc will produce
tin inconsiderable effect on the result. Titus ill 100 pounds
absolute wilh atmospheric pressure in the calorimeter, 10 F. of
superheating indicates 0.0,^5 priming, und 15 F. indicates 0.032
priming. ^ l > l' H slight error in the gaugereading has little
eiTed. Suppose the muling to lie apparently 100.5 pounds
absolute instead of 100, then wilh 10 of superheating the prim
ing appears to lie 0.0,1.1 instead of 0.039.
H hna been found by experiment that no allowant'C need be
miuk 1 hr radial ion trnm ihi.H calorinii'lrr if niiulc a.s described,
provided ihnt aoo jioundH of sLeam ure run thvoiigh it per hour.
Now ihlfl (imnlily will flow through nn urifiai onefourth of i\n
inch in diameter under the pressure of 70 pounds by the gauge,
stt thai if the throttlevalve be. replaced by such tin orifice the
([iH'Htion of rudialion need not be considered. In such case a
stopvalve will be placed on the pipe to shut off the calorimeter
when not in use; U is opened wide when a test is made. If an
orifice i not provided the ihrolllevalve may be opened at first
a small amount, ftnd the itmptmUia in the cntorimclcr noted;
after a few mlnulcs the vnlvc muy be opened a trifle more, where
upon the temperature may rise, if loo Hulu steam was used at
first. If the valve la opened Halo by little: till the temperature
Blops rising, it will then be certain that enough sicnm is used to
reduce the error from radiation to a very small amount.
SflparatlngCalorlmcter. if steam contains more tlmn
three per cent of moisture the priming may be determined by
a good separator which will remove nearly all the moisture.
h remains to measure the steam and water separately. The
water may be best measured in a calibrated vessel or receiver,
while the steam may he condensed and weighed, or may be
gauged by allowing it to flow through an orifice of known sixc,
A form of scparatingcalorimctcr devised by Professor Carpenter *
is shown by Fig. 49.
Steam enters a space at the top
which has sides of wire gauze and a
convex cup at the bottom. The water
is thrown against the cup and finds its
way through the gauze into an inside
chamber or receiver and rises in a
waterglass outside. The receiver is
calibrated by trial, so that the amount of
water may be read directly from a gradu
ated scale. The .steam meanwhile passes
into Hie outer chamber which surrounds
the inner receiver and escapes from an
orifice at the bottom. The steam may
be determined by condensing, collecting,
and weighing it; or it may be calculated
from the pressure and the size of the
orifice. When the steam is weighed
there is no radiation error, since the
inner chamber is protected by the steam in the outer chamber.
This instrument may be guarded against radiation by wrapping
and lagging, and then if steam enough is used ihc radiation will
be insignificant, just as was found to be ihc case for the
ihroltlingcalarimcler.
The Thomas Electric Calorimeter. The essential feature of this
instrument (Fig. 50) is the drying and superheating of the steam
by a measured amount of electric energy. Steam is admitted
at # and passes through numerous holes in a block of soapstonc
which occupies the middle of the instrument; these holes arc
partially filled with coils of German silver wire which are healed
by an electric current that enters and leaves at the binding
screws. The steam emerges dry or superheated at the upper
part of the chamber and passes clown through wire gauze, which
surrounds the central escape pipe; this central pipe surrounds
* Trans. Am. Sac, Meek, Rugs., vol. xvli, p. 608.
FIG. 49.
o *
the thermometer cup, and leads to the exit at the top, which has
two orifices, either of which may be piped to a condenser or
elsewhere.
To use the instrument it j s
properly connected by a sampling.
lube to the space from which
steam is drawn, and valves arc
adjusted lo supply a convenient
amount of steam which is assumed
lo be uniform for steady pressure
this last is a mailer of some im
portance.
The current of electricity is
llum adjusted lo dry the steam;
this may be determined by noting
the lemperfilure by the thermom
eter in (he mural thermometer
cup, because that thermomclcr
will show a slight rise corres
ponding lo a very small degree
of superheating which is sufficient
lo indicate the disappearance of
moisture, but not enough to affect
the determination of quality by
the instrument. The wire gauze
surrounding the thermometer is an essential feature of this
opcralion, as it insures the homogeneity of the steam, which,
without the gauiic, would be likely lo be a mixture of super
heated steam and moist steam. Readings arc lakcn of the
proper electrical Inslrumcnls from which ihc clcclrical energy
imparted can be determined in watts; let this energy required to
dry Ihc steam be denoted by JS r Now let Ihc electric current be
increased till the steam is superheated 30, and let , be the
increase of electric input which Is required lo superheat ihe
sleam.
If W is ihc weight of steam flowing per hour through the
PlO. JO.
THE THOMAS ELECTRIC CALORIMETER
197
instrument under the first conditions, the weight when super
heated will be CW t where C is a factor less than unity which
has been determined by exhaustive tests on the instrument.
The amount of electric energy required to superheat one pound
of steam 30 from saturation at various pressures has also been
determined and may be represented by S; this constant has been
so determined as to include an allowance for radiation, and is
more convenient than the specific heat of superheated steam, in
this place. Making use of the factors C and 5, we may write
which affords n means of eliminating the weight of steam used;
this is an important feature in the use of the instrument.
Returning now to the first condition of the instrument when
steam is dried by the application of B, watts of electric energy,
we have for the equivalent heat
3.42 ,;
and dividing by the expression for the weight of steam flowing
per hour, we have for the heat required to dry one pound of
steam
3.42 E. E.
W
= 342 CS
x)r,
where r is the heat of vaporization and i x is the amount of
water in one pound of moist steam.
Solving the above equation for .v, we have
3.42 CS E^
X ~ l ~ r V
Jf desired, the constant factors may be united into one term, and
the equation may be written
K E.
With each instrument is furnished a diagram giving values of
K for all pressures, so that the use of the instrument involves
only two readings of a wattmeter and the application of the above
simple cqwilion.
For example, suppose that the use of the instrument in a
particular case gave the values E l  240, and /, = 93,0 for
the absolute pressure 100 pounds per square inch. The value
of K from the diagram is 54.2, and r from the steamtables is 884,
consequently
2dO
3=1 I "*  '  ' E=J O.Q<1
88 4 930
Method of Sampling Steam. It is customary to take a sample
of steam for a calorimeter or priminggauge through a small
pipe leading from the main sicampipc. The best method of
securing a sample is an open question; indeed, il is a question
whether we ever get a fair sample. There is no question bill
that the composition of the sample Is correctly shown by any of
the calorimeters described, when the observer makes tests with
proper care and skill. It is probable that the best way is to
lake steam through a pipe which reaches at least halfway across
the main steampipe, and which is closed at the end and drilled
full of small holes. Il Is better to have the samplingpipe at
the side or top of the main, and it is better to take a sample
from a pipe through which steam flows vertically upward. The
samplingpipe should be short and well wrapped to avoid
radiation.
CHAPTER XI.
INFLUENCE OF THE CYLINDER WALLS.
IN this chapter a discussion will be given of the discrepancy
between the theory of the stcamcnginc as detailed in the previous
chapter, and the actual performance as determined by tests on
engines. It was early evident that this discrepancy was due
to the interference of the metal of the cylinder walls which
abstracted heat from the steam at high pressure and gave it out
at low pressure. In consequence there followed a long struggle
to determine precisely what action the walls exerted and how to
allow for that action in the design of new engines. The first
part has been accomplished; we can determine lo a nicety the
influence of the cylinder walls for any engine already built and
tested; but as yet all attempts to systematize the information
derived from such tests in such a manner that it can be used
m the design of new engines has been utterly futile. Conse
quently the discussion in this chapter is important mainly
in that it allows us to understand the real action of certain
devices that arc intended to improve the economy of engines,
and to form a just opinion on the probability of future im
provements.
As soon as the investigations by Clausius and Rankine
and the experiments by Ilcgnault made a precise theory of
the steam engine possible, it became evident that engines used
from quarter to half again as much steam as the ad ia ha tic
theory indicated, and in particular that expansion down to
the back pressure was inadvisable. An early and a satis
factory exposition of these points was made by Ishcrwood
after his tests on the U. S. S. Michigan, which arc given in
Table III.
199
INKUJUNCK OK THK CYUNUKK WALLS
TAIM.K III.
TKSTS ON THK KNfilNK OK TUK U. S. S. MICHIGAN.
OVUNIWK PUMKrKW, ,*d INfllKHJ HTHtlKK, K VWf.
Ily ChlctKnKlncrr IHIIKUWWW, Resetircliat !n llxl>erlir>itai Stenm
Duntllnn, hiiu
Cuttiff
Revolution* HT iiilnutr
Holler prrawuir,
KT
1 1 U mi i IP lc r, Inrhen of nifnury .....
Vnrtiuni, Inclita uf mrn ury ......
Strum KT Itnnw (niwrr jtrr Imur, iiuiU
I'cr rent of wnlcr In rvUmlrr t nlcnw .
1.
71
1 t/u
JO.fl
11.
7/m
Jfi.l
.1.1
'5.1
4/u
'71,
.137
In the firm >JUT tin Jnl cronomy /or thw engine ww 33.
pounds inHlcntl of 36.5 pounds tin nilfiilatcd )>y the expression
deduced on
U.O.H MICHIGAN
nl 60
OnllMf* Jj*w04 of HAM))
77 (', ( q l  Ay,  qj
:.)( fur iht> HiuiinvronHiirnpiitm /or a noncon
dueling engine with
cnmplcic expansion,
Thia result was ob
Uiincd with cutoft at
fourninths of the
slrolu which gave a
terminal pressure ol
one pound above the
atmosphere,
Tinmanner of the
vfirliiiionoflhcatcam
consumption with ihc
" cuioft Is clearly
shown by Fig. 51, in
which the fraction of stroku tit culoff fa ttikcn for absclssm and
the atcumeonhumptionti us ordlniitoH.
Ot
Km. ii.
INFLUENCE QK THE CYLINDER WALLS
2OI
To make the diagram clear and compact, the axis of abscissa:
is taken at 30 pounds of steam per horsepower per hour. An
inspection of this diagram and of the figures in the table shows
a, regularity in the results which can be attained only when tesls
arc made with care and skill. The only condition purposely
varied is the cutoff; the only condition showing important acci
dental variation is the vacuum, and consequently the back
pressure in the cylinder. To allow for the small variations in
the backpressure Ishcrwood changed the mean effective pressure
for each test by adding or subtracting, as the case might require,
the difference between the actual back pressure and the mean
backpressure of 2.7 pounds per square inch, as deduced from
all the tests.
An inspection of any such a scries of tests having a wide range
of expansions will show that the steamconsumption decreases
as the cutoff is shortened till a minimum is reached, usually at
i to stroke; any further shortening of the cutoff will be accom
panied by an increased steamconsumption, which may become
excessive Jf Ihc cutoff is made very short. Some insight inlo
the reason for this may be had from the per cent of water in the
cylinder, calculated from the dimensions of the cylinder and the
pressures in the cylinder taken from the indicatordiagram.
The method of the calculation will be given in detail a little later
In connection with Hirn's analysis. It will be sufficient now to
notice that the amount of water in the cylinder of the engine of
the Michigan at release increased from 10.7 per cent for a cutoff
at 14 of the stroke to 45.1 per cent for a cutoff at & of the
stroke. Now all the water in the cylinder at release is vaporized
during the exhaust, the heat for this purpose being abstracted
from the cylinder Avails, and the heat thus abstracted is wasted,
without any compensation. The walls may be warmed to some
extent in consequence of the rise of pressure and temperature
during compression, but by far the greater part of the heat
abstracted during exhaust must be supplied by the incoming
steam at admission. There is, therefore, a large condensation
of steam during admission and up to cutoff, and the greater part
INKM/KNCK OK THK CVUNDRK WALLS
of Ihc steam limn condensed remtuns in the form of water and
docs little if anything lowiird producing work. This may De
scon by inspection of the mhlc. of results of Dixwcll's tests on
page 370. With jmliiralcd Hlctun ami with cuioff at 0,217 of the
stroke, 53.3 per cent of live working substance in the cylinder
wan water. Of this lo.K per cent, wus relivaporatcd during ex
punsiun, and 32.4 PIT cent remained at release lobcrcCvaporatcd
during cxlmnsl. When the cultifT was lengthened to 0.689 of
lire .slrnkc, llicre wus a?.y per mil of wuiw at cutoff and 23.9
per cent ul release. The stulenunl in percentages gives a
correct idea of Ihc preponderating influence of the cylinder walls
when the cut off in unduly .shortened; it is, however, not true
lluit ihere is more comleimlion with a nhorl than with a long
culnff. On llu* ronirnry, there is more waler condensed in
the cylinder when ihc rulnft is long, only the condensation
does nol (ncrcnac us fust ti do the weight of alcam supplied to
the. cylinder nnd llie work done, nnd consequently the conden
sation liua a less effect.
Graphical RoprcBcntatlon. 'I'hc divergence of ihc nctua!
expansion line from the
ndinhaiic line can be
shown in a sinking manner
hy plotting ihc former on
the icmpcralurcontropy
diagnvin ua shown In
WK 5^ which is con
structed from the Indicator
diagram in Fig. 51, shown with the nxea of /.oro pressure and
xero volume clrnwn in the imual manner, allowing for clearance
and for (he prcaaurt of the atmosphere.
[n order ui unclcrinkc this conafruciion ihu weight of slw
per stroke. W nn determined from the test of Ihc engine during
which the diagram.* were taken, rmml be determined, and the
.weight of slcam W a caught in the clearance must he computed
Tram the pressure nnd volume/, (he, beginning of compression.
The dry steam line (Fig. 5 J> ' drawn by the following process:
Km. ,*.
GRAPHICAL REPRESENTATION
203
a line ae is drawn at a convenient pressure, and on it is laid off
the volume of W I W pounds of dry steam as determined
from the slcamlablc lo the proper scale of the drawing. Thus
if s e is the specific volume of (he .steam at the prowre />, l)if
volume of steam present if dry ami .saturated would be
(W I W ) s..
Rut the length of the diagram L, in inchc.s is proportional lo
the piston displacement D in cubic feel. The latter is obtained
by multiplying the area of the piston in square ftrt by flu wlmlu
in feet. For the crank end (he net arm of the pwton i.s lo br
allowing for the pistonrod. Consequently tin* proper ul
representing the volume is obtained by nmltiplytuK by ' , Ki'viiiK
(W I W ) A
s . ..^ .
and of this all except s IH a constant for which a numerual result
can be found.
The diagram shown by Fip;. 52 was taken from ihe head end
of the highpressure cylinder of an experimental engine in the
laboratory of the Massachusetts fnRtflutc of Technology. The
value of W { W 9 was found lo IK; 0.075 of a pound; the platan
displacement was 1.103 cubit: fuel, and Ibc Irnglli of Die tHn^rnm
was 3.69 inches; consequently
W ) '<
. ^o/._ , 4 , a [j r .
The line ae was drawn at no pouncla nlisoluie fit which s * \M
cubic feet; the length of the lino ae wwt connrqut.nlly
0.251 X f.8fi r.aa inch.
Neglecting (he volume; of (he water present, the volume of
steam actually present bore the flame ratio to the volume of the
steam when saturated, that ac had lo ae. This nvc in the /wire
at c
ac o.Qii
X't ICOT "~ tm ~^~l* px, Q fj I
ae
304
INFLUENCE OF THE CYLINDER WALLS
MO
.11 O.M,9A
To plot the point e on the Icmpcrulurconirony dit
Fiff' 53i wt  inft y fid ll' c temperature at 90 pounds ab
namely, 320 F., (ind on a line with thai temperature ns ai
nalc we may interpolate between the lines for constant
of .v. Other poir
be drawn in a )ikt
ncr, and the curve
be sketched in; s
that (he steam co
to yield heat lo ihi
der walls from cut"
in reached on Fig.
pcrhiips a trifle
Beyond c the sic
ci'iveH heat from tl
until exhaust opcr
The same feature in exhibited in ]')/?. 53, by draw
udiabalic line xdn from the point of cuiotT. The point a
located by multiplying the length ae t which represents the
of .steam in the cylinder when dry by (he value of x aft
Imlic expansion from the point of rutoft . This po
readily included in the preceding investigation, no that x,
determined. Locating n on the temperatureentropy d
' ; '8' S3i wc mn y { ' mw tlirciiiKh il 'i vcrticitl constant cntr
and note where it culs the lines rorrcsjwnding lo the
lines like ac in I'ig. 52, and inler[>olale for the valu<
For example, the entropy at n in Fig. 53 appears to
and at 320 I 1 '., which corresponds lo go pounds, (his
line givca by interpolation 0.78, so that the length of ad
0.78 X 1.23 r* o.p$.
In this discussion no attempt is made lo distinguish the
which may be in contact with the wall from the rcma
Blcam and water in the cylinder. Tn reality that moia
furnished the heal which the cylinder walls acquire
admission, and it abstracts heal from the walls during th
KIRN'S ANALYSIS
305
sion. The mixture, moreover, is not homogeneous, because the
moisture on the cylinder walls is likely to be colder limn the
steam, though naturally it cannot be warmer.
Finally, the indicatorpencil is subject to a friction Ing llml
operates lo produce the effect shown by Figa, 53 and 53 und in
liable lo exaggerate them. That is to my, thu pencil draws IL
horizontal line and lends to remain at the same height after (he
steampressure falls. It then lets go and falls sharply aomo
little time after ihc valve 1ms closed at culolT. AftcrwnrclH il
lags behind and shows a higher pressure than it should.
Hirn's Analysis. Though the methods jiml illiiHlrnttil
give a correct idea of (he influence: of the walls of tin cylinder
of a steamengine, our firsl clear insight into Ihr. nrlinn f the
walls is due lo Him,* who accompanied hix expuiiiirm by rjimii
titativc results from certain engine te.Hls. Thu .sl/mmnil of hi*
method which will be given hero ia derived from a menmir by
DwelslwuvcTSDcry.f
Let Fig. 54 represent the cylinder of a HlMimenfflno And (lie
diagram of iho actual cycle. For sake of Blmplk'lLy the diagram
is represented without lead of admiasion
or release, but tltc equations lo be deduced
apply to engines having either or 1ml h.
The points i, 2, 3, and o are the points of
cutoff, release, compression, and admission.
The part of the cycle from o lo r, that in,
from admission to cutoff, is represented
by a; in like manner, b t c, and r/ represent
the purls of the cycle during expansion,
Pia.
exhaust, and compression. The numbers will be unccl .. ..
scripts lo designate the properties of thu working fluid under
the conditions represented by the points indicated, nncl the
letters will be used in connection with the operations! inking
place during the several parts of the cycle. Thus at culiifT tlic
* Bulletin >h la Sac. hid. ik Multiffme, rS/j; Thtorh A fa/mitten* tt f.i ( 'baiw.
vol. II, 1876.
 Revue uiiherselh des Mtnas, vol. vlll, p. 363,
206
INFLUENCE OF THE CYLINDER WALLS
pressure is p t , and the temperature, heat of the liquid, heat of
vaporization, quality, etc., arc represented by / q lt r v x lt etc.
The external work from cutoff to release is H\, and the heat
yielded by the walls of the cylinder due to rcSvaporation is Q$.
Suppose that M pounds of steam are admitted to the cylinder
per stroke, having in the supplypipe the pressure p and the
condition x; that is, each pound is x part steam mingled with
i  .v of water. The heat brought into the cylinder per stroke,
reckoned from freezingpoint, is
Q = M (q + xr]
053)
Should thu steam be superheated in the supplypipe to the
temperature / then
Q = M (r + q + ffdfl ...... (154)
for which a numerical value can be found in the temperature
cnlropy table.
Let the heatequivalent of the intrinsic energy of the entire
weight of water and steam in the cylinder at any point of the
cycle be represented by /; then at admission, cutoff, release,
and compression we have
7,= (M
/ 3 = (M
+.%vO; ...... (156)
f *y> a )j ...... (157)
in which p is the heatequivalent of the internal work due to
vaporization of one pound of steam, and M is the weight of
water and steam caught in the cylinder at compression, calculated
in a manner to be described hereafter.
At admission the heatequivalent of the fluid in the cylinder
is /, and the heat supplied by the entering steam up to the point
of cutoff is Q. Of the sum of these quantities a part, A.W Q) is
used in doing external work, and a part remains as intrinsic
energy at cutoff. The remainder must have been absorbed by
HIRN'S ANALYSIS
the walls of the cylinder, and will be represented by Q a , Hence
(?"<? I /,/, 4 W n .
From cutoff to release the external work W L is done, and at
release the heatequivalent of the intrinsic energy is / 3 . Usually
the walls of the cylinder, during expansion, supply heat lo the
steam and water in the cylinder. To be more explicit, some
of the water condensed on the cylinder walls during admission
and up lo cutoff is evaporated during expansion. This action
is so energetic that 7, is commonly larger limn /. Since licat
absorbed by the walls is given a positive aign, the contrary sign
should be given lo heat yielded by them; it is, however, con
venient to give a positive sign to nil the. interchanges of heal in
the equations, and thon in numerical problems a negative sign
will indicate that heat is yielded during the operation under
consideration, For expansion, then,
Qt,  /,  /, AW lt
During the exhaust the external work W e is done by the engine
on the steam, the water resulting from the condensation of the
steam in the condenser curries away the heal Mq^ the cooling
water carries away Die hcut G (q t  ?,), nd there remains at
compression the heatequivalent of intrinsic energy T y So that
6*  A
G
 A W c ,
in which % is the heat of the liquid of the condensed steam, and
G is the weight of cooling water per stroke which has on entering
the heat of the liquid </ and on leaving the heal of the liquid q t .
During compression the external work W, t is done by the
engine on the fluid in the cylinder, and at the end of compression,
i.e., at admission, the heatequivalent of the intrinsic energy is / .
Hence
It should be noted (Fig. 54) that the work W n is represented
20 g INKI.URNCK OK TtlK CYI.1NDKR WALLS
by the area which i* hounded by the slnim line, the ordinatcs
through o ami i and by the \mw lint. And in like manner the
works W h W et and II',, are repiisenled by nrcns which extend
to the base line. In working up Ihe analysis from a test the
line of absolute zero of pressure may be
drawn under the atmospheric line asm
Kig. 55, or proper allowance may be
made after ihe calculation has been made
with reference to the atmospheric line.
For convenience these four equa
tions will lie assembled as follows:
Q.Q I'. V'lH'..
Q. /, V '">'  (
Oi /j /I HI'.' 
(iS9)
(160)
/UK, . (161)
(162)
A consideration of Ihw eijuiUioiiH shows that all the quanti
ties of the righihnnd member* can bu obtained directly from
tin* proper (iliHerviiliwiH of nn engine lest except the several
values of /, UK: heat rtLuivnleniH "f Ihe intrinsic energies in the
cylinder. These qurmiilies are represented by equations (155)
to (158), in which there, are five unknown quantities, namely,
#o *n x v x v um * '^'
Let Ihe volume of the clearance splice between the valve and
the piston when It to nt the end of its Kiroku be K n ; and let the
volumes dc'vdopcvl by (Ju piston up U> cutoff and release bo
V l and K 3 ; finally, let V t reprntenl ihe corresponding volume
HI romprewiiim. Tlic spccilic volume of one pound of mixed
water and steam in
v * xit ( ff,
and the volume of A/ poumln is
V ^fv " M (xu } v).
TURN'S ANALYSIS 30<;
At the points of admission, cutoff, release, and compression,
(M I ;V/
There is suflicicnt evidence UmL the slcnm in the cylinder
at compression is nearly if not quite dry, and an there is rom
parativcly little steam present at tlml lime, there cannot he
much error in assuming
$ 3 ** i.
This assumption gives, by equation (166),
in which % is the density or weight ol one iuliU: fttot (tf dry
steam sit compression.
Applying this result to equations (263) to (365) Hives
. . (iftt;)
We arc now in condition to find the vnluoa of f t , /,, /,, nncl
/ and consequently can calcululc all iho Interclmngo f hntt
by equations (159) to (162),
Should the value of x in any case appear to lie greater tluin
unity it indicates that the steam is supcrhatlccl; thin may liai*cn
for * , and then as the weight of steam 4/ ii relatively suniill,
and as the superheating is usually slight, it will be nuflirkni in
make * e equal to unity. It is unlikely to be ihc case for ,v, or .v,,
even though the steam is strongly superheated in the aLcnnvpljw;
should the computation give a value slightly larger than unity
the steam may be assumed to be dry without appreciable error,
and the work may proceed as indicated. If in the use of very
strongly superheated steam a computed value of x t is appre
ciably larger than unity, we may replace the equation (166) by
V + V, = (M + M )
where v 2 is the specific volume of superheated steam; conse
quently
v .Y1L.
2 M + M
By aid of the temperatureentropy table we may find (by inter
polation if necessary) the corresponding temperature / 3 and the
value of the heatcontents or total heat. The heatequivalent
of the intrinsic energy is then equal to this quantity minus Ap t v y
In the diagram, Fig. 54, the external work during exhaust is
all work done by the piston on the fluid, since the release is
assumed to be at the end of the stroke. If the release occurs
before the end of the stroke, some of the workj namely, from
release to the end of the stroke, will be done by the steam on the
piston, and the remainder, from the end of the stroke back lo
compression, will be done by the piston on the fluid. In such
case W e will be the difference between the second and the first
quantities. If an engine has lead of admission, a similar method
may be employed; but at that part of the diagram the curves of
compression and admission can be distinguished with difficulty,
if at all, and little error can arise from neglecting the lead.
The several pressures at admission, cutoff, release, find
compression are determined by the aid of the indicatordiagram,
and the pressures in the steam pipe and exhaust pipe or con
denser are determined by gauges. The weight M of steam
supplied to the cylinder per stroke is best determined by con
densing the exhauststeam in a surfacecondenser and collecting
and weighing it in a tank. If the engine is noncondensing, or
if it has a jetcondenser, or if for any reason this method cannot
be used, then the feedwater delivered to the boiler may be deter
mined instead. The cooling or condensing water, either on
the way to the condenser or when flowing from it, may be weighed,
or for engines of large size may be measured by a metre or gauged
by causing it to flow over a weir or through an orifice. The
several temperatures (*, C f , and t k must be taken by proper ther
mometers. When a jetcondenser is used, and the condensing
water mingles with the steam, / 4 is identical with t k . The quality
x of the steam in the supplypipe must be determined by a steam
calorimeter, A boiler with sufficient steamspace will usually
deliver nearly dry steam; that is, x will be nearly unity. If
the steam is superheated, its temperature I, may be taken by a
thermometer.
Let the heat lost by radiation, conduction, etc., be Q e ; this
is commonly called the radiation. Let the heat supplied by
the jacket be Q f . Of the heat supplied to the cylinder per stroke,
a portion is changed into work, a part is carried away by the
condensed steam and the cooling or condensing water, and
the remainder is lost by radiation; therefore
(171)
The heat Qj supplied by a steamjacket may be calculated
by the equation
g> j") . . . . (172)
in which m is the weight of water collected per stroke from the
jacket; tf, r', and <f are the quality, the heat of vaporization,
and the heat of the liquid of the steam supplied; and <?" is the
heat of the liquid when the water is withdrawn. When the
jacket is supplied from the main steampipe, oc' is the same as
the quality in that pipe. When supplied direct from the boiler,
x' may be assumed to be unity. If the jacket is supplied
through a reducing valve, the pressure and quality may be
determined either before or after passing the valve, since throt
tling does not change the amount of heat in the steam. Should
the steam applied lo the jacket be superheated from any cause
we may use the equation
f) , lit tr 1 l./i'.l. f (I ' . l'\ n'l\ ,
\/j ' in \r rj r Cp (,'.[ i ) if \ , , . (171}
in which r 1 and q' are the heat of vaporization and heat of
the liquid of saturated steam at the temperature /', and /'' f s
the lempcrature of the superheated slcam,
Equation (171) furnishes a method of calculating the heat
lost by radiation and conduction; hut since Q t is obtained by
.HUblmclion ami Js small compared with the quantities on the
righthand side of the equation, the error of this de terminal ion
may be large compared with (> itself. The usual way of deter
mining Q for an engine with a jacket is to collect the water
condensed in the jacket for a known time, un hour for example,
when the engine is at resl, and then the radiation of heat per
hour may be calculated. If it be assumed thai the rate of radia
lion at rest is ihc same as when the engine is running, ihc radia
tion for any test may be inferred from I he time nf the lest and the
determined rate. Ikil Ihc engine always loses heal more rapidly
when running than when al rest, so Ihnl this method of
determining radialion always gives a result which is loo
small.
If a steamengine has no jacket it is difficult or impossible
lo dclcrminc ihc rale of radiation. The only available way
appears lo infer the rale /rom Ihnl of some mmilnr engine wiih
a jacket. Probably the best way is lo get an average value o
Q a from the application of equation (171) lo a scries of care
fully made lests.
It is well to apply equation (171) to any Icat before beginning
ihc calculation for Hint's analysis, as any serious error is likely to
be revealed, and so time may be saved.
When Ihc radiation Q a is known from a direct dcterminalion
of the rale of radialion, we may apply Hlrn's analysis to a lest
on an engine even though the quanlilics depending on Ihc con
denser have not been obtained. For from equation (171)
and consequently
Q, /,/ 6  & "I Q 
Thus it is possible u> apply the analysis to a noncon
densing engine or to the highpressure cylinder of a compound
engine.
It is apparent llml the heal Q c , thrown out from the walls
of the cylinder during exhaust, passes without compensation
lo the condenser, and is a direct loss. Frequently it is the
largest source of loss, and for this reason Him proposed to make
H a test of the performance and perfection of the engine; but
such a use of this quantity is not justifiable, and is likely to
lead to confusion.
The heat Q t that is restored during expansion is supplied at
a varying and lower temperature than that of the source of heat,
namely, the boiler, and, though not: absolutely wasted, is used
iit a disadvantage. It has been suggested that an early com
pression, as found in engines with high rotative speed, warms
up the cylinder and so checks initial condensation, thereby
reducing Q a and finally (? also. Such a storing of heat during
compression and restoring during expansion is considered to
act like the regenerator of a hoiair engine, and lo make the
efficiency of the actual cycle approach ihc cfTkicncy of the ideal
cycle more nearly than would be the case without compression.
It docs not, however, appear that engines of thai type have
exceeded, If they have equalled, the performance of slowspeed
engines with small clearance and little compression.
Application. In order lo show ilie details of the method of
applying Hirn's analysis Ihc complete calculation for a test
made on a small Corliss engine in the laboratory of the Massa
chusetts Institute of Technology will be given. Its usefulness is
mainly as a guide to any one who may wish to apply the method
for the first time.
Diameter 01 the cyumirr 8 inches.
Stroke of the piston a feet.
Piston dlaplnccmcnt: crank end o,6ji)i ca. ft.
head end 0.7016 " "
Clearance, per cent of piston displacement:
crank end . 3.73
hcnd end 5.41
Ilollcrprcasiiri' liy KflURp 77.4 pounds,
nanimeter 148 "
Condition of steam, two per cent of moisture,
Kvcnis of the stroke:
Cutoff: crftnk end 0.306 of stroke.
head end 0.330 "
Release at end of stroke.
Compression: crank end 0.013 of stroke.
head end 0.0301 "
Dunilion of the test, one hour.
Tntnl number of revaluilona 360.3
Weight of uteAiii until 548 pounds.
Weight of condensing water used 14,568 "
Temperatures ;
Condensed atonm ', " t4i.i F
Condeiwlng water: cold 'i 5 3 9F
F.
* AnSOLUTB PRRSSURKS, FUONt INniCATORDIAORAMS, AND
PROPRRTIRS OF SATURATED STEAM.
ttmi. HAII Bun.
f>
Cutoff . .
Comnrcaslon .
Admission .
83.6
M!?
aR.i . a
317. a
iBr.i
901.3
864.8
803. a
877..,
3.190
13934
ao.,u.
iR3'll
39. B
333.
aicj.o
813.3
93^
863. 9
.
11.804
a 6. 164
13.664
* Thou vnliios nro tnkon from tho Jlrat edition of the Tables of I'rojwnlos ol
Snturatfid Stonm.
APPLICATION"
2I 5
MEAN PRESSURES, AND HEATEQUIVALENTS OF EXTERNAL
WORKS.
CRANK END.
HBAD Eun.
Man Prtsmrts.
Equivalents of
Work.
Mean Pressure).
Equivalent! of
Work.
Admission ....
Kxpansion ....
87.7
445
148
78.3
3369
3.877
1.836
0.0295
893
4?.i
14.8
21.3
37II
4159
1.847
o. 1104
Compression . . .
VOLUMES, CUBIC FKET.
CRANK END.
HEAD HNO.
At cutoff, V + V,
At release, V t V t
At (he boilerpressure, 92.1 pounds absolute, we have
r =. 888.4, q = 291.7.
The steam used per stroke is
M
2 X 3692
,
= 0.0742 pound.
'^ '
The steam caught in the clearance space at compression, on
the assumption that the steam is then dry and saturated, is
obtained by multiplying the mean volume at that point by the
weight of one cubic foot of steam at the pressure at compression,
which is 0.03781 of a pound.
,, 0.0341 +
* = J ^ J
i n f j
^ X 0.03781 = 0.0019 f a pound;
b = 0.0742 + 0.0019 = 0.0761 pound.
The condensing water used per stroke is
G
14568
2 X 3692
= 1973
fi'l (,\
" A
. . __
* aooigX HiS.Ml 113.664) a.4XKi8.344 +13.664)
TlviR Indlcnicft ilwl the alcam is Bupcrhcnlccl ni admission.
Such niny l)f ihc casr, or llic nppcnmncc may be due to an
error in llic nsaumpllon f dry alcnm fil comprusHion, or to errors
of ubacrvailon. U is convenient, lo ftsaume \\ i.
v.
1 0.0761 X 4 (5190 4 5.307) 63.4 X 4(519 15207)
 0.6336.
V.
3 "" (A/
' '0.0761X4(13.034413.804)
* 0.7088.
.'. /,  4 X 0.0019 [201.5 + 3190 + J 00 ( 8 77'4 "I
^ 2.054.
7,  (A/ IA/J (9, I Vi)i
.'. /,  i X 0.0761 [1*84.6 H 3844 + 0.6336 (813.0+813.3)]
* 60.238.
.'. /, 1 X 0.0761 [317.8+222.0 +0.7088 (864.8 +861.8)]
63.311,
.'. 7  0.0019 (181.1 + 893.2)  3.041
Q a = 86.243 + 2.054  60.238  4 (3.369 +3.711 ) = 24.519,
Q b = 60.238  63.311  } (3.877 + 4159)   709 1 '
Q e = /,  h  M&  C (ft  ?,) + <W e ;
Qp = 63.311 2.041 0.0742 X 109.3
 i973 (5 6 35  21.01) + i (1.836 + 1.847)
=  14.721.
Qa /, /o +^4^;
Q c[ = 2.041  2.054 + i (0.0299 + 0.1104) = 0.157.
Qa Q. +& +Qc +Qj = 2.764.
Also, equation (171) for this case gives
= 86.243 8.110 69.723 (3.54044.018 1.841 0.070)
= 86.243 8.110 69.7235.647 = 2.764.
It is (o be remembered that the heat lost by radiation and
conduction per stroke, when estimated in this manner, is affected
by the accumulated errors of observation and computation,
which may be a large part of the total value of Q e .
Dropping superfluous significant figures, we have in B.T.U.
Q b = 7.1,
Q e = 2.8.
Q  86.2, Q a = 24.5,
Q.   14.7* Qd = 06,
Noting that 5.647 arc the B.T.U. changed into work per stroke
and 3692 the total revolutions the horsepower of the engine is
778 X 5647 X 3692 X s _ i6 IUV
60 X 33000
and the steam per horsepower per hour is
548
16.35
= 335 pounds.
For data and results of this test and others see Table IV.
Effect of Varying Cutoff. An inspection of the interchanges
o heat shows that the values of Q at the heat absorbed by the
walls during admission, increase regularly as the cutoff is
lengthened, and that the heat returned during expansion decreases
at the same time, so that there is a considerable increase in the
value of the heat Q e which is rejected during exhaust. Never
theless there is a large gain in economy from restricting the
cutoff so that it shall not come earlier than onethird stroke.
Unfortunately tests on this engine with longer cutoff than one
third stroke have not been made, and consequently the poorer
economy for long cutoff cannot be shown for this engine as for
the engine of the Michigan.
Hallauei's Tests. In Table V are given the results of a
number of tests made by Hallaucr on two engines, one built by
Him having four flat gridiron valves, and the other a Corliss
engine having a steamjacket. Two tests were made on the
former with saturated steam and six with superheated steam.
Three tests were made on the latter with saturated steam and
with steam supplied to the jackets. These tests have a historic
interest, for though not (he first to which Hint's analysis was
applied, they are the most widely known, and brought about the
acceptance of his method. They have also a great intrinsic
value, as they exhibit the action of two different methods of
ameliorating the effect of the action of the cylinder walls, namely,
by the use of superheated steam and of the steamjacket. In all
these tests there was little compression, and Q^ (he interchange
of heat during compression, is ignored.
Superheated Steam. Stcnm from a boiler is usually slightly
moist, x, the quality, being commonly 0.98 or 0.99. Some boilers,
such as vertical boilers with tubes through the steam space, give
steam which is somewhat superheated, that is, the steam has a
temperature higher than that of saturated steam at the boiler
pressure. Strongly superheated steam is commonly obtained by
passing moist steam from a boiler through a coil of pipe, or a
system o piping, which is exposed to hot gases beyond the
boiler.
H(U)I .Bill
Until in ji[
M'K'W'trj/II
vjtunod 'aini
'MiwMjd'^
liiunott
innin
*O "t
>. in
6 ro
1/1 i~
1^ Q O M K
I. (^O M OQ
sn
in iwj in ci
(i o> i O 4
w
O t* M M
<O "" l00 O
M M M M P
M irtO
tk It N l> \f\
n O >O f >O N
i o> M n in
o *r
O O
MW
aw
O M "O
fi M Q.
I w
g
Superheated steam may yield a considerable amount of heat
before it begins to condense; consequently where superheated
steam is used in an engine a portion of the heat absorbed by the
walls during admission is supplied by the superheat of the steam
and less condensation of steam occurs. This is very evident in
Dixwcll's tests given by Table XXV, on page 271, where the
water in the cylinder at cutoff is reduced from 52.2 per cent to
27.4 per cent, when the cutoff is twotenths of the stroke, by
the use of superheated steam; with longer cutoff the effect is
even greater. This reduction of condensation is accompanied
by a very marked gain in economy.
The way in which superheated steam diminishes the action.
of the cylinder walls and improves the economy of the engine is
made clear by Hallauer's tests in Table V. A comparison of
tests i and 3, having six expansions, shows that the heat Q a
absorbed during admission is reduced from 28.3 to 22.4 per cent
of the total heat supplied, and that the exhaust waste is corre
spondingly reduced from. 21.6 to 12.5 per cent. A similar
comparison of tests 2 and 5, having nearly four expansions,
shows even more reduction of the action of the cylinder walls.
The effect on the restoration of heat Q t during expansion appears
to be contradictory: in one case there is more and in the other
case less. It does not appear profitable to speculate on the
meaning of this discrepancy, as it may be in part due to errors
and is certainly affected by the unequal degree of superheating
in tests 3 and 5. It may be noted that the actual value of Q e in
calorics is nearly the same for tests i and 2, there being a small
apparent increase with the increase of cutoff, which is, however,
less than the probable error of the tests. The exhaust waste Q e
is much more irregular for tests 3 to 7 for superheated steam.
The increase from Si to 87 B.T.U. from test 6 to test 7 may
properly be attributed to a less degree of superheating; the
increase from 66 to 81 B.T.U. for tests 5 and 6 is due to longer
cutoff and less superheating; finally, the steady reduction from
75 to 66 B.T.U. for the three tests 3, 4, and 5 is probably due to
the rise of temperature of the superheated steam, which more
than compensate* for the effect of lengthening the cutoff
Finally in lest 8 the exhaust waste is practically reduced to
/cro by the use of .strongly superheated steam in a noncon
densing engine; tins shows clearly that the exhaust waste Q e by
ilsilf is no erilcrum of the value, of a certain method of using
steam.
Steamjackets. If the walla of the cylinder of a steam
engine, are made double, and if the apace between the walls is
filled with allam, the cylinder is said to he steamjacketed.
Holh barrel and heads may be jacketed, or the barrel only may
have a jarkel; less frequently the heads only are jacketed. The
principal iffccl of a si earn jacket i.s to supply heat during the
vaporisation of any water which may be condensed on ihe
cylinder walls. The consequence is that more heal la returned
to ihe slcam during expansion and the walls arc holler al the
end of exhausl limn would be Ihe case for an unjackclcd engine.
This is evident from a comparison of leslH i and IT in Table V.
.In ufli i only n small part of ihe heat absorbed during admission
is returned during expansion, and by far the larger part is wasted
during exhaust. In test H the, heat relumed during expansion
is equal to twothirds that absorbed during admission, though a
part of this heat of course comes from ihe jackel. About half
aa much ia wasted during exhausl as ia absorbed during admission.
The condensation of slcam is ihus reduced indirectly; that is,
Ihe chilling of ihe cylinder during expansion, and especially
during exhaust, Is in part prevented by ihe jacket, and conse
quently there is less Initial condensation and less exhaust waste,
and in general a gain in economy. The heat supplied during
expansion, though il docs some work, is first subjected to a
loss of temperature in passing from the steam in the jacket to
the cooler water on the walla of the cylinder, and such a non
reversible process is necessarily accompanied by a loss of effi
ciency. On the oilier hand, the heat supplied by a jacket during
exhaust piiSBca with ihe sleana directly into the exhaustpipe.
Il appears, then, that the direct effect of a steamjacket is to
waste heat; the indirect effect (drying and warming the cylinder)
educes the initial condensation and the exhaust waste and often
jives a notable gain in economy.
Application to Multipleexpansion Engines. The application
jf Him 's analysis to the highpressure cylinder of a compound or
miltiplecxpansion engine may be made by using equations
(159), (160), urw ] ( : 6 2 ) for calculating Q a , Q b , and Q d > while
equation (174) m a y be used to find Q .
A similar set of equations may be written for thencxt cylinder,
whether it be the lowpressure cylinder of a compound engine
or the intermediate cylinder of a triple engine, provided we can
determine the value of Q', the heat supplied to that cylinder.
But of the heat supplied to the high pressure cylinder a part
is changed into work, a part is radiated, and a part is rejected
in the exhaust "waste. The heat rejected is represented by
Q+Q t AW Q. ...... (i?5)
where Q is the heat supplied by the steam entering the cylinder,
Qj is the heat supplier! by the jacket, AW is the heatequivalent
of the work clone in the cylinder, and Q e is the heat radiated.
Suppose ihc steam from the highpressure cylinder passes to an
intermediate receiver, which by means of a tubular rchcater or
by other means supplies the heat Q r , while there is an external
radiation Q ra . The heat supplied to the next cylinder is con
sequently
Q'  Q + QJ ~ AW  Q* + Qr  Qr. . 
In a like manner we may find the heat Q" supplied to the
next cylinder; for example, to the lowpressure cylinder of a
triple engine.
It is clear that such an application of Kirn's analysis can be
made only when the several steamjackets on the high and the
lowpressure cylinders, and the reheater of the receiver, etc.,
can be drained separately, so that the heat supplied to each
may be determined individually.
Table VI gives applications of Hirn's analysis to four tests
on (he experimental tripleexpansion engine in the laboratory
of the Massachusetts Institute of Technology.
334
INFLUENCE OF THK CYLINDER WALLS
It will be noted lhal the steam in the cylinders becomes drier
in Us course 1 through the engine, under the influence of thorough
steamjacketing with steam nl boileriiressure, and is practically
dry nl release in the lowpressure cylinder. All of the tcsu
show superheating in the lowpressure cylinder, which is of
course possible, for the steam in the jackets is at full boiler
pressure while the steam in the cylinder is below atmospheric
pressure. The superheating was small In all cases not more
than would be accounted for by the errors of the tests. The
exhaust waste Q," from the lowpressure cylinder in the triple
expansion tests is very small in all cases less than (wo per cent
of the heal supplied to the cylinders. The apparent absurdity of
a positive value, for Q," in two of the tests (indicating an absorp
tion of heat by the cylinder walls during exhaust) may properly
lie attributed In the unavoidable errors of the teat.
In the fourth lest, when the engine was developing 120.3
horsepower, there were 1305 pounds of Hitam supplied to [he
cylinders in an, hour t and 315 pounds lo the Hlcam jackets; so
thai the steam per horsepower per hour passing through ihe
cylinders was
1305 * iao..i ia.86 pounds,
while the condensation In the jackets was
345 + 130..1 " 3.87 pounds.
So that, as shown on page MS. the n.r.u. per horse power per
minute supplied lo the cylinders by the entering sleam TOS
ini. i, while the jackets supplied 40.6 n/r.u., making in nil
311.7 n.r.u. per horse power per minute for the heatconsumption
of Ihe engine. In the same connection it was shown that Ihe
thermal efficiency of the engine for ibis lest was 0.183, while
the efficiency for incomplete expansion in a nonconducting
cylinder* corresponding lo the conditions of the test was 0.222;
so thai the engine was running with 0.824 of the possible efficiency.
In light of this satisfactory conclusion some facts with regard to
the teal arc interesting.
APPLICATION OF IIIRN'S ANALYSIS
TABLE Vf.
225
APPLICATION OF IIIRN'S ANALYSIS TO THE EXPERIMENTAL
ENGINE IN Til!' EMIGRATORY QV THIS MASSACHUSETTS
INSTITUTE OF TKCIINOLOCJY.
TRIFLEEXPANSION; CYUNOKH UMUCTKRS, Q, ift, ANII ai tttctiKa ; STROKE, 30
KRS, Q, ift,
INCHKS.
Traas AM, .Sto. ^/<fc//. Kitgrs,, vol. xtl, p. 740.
Durnltott of (cat, tnitititea .
Total number of revolutions
Revolutions per minulu . . . . .
Steamconsumption dining leat, Mm.:
Passing through cyliwlws
Condensation in h.p. jacket
in first receive rjnckcl
fn fnler. jacket . . .
In second rccoivcrjw:kl
In l.p. jackal . .
Total
Condensing wutcr for lest, ll>n.
Priming, by calorimeter .
Temperatures, Fnhronhcli:
Condensed s ten in . . .
CondcnslngwnU'r, cold
Conrlcnsfngwnicr, Jiot .
Pressure of the ntmosplicr
barometer, Iba. >or nq. in.
Holler pressure, Iba. jicr s({. in,
luio
Vacuum in condenser, liu
cury
EvcrUsof iltofllroke:
Hlghpressuro cylinder
Cutoft, crank end
liertd end ....
Rclctise, bolli unda
Compression, crnnk end ,
licnd end . . .
Jjilcrmctlidle cylinder
Cutoff, Ixilli ends
Uclctisc, lx)lh ends
Compression, cnink end
bend end . . .
Low pressure) cylinder 1
Cutoff, crnnft ond
lieflt) end , , ,
Release, both cmla
I.
ir.
nr.
IV.
. . , ,
60
s*w
SK.I
flo
5^
8j i
60
5 'H a
60
5M
cat, Ibis,:
Cl ...
1*03
57
61
He
"57
5<>
64
I33.f
ao
( }
05.0
r.3S
J
73
L . . . .
ij
50
S3
iS
51
87
Kl8
i.iSn
)H. ...
aa8.(7
33T86
aoa^,j
20353
. . . .
.11.9
43.1
96 6
43
J0 53
43.8
is, 1>y ihc
111. ftllSO
M.8
Mfl
14.7
1.1.7
} o( nier
*S77
a 39
o3S
1 . . . .
0.05
0.05
O.O4
O.Oi)
1 . . . .
0.03
0.03
O^O^
0.03
0.18
0.18
INFMJKNCK OF THK CYUNDKR WALLS
TAUUK VI Continued.
lisiiluir hrr^urr* in lli< yllmlrr,
IK nl in IN nT B' III.!
Hiltliiirrsuturr i yUrnUr
11.
IS"
?v
.17 ^
XS.1
M
ao>
JJ.K
i j.d
t J..
IS
57
A. j
10.7
I 1,0.
8.i;
.(
Q.(
7.
7
0
q
HI IV.
38.8 138,3
to. J 140,6
447 48.4
'"57 ^9.8
S4 S Ci.o
7.a 3i.s
86.7 57.8
38.6 40.9
,106 43.6
11.7 160
H.Q 16.0
303 33.^
33.3 1 31.1
3>1.3 1 90.;
I2.I 13 3
V' 51
5.1) 6.4
46 47
7.00 8,19
11 .33 1 11.09
R..11 9os
073 
Q.(Jl 10.64
10.37 n.H
HA'
<M5
7.S.1
'!t4
JO.t
i J. i
5' 4
4..1
S7
ft. ft
la.ft
to.K
77
8.0
U.1
o.(
7.5
?
rciiil>rewtl"M, trunk rll<l . .
MlmMun, \ rank rwl
Irfivvcrruuirr < vllnilrr
UrlniWt t ra\\"k n\t\
i rattk rin! 
HraliiulvaUitl* nf rtlrrnnl Wiifk
H.T.U., frtun rctuiit Indii ni
Utah prr&iurt 1 tylliultr
ttunnu n(tm(aftlUi
IturluK rxinnniun (
tlurliiu (timprrtoliiiip
liilcrmrcllnlr tvllmlrr
DurliiK in tin Union,
/III/, iwnk mil ....
fHirinu cxiwn^innj
ij.i;
rj.3
__ .
APPLICATION OF HIRN'S ANALYSIS
TABLE VI Continued.
227
I.
II.
III.
tv.
Intermediate cylinder
During exhaust,
10,18
During compression,
0.78
0.84
Lowpressure cylinder
During admission,
A\V t ", crank end
833
8.QJ
8. 19
8.66
During expansion,
6.81
6.86
6.87
7.87
During exhaust,
5.08
c.ofi
"!.o8
5.16
4.81
During compression,
Quality of the steam in the cylinder.
At admission and nt compression
the steam was assumed to be dry
and saturated:
Highpressure cylinder
0.848
0.875
Intermediate cylinder
* # *
* # *
* * *
Iowprcssurc cylinder
A( cutoff A'I" .
* f #
* * *
* * *
* * *'
* * *
Inlerchanges of heat between llic
steam and Ihe walls of the cylin
ders, in 11. T. u. Quantities
affected by the positive sign are
absorbed by the cylinder walls;
quantities afTectcd by the negative
sign are yielded by the walls: . .
Highpressure cylinder
Brought in by steam . Q . . .
During admission . . . Qt . .
During expansion . . . Qt, . .
During exhaust . . . . Q, . .
During compression . . Q* . ,
Supplied by jacket  . Qj . .
7,ost by radiation . . . Q,
First Intermediate receiver
Supplied by jacket . . Q f . .
Lost by radiation . . . () . .
132.93
= 351
18.69
 8.36
o.4S
4S&
1.50
4.93
0.58
13077
23 43
19. 28
 7.22
o. 5 i
408
1.52
5.20
0.58
141. t i
17.49
iS33
 35
019
239
i.$4
56?
59
14984
1493
1403.
 2.38
0.52
2.50
t54
595
0.50
* Superheated.
238
1NKLUKNCK UK T11K UYUNUER WALLS
TAJH.K VJ Continual,
I.
11.
111.
IV.
Jnlrrmnlitiir i ylimlrr
^
HmviRlH In by siriitn . y  .
i.lt. KJ
UiJ.dt
>377
1.16.64
1 1. 11
UuriK cxtmiialon . . . (_'' .
in.ftj
i U u .
1 ii . n.l
oj
'30.10
jji
(Hiring rximuti . . . . (V
O. Jj
'57
31.88
Uurlitft (tirti"rcftilnn . . ^'/ .
Suiillr(( liy jiukrl . . (>/ .
o.ll
O.Kj
n5'
750
0.6l
707
si
1.4 ml i)' r<nlliHl"ii . . . ^V . .
J  15
j , ,iK
Set mill liilrrmcillntr rci river
. Ji S'
Supjiliril liy Jnikft . . ^'/'
IJMI liy miiifiilim . . V*'
 JO
I. Ju
I. ol
i . jj
1.3?
1.33
1.W
IXIH "MHifr r yllwlrr
1
Hrmiglii In liy Pimm . t>"
During nclml&sliin . . . (.V
'';;*!
i .10 . 50
S.i?
H7JJ
I Hiring cxintiialoii . . . ^'*"
ij.S<
7 (")
n . fi<
 10 M
f hiring oxniuiit .... (J,"
J..S.I
'M
 1.14
O.I I
Ihirinu umiirra'tttii . . ^'j"
O.l.l
o.ot
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0.00
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y.riH
ft. jo
7. II
7M
Ijitnt t>y mill ui lii ii . t't
1 .11
1 i o
.1 . je
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if
Hy (frrUfiilnary ir^ii . 3C('
1 f,ti7
10. JO
IO.JI
(0 ,
liy ntimllini (170 . . .
U.ftK
10. M)
75
8.0)
I'covrr ftnn mummy;
1
Hrwl riitlvAlcnu n( wurk \<rt
M.l'. .yllti'lir . . . . A\\' .
,,,,
.,VI
u. 17
fittrrtn. i vllmlrr. . . . AW
7.U
f'.ijs
777
8.41
1.. 1'. lyllmtvr /Ml""
y.f I
1 o . of i
10. B 7
Tulnh . ....
tf,. JH
J5..V1
3?. Hi
""^H"
TotJt) h*fll fiirnlshnl ly jai \tet9 . .
J? ^
J?,fU
J77'
*
Uimriliullnn n( wtirb
Il'fifi (ift*iiirf f vldtrlrr . , . i
t .ceo
t.(*o
1.00
f.CO
Init<rme<Unip tyUndrr
O.HI
a. Bj
0.85
o.SS
i.i i
1. Ji
l.IQ
1.14
Ilnrw(tiiWrr
ItM.iJ
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"31
190.3
Siritm iwr H P. *r Iwuf ...
1 4 . 65
i I  A '
1300
'3M
iri'.r. j^r If I'. r mtmiir . ,
M7
Ml
336
h will IK nutitl ilmi fiir tri IV i.g.8. n.r.u. per stroke are,
bmuf{Ul in liy tlu htcum Mipplictl to ilu hiffhprcflBurc cylinder
nnd llinl a8..j; n.t.u, ]n*r slrtikc iirr HUppIU'd hy llic siciimJftckeU!
and tfmi, funlur, jcjvj n.T.U, lire chnngid into work while 10.35
nrc riuiiutnt. Thu<t it 'a(i(ienn* llmi (lie jckcla furnished almost
o much Jirat was rcquiml ic dn nil i)u? work developed. Of
llir l>cal furnthhrd by ihr jnrkriit jiitinrlhing moro than ft third
QUALITY OF STEAM AT COMPRESSION
229
was radiated; the other twothirds may fairly be considered
to have been changed into work, since the exhaust waste of the
lowpressure cylinder was practically zero.
Quality of Steam at Compression. In all the work of this
chapter the steam in the cylinder at compression has been con
sidered to be dry and saturated, and it has been asserted that
little if any error can arise from this assumption. It is clear
that some justification for such an assumption is needed, for a
relatively large weight of water in the cylinder would occupy
a small volume and might well be found adhering to the cylinder
walls in the form of a film or in drops; such a weight of water
would entirely change our calculations of the interchanges of
heat. The only valid objection to Hirn's analysis is directed
against the assumption of dry steam at compression. Indeed,
when the analysis was first presented some critics asserted that
the assumption of a proper amount of water in the cylinder is
all that is required to reduce the calculated interchanges of heat
to aero. It is not difficult to refute such an assertion from
almost any set of analyses, but unfortunately such a refutation
cannot be made to show conclusively that there is little or no
water in the cylinder at compression; in every case it will show
only that there must be a considerable interchange of heat.
For the several tests on the Him engine given in Table V,
Hallaucr determined the amount of moisture in the steam in the
exhaustpipe, and found it to vary from 3 to 10 per cent. Professor
Carpenter* says that the steam exhausted from the highpressure
cylinder of a compound engine showed 12 to 14 per cent of
moisture. Numerous tests made in the laboratory of the
Massachusetts Institute of Technology show there is never a
large percentage of water in exhauststeam. Finally, such a
conclusion is evident from ordinary observation. Starting from
this fact and assuming that the steam in the cylinder at com
pression is at least as dry as the steam in the exhaustpipe, we
are easily led to the conclusion that our assumption of dry steam
is proper. Professor Carpenter reports also that a calorimeter
" Trans. Am. Soc. i\fccft. F.ngrs., vol. xif, p. 8n.
23
INFLUENCE OF THE CYLINDER WALLS
test of steam drawn from the cylinder during compression
showed little or no moisture. Nevertheless, there would still
remain some doubt whether the assumption of dry steam at
compression is really justified, were we not so fortunate as to
have direct experimental knowledge of the fluctuations of tem
perature in the cylinder walls.
Dr. Hall's Investigations, For the purpose of studying
the temperatures of the cylinder walls Dr. E. H. Hall used a
thermoelectric couple, represented by Fig. 56. / is a cast
iron plug about threequar
ters of an inch in diameter,
which could be screwed lr*to
the hole provided for attach'
ing an indicatorcock to the
The inner end of the plug
which was assumed to act as
To
FIG. 36.
cylinder of a slcamengme.
carried a thin castiron disk,
a part of the cylinder wall when the plug was in place,
study the temperature of the outside surface of the disk a nickel
rod N was soldered to it, making a thermoelectric couple.
Wires from / and W led to another couple made by soldering
together castiron and nickel, and this second couple was placed
in a bath of paraffinc which could be maintained at any desired
temperature. In the electric circuit formed by the wires joining
the two Ihermoclcctric couples there was placed a galvanometer
and a circuitbreaker. The circuitbreaker was closed by a
cam on the crankshaft, which could be set to act at any point
of the revolution. If the temperature of the outside of the dbk
S differed from the temperature of the paraflmc bath at the instant
when contact was made by the cam, a current passed through
the wires and was indicated by the galvanometer. By property
regulating the temperature of the bath, the current could be
reduced and made to cease, and then a thermometer in the bath
gave the temperature at the surface of the disk for the instant .
when the cam closed the electric circuit. Two points in the
steamcycle were chosen for investigation, one immediately
after cutoff and the other immediately after compression, since
CALLENDAR AND NICOLSON'S INVESTIGATIONS
2 3 I
they gave the means of investigating the heat absorbed during
compression and admission of steam, and the heat given up
during expansion and exhaust.
Three different disks were used: the first one half a millimetre
thick, the second one millimetre thick, and a third two milli
metres thick. From the fluctuations of temperature at these
distances from the inside surface of the wall some idea could be
obtained concerning the variations of temperature at the inner
surface of the cylinder, and also how far the heating and cooling
of the walls extended.
The account given here is intended only to show the general
idea of the method, and does not adequately indicate the labor
difficulties of the investigation which involved many secondary
investigations, such as the determination of the conductivity of
nickel. Having shown conclusively that there is an energetic
action of the walls of the cylinder, Dr. Hall was unable to continue
his investigations.
Callendar and Nkolson's Investigations. A very rcfmcd
and complete investigation of the temperature of the cylinder
walls and also of the steam in the cylinder was made by
Callendar and Nicolson * in 1895 at the McGill University,
by the thermoelectric method.
The wall temperatures were determined by a thermoelectric
couple of which the cylinder itself was one clement and a wrouglit
iron wire was the other element. To make such a couple, the
cylinder wall was drilled nearly through, and the wire was
soldered to the bottom of the hole. Eight such couples wero
established in the cylinderhead, the thickness of the unbroken
wall varying from o.oi of an inch to 0.64 of an inch. Four pairs
of couples were established along the cylinderbarrel, one near
the head, and the others at 4 inches, 6 inches, and 12 inches
from the head. One of each pair of wall couples was bored to
within 0.04 of an inch, and the other to 0.5 of an inch of the
inside surface of the cylinder. Other couples were established
along the side of the cylinder to study the flow of heat from the
* Proceedings of the Insl. Ctv. Engrs., vol.
1NK1.UKNCK OK T1IK I'VUNllKR WALLS
heiid toward llu uank end. Thr Umpinuuru ol Ihc sleam
near \\w iylindrr head was measured l>y a platinum thcrmomciet
tapulilf of militating urmrlly rapid tlm illations of temperature
Tlit uigim " s <il for UK invesiigJilioMs WHS highspeed
engine, with a halamed slide valve tnnirolU'tl by a fly. wM
governor. During ihr invisligiiliunH the enioft Wis sci at a
fixed point lalitHil OIK liflh Mrokr). and the speed was controlled
iMitrutlly. My ihi addition of a u(Vaiciu amount of lap io
pfivcnl UK vatvt front taking sinim at liu ttank end Ihc engine
was rniulc silicic at ling. Tin normal fpccd of the engine was
from .jo in i/o rrvuhuion*. JKT ininutr. Thcdinrociorrfihe
tyllndiT wan to."; imhiH and tin himke of the piston was n
im IUT. Tlu* flt'iiram r wai ttn JUT nnl if tlu piston displftccmem.
From the indualor iliiigmnih an unalyiH, nearly equivalent to
llirn'a imuly. 1 *^, ohuwnl tlu* Inal yicldnl to or ttikcn from tjic
wiilU tiy thi* Mnim; *m (lit oilitr hnml (In thermal mcflstircmcnts
\r nit iruliudion of ihr JHJI! gninnl )>y or yielded by the walls,
an* ulun in ihr futluwinK lahli'j nnd considering ifc
of ihr invi'^iigaiion ml UK* lurgi ullowtmcc forlcakngc,
tin* toniurdumr mul In* adnuttnl to he very muia factory,
VII.
iNM.i'1'.N'ft
TW.
Ml.
] rni: CVLJNDKR.
if t'iv.
IV.
tit r.^u
(wl
j^di tnittuir
ilD't lc4<ft l t
ll(4 ftl*B1 IP!
psw ij ittld '
4) J I 1" 4
IK 4 , W '
" 14
t '
Mf , "
^
i " ^
' ,i
f> n
t ,& t i
4U
j old
. <,
I
>\ ( "
'*i/
 & *!
. f
t
,,
41
' (HI
1, '
UftS
t , t ta
,, . .
.*. i 4
"1
41 r>f
'."*.
*
 '*'' "
;;i
' Cl FlOlft
71 4
gi o
o 10)4
o o$j6
o.oioo
0.040! i O.tj)
0.04)4 !(*
0.0090 ' O.Ml
0.0066 1 a.Hj
I 0,0041 0t4.
0.0ll6 0.09
'7.11 M
jft0 ' I) I
CALLENDAK AND NICOLSON'S INVKSTIGATION.H
'33
The platinum thermometer near the cylinderlira*! .shownl
superheating throughout compression, thus amfirmintf our inVn
that steam can be irc.ited as dry and snluratrd )it I In* beginning
of compression. This same thermometer fell rapidly during
admission and showed saturation practically up lo filloff, its
of course it should; after ailoff it began again In show n trm
peraturc higher than that clue to tin indicated pressure, whit h
shows that the cylinderhead probably evaporated all I hi moist wr
from its surface soon after cutoff. Jf this conduMim is rnrrn I.
there would appear to be little advantage from steam jarkriititf
a cylinderhead, a conclusion which is borne out by tests im I In*
experimcnUi! engine at the Massachusetts Institute of TirlmnluKy.
The following table gives the areas, temperatures, and lire limi
absorbed during a given test by (lit vitrloiw mirfiurn rxidsiil to
steam at the end of the stroke, i.e., I he clennuicc
CYCLICAL FIKATAnsC}f<l''I'fON KO14 C'UCAKANC'K NKKFACKK
POII loin of surface consMnreil.
Ara
of inirlact,
aqiiftrg fail.
Mean
itmitemlutt,
V,
*"Vtl.
Cover face, 10.5 Inchw (Hnmetcr . .
I'iston fnto, 10.5 fnchci diameter. . .
"05
MU
s
The heat absorbed by the aide of the cylinder wall unnivmtl
by the piston up to 0.25 of the stroke was estimated let lir 5$
B.T.U. per minute, which added to the above sum given 585 II.T.II.;
from which it appears that 90 per cent of the comU'nwUinn '">
chargeable to the clearance aurfaccH, which were (.'xrcplioimlly
large for this type of engine. Further InHpccllon HIWH thai
the condensation on the piston and the barrel Is mu.h morn
energetic than on the cover or head. For example, the face of
the piston absorbs no B.T.U., while the face of the cover absorbs
only 68 B.T.U., and the sides of the cover and of the barrel, each
3 inches long, absorb 79 and 123 B.T.U. respectively. This
relatively small action of the surface of the head indicates in
another form that less gain is to be anticipated from the appli
cation of a steamjacket lo the head than to the barrel of. a
steamengine.
The exposed surfaces at the side of the cylinderhead and
the corresponding side of the barrel arc due to the use of a
deeply cored head which protrudes three inches into the counter
bore of the cylinder, and which has the steamtight joint at the
flange of the head. It would appear from this that a notable
reduction of condensation could be obtained by the simple expe
dient of making a thin cylinderhead.
Leakage of Valves. Preliminary tests when the engine was
at re.st showed that the valve and piston were tight. The valvo
was further tested by running it by an electric motor when the
piston was blocked, the stroke of the valve being regulated so
that it did not quite open the port, whereupon it appeared thai
there was a perceptible but not an important leak past the valve
into the cylinder. There was also found to be a small leakage
past the piston from the head to the crank end.
But the most unexpected result was the large amount of leakage
past the valve from the steamchest into the exhaust. This was
determined by blocking up the ports with lead and running the
valve in the normal manner by an electric motor. This leak
age appeared to be proportional to the difference of pressure
causing the leak, and to be independent of the number oC
reciprocations of the valve per minute. From the tests thus
made on the leakage to the exhaust, the leakage correction in
Table VII was estimated. Although the investigators concluded
that their experimental rate of leakage was quite definite, It
Would appear that much of the discrepancy between the indicated
and calculated condensation and vaporization can be attributed
to this correction, which was two or three times as large as ihc
LEAKAGE OF VALVES
weight of steam passing through the cylinder. Under the most
favorable condition (for the seventh test) the leakage wa,s
0.0494 of a pound per stroke, and since there were 97 stroke?
per minute, it amounted to
0.0494 X 97 X 60 = 287.5
pounds per hour, or 32.6 pounds per horsepower per hour, so
that the steam supplied per horsepower pet hour amounted to
56.4 pounds. If it be assumed that the horsepower is propor
tional to the number of revolutions, then the engine running
doubleacting will develop about 44 horsepower, and the leak
age then would be reduced to 6.5 pounds per horsepower
per hour. Such a leakage would have the effect of increas
ing the steamconsumption fr.om 23.5 to 30 pounds of steam per
horsepower per hour.
To substantiate the conclusions just given concerning the
leakage to the exhaust, the investigators made similar tests on
the leakage of the valves of a quadrupleexpansion engine, which
had plain unbalanced slidevalves. The valves chosen were the
largest and smallest; both were in good condition, the largest
being absolutely tight when at rest. Allowing for the size and
form of the valve and for the pressure, substantially identical
results were obtained.
The following provisional equation is proposed for calculat
ing the leakage to the exhaust for slidevalves:
i i
leakage =
t
where I is the lap and e is tbc perimeter of the valve, both in
inches, and p is the pressure in pounds in the steamchest in
excess of the exhaustpressure. The value of the constant
in the above equation is 0.021 for the highspeed engine used by
Callcndar and Nicolson, and is 0.019 for onc tcst cach of the
valves for the quadruple engine, while another tcst on the large
valve gave 0.021.
This mutter of iliu leakage lo the exhaust is worthy of further
investigation. Should it be found lo apply in general to slide
valv and pistonvivlve endues it would RU Ear towards explaining
the superior economy of engines with separate admission, and
cxIwuHl'vnlves, und especially of engines with automatic drop
a\U>lT viilvwt which are practically ut rest when dosed. \\
may IK remarked ilml the excessive leakage for the engine
(ijiti'd upp(.'iirn lo In due to tlu 1 sl/e und form o[ valves. The
valve wan hirKi 1 HO its l<> Rive fl K ( l portopening wlicn the cutoff
with Hhorienecl l>y llw Hywheel governor, and was faced off on
both aklwi c> llial it could Midi' IjiUvuun the valvescat and a
massive covrrpliLie. The coverplule was rocossccl opposite
tilt HlenmporlH, ami llie valve was constructed so as lo admit
wlt'iun til both IHITK; from one ihc sleam ptissed divccUy into the
cyiinder, and from the ollur it pnaswl into the coverplate and
thence Into tin 1 HUamport. Thi type of valve 1ms long been
urnl tin Vlu 1'orUr AUeu and Uw SiiulKUtllne engines; the former,
litiwcvcr, lw st'paraU 1 Hlcam and exIuiUHlvulvcs. Such a valve
IUIH a very long perimeter which iiccounW for the very large cftcd
of \\w leiikiiKC.
Oillemlnr anil NicoUon ron.sidtr that the leakage is probably
in the form of water which is formed by condensation ot stenm
on Uw surface of the valvescat uncovered by the valve, and say
further, that it h modified by the condition of lubrication of
the valveawil, OH oil hinders the leakage.
CHAPTER XII.
ECONOMY OF STKAMKNGINRS.
IN this chapter an attempt is made to give an idea of the
economy (o he expected from various types of steamengines
and the effects of the various means that are employed when
the best performance is desired.
Table X gives the economy of various types; of engines, and
represents the present slate of the art of steamengine construc
tion. It must be considered thai in general the various engines
for which results arc given in the table were carefully worked up
to their best performance when these, tests were made. In
ordinary service these engines under favorable conditions may
consume five or ten per cent more steam or heat; under unfavor
able conditions the consumption may be half again or twice as
much.
All the examples in the table arc taken from reliable tests; a
few of these tests arc stated at length in the chapter on the influ
ence of (he cylinder walls; others arc taken from various series
of tests which will be quoted in connection with the discussion
of the effects of such conditions as steam jacketing and com
pounding; the remaining tests \vill be given here, together with
some description of the engines on which the tests were made.
These tables of details arc to be consulted in case fuller informa
tion concerning particular tests is desired.
The first engine named in the table is at the Chestnut Hilt
pumpingstation for the city of Boston. Its performance is
the best known to the writer for engines using saturated steam.
Some engines using superheated steam have a notably less steam
consumption ; but the heatconsumption, which is a better criterion
of engine performance for such tests, is little if any better. The
first compound engine for which results are given, used 9.6
237
TADI.K X.
EXAMPLES UK STKAMKNUINK Kl'ONOMY.
Ty r ot
lrnvill iillniirtK enflinr nl ('limliuil 11111
Sul if r nilltrliti'ic 'it AuCMhurt{
Kxtrnmrnliil rnulnc< nl lltr
JiiiliUiU* nf Yrihriulony
M urine rriftliif limn
Mnrinr
mtlwrUealcd
Rrtlllfrtlccl
Mnrlur vrififnr Rush . . .
Mnrinr cnjtlnr }>uti Vnmn
SIntitr
Curtis rriRlnt 1 wl Crruwil . . .
Ciirtitui tltlf wUlmiil Jiukcl . .
IliirrU Cnr l(w niftdtr nt C'lni (imnll
Mnrine cnRinu tiallalhi ....
Simple ruglnen, niiiicnnilpnqin( :
C'urlliui PHKl'lP itl Crruwil . , .
CorUss cnijfoti wlihmiL Jn kct . .
llflrHeCarliaa engine nl t'lm Irmull
IlattittC'ttrlt^ PtiKlnp nt \\w Mnwntlttiiwiib
liisliiuleof 'i'cclinolofjy
l)tmtaclli m
Mrr niii[i nt llie
tif Tn hnolttftX
at reduced JMIWCT
Stcnrn nnil frnl (lump tin llir .\tlnnea full*
nt minted IKIVVCT
50, 1 1
5"
7^
tX.r,
7'
fK)
.W
CM
hi
fu
*i0
*ca
'17
H5
1.17
'HJ
fit
fts
yf
77
7ft
fii.l
37i
'IS
n.a
n.. i
13
13
'5.
n!l
31.
Ifi..
II).
tfJ
It.
J..
'5
313
30,
548
j'.S
pounds of Blcnm ftnd IQQ II.T.U. ptr minute, the gnin being
hnrdly more limn the variation that might he attributed lo differ
cncc in apparatus, etc. The Chcainul Hill engine, which was de
* Slrttkra icr mlnuic.
signed by Mr. E. D. Lcavitt, has three vertical cylinders with their
pistons connected to cranks at iao. Each cylinder has four
gridiron valves, each valve being actuated by its own cam on a
common camshaft; the cutoff for the highpressure cylinder is
controlled by a governor. Steamjackets are applied to the
heads and barrels of each cylinder, and tubular reheaters are
placed between the cylinders. Steam at boilerpressure is sup
plied to all the jackets and to the tubular reheaters.
TABLE XI.
TRIPLEEXPANSION LEAVITT PUMPINGENGINE AT THE
CHESTNUT HILT, STATION, BOSTON, MASSACHUSETTS.
CYL1NDEK DIAMETERS T37, 24. ,175, AND 39 l^CHKS; STROKE 6 PERT.
By Professor K. F. MILLKB, Technology Quarterly, vol. ix, p. 72.
Duration, Jiours ...................... 34
Totnl expansion ........................ si
Revolutions per minute ..................... 50.6
.Si earn pressure abort atmosphere, pounds per square inch ...... 175. 7
Barometer, pounds per square inch ......... ...... '49
Vacuum In condenser, inches of mercury .............. 27.25
Pressure In high and intermediate jacket ficid rehcalers, pounds per
square inch ......................... 1 75 . y
Pressure in lowpressure jacket, pounds per square inch ....... 996
Horsepower .......................... 5757
Steam per horsepower per hour, pounds .............. 11.2
Thermal units per horsepower per minulc ............. 3 43
Thermal efficiency of engine, per cent ............... 20.8
Efficiency for nonconducting engine, per cent ........... aS.o
Ratio of efficiencies, per cent ................... 74
Coal per horsepower per hour, pounds ............. i . i.}6
Duty per 1,000,000 B.T.U .................... 141,855,000
Efficiency of mechanism, per cent .... ........... 89 . 5
The Sulzcr engine at Augsburg has four cylinders in all, a high
pressure, an intermediate, and two lowpressure cylinders. The
highpressure cylinder and one lowpressure cylinder are in line,
with their pistons on one continuous rod, and the intermediate
cylinder is arranged in .similar way with ihc olhcr lowpressure
cylinder. The engine hits iwti cranks at right angles, between
which in i hi lly wheel, grooved far ropedriving. Kach cylinder
hiis four double acting poppetvalves, actuated by eccentrics
links, iiinl lever* frm n valveshaft. The admissionvalves
re i oiKrcilIcrl by the governors. Four teats were made on this
engine, us recorded in Table XII,
TAIII.K XU.
THll'l.l: KXI'ANSKIN MdKIWlNTM. MU.1,KNfJINR.
K iMAUKri^WS j.ij. ,\.\.$, AND TWf) OK 51/1 INfllKH; BTKOKK 78.7
INi'ltKH.
Hulli l,y SutJkK "( Wlnirrlltur, Mlvhrl/t tin Vtrfins Deulsclier Iiigtniei ire
vul, \l, ji. 5j.j,
Urviillllliinn r inlniUr .....
Slmm'irrruuiir, niini'li wr wjltnrr Im It
Vrttuuni, Imlnu <i( tnrrdiry . , . .
?r hnrBFiKiwcr KT Imu
Mcnn fr fniir tcotn ....
CVial njr Imrw jwiWf r KT limir,
\rean lir four (eaia ....
Sirnm fwr IKJII nil nf fnl .
n..A
jHiitrn
t,,io
1
II
III
IV
*$,.,>
' 5 ft  ' H
56.18
S6.l8
i '1 5 ' *
117 .0
i,8.,
T100
inJI' 4 " 1
37.30
37.30
1850
1$ t()
i ' 5.1
ii ..()
ll. .19
"33
' .17
..1"
13Q
1.19
H. 7 H
R..IO
R...7
0.6]
The lest fin (he cxpcrimrninl engine ul the Massucluisclts
Institute of Trcluuitti^y is fjuoled here because its efficiency
nncl t'concimy nro chosen for clUruftaiun in Chapter Vtll. Taking
Sis [terformunce as a basin, il appears on page i.8 that with 150
pounds holler pressure and 1.5 pounds absolute backpressure
auch an engine may be expected to give a horsepower for 11.5
pounds of steam, from which it appears thai under the same
conditions Us performance compares favorably with the Suher
engine or even the Lravltl engine.
TABLF, XIII.
MARINEENGINE TRIALS.
By Professor ALEXANDKR S. \V. KENNEDY, Proc. hist. Mech. Engrs., 18891892;
summary by Professor H. T. BF.ARK, 1894, p. 33.
1
u.
$
"3
u
C.
30
ViUe de 
Douvres. j
Meteor.
3
o
C.
C.
50. t
72
9
105.8
472
6.0
2977
30.8
367
8 '.97
T.
41
70.1
48
!0.6
= 73
33
1994
15.0
2.OI
7.46
139
T.
21 .t)
57
30
i ft
19.0
<5r.r
o. 70
1.8
134
250
1.46
9iS
70 r
S3
33
M
rt i
57
36
10.9
6.1
S6
80.5
351
34
IO22
568
2.J?
38
S (com pressure above nimosphcrc, pounds per square
Pressure in condenser, absolute, pounds per srjuare
Ii nek pressure, absolute, pounds per scjuarc inch . . .
380
2.66
7.9(1
603
398
2.9
740
Weight of machinery per Jiorsc)Qivcr, pounds . . .
The engines of the S. S. /owa have an unusually large expansion
and give a correspondingly good economy. The engines of the
Meteor and of the Brookline give the usual economy to be
expected from mediumsized marine engines. Table XIII
gives details of tests on the engines of the first two ships
mentioned, together with tests on compound marine engines.
Table XIV gives tests on the engine of the Brookline. It
appears probable that (he relatively poor economy of marine
engines compared with stationary engines is due to the
smaller degree of expansion, which is accepted to avoid using
large and heavy engines.
ECONOMY OF J
TABL;
TESTS ON THE ENGINE
CYLINDER DIAMETERS 23, $5, AN
By F. T. MILLER and R, G. II
Duration, hours
Revolutions per minute ....,.,
Steampressure, pounds per square inch
mmphere
Vacuum, Inches of mercury . . . , .
Horsepower
Steam per honepower per hour, pounds
Coal per horsepower per hciur, pounds
B.T.U. per horsepower per minute .
The horizontal millengine w;
engines in Table X, is a tandi
arc given in Table XXVI on j:
superheated steam is tht %
with saturated steam is a trifle
engine,
TABL
COMPOUND LEAVITT PUMP]
KEN!
CYUNDftR 37.2 AMD
By F. W, BEAM, TVww. Am. $
AUTOMATIC
XVII.
ENGINES OF THE V. S. RKVKNUK
i Inttif 4
l)iamrtt*rf ryiii
Stroke t inche* .,...*
Duration, hour* , , ,
Revolutions er ttilmilf
Stramt*JUH* lit ftt
Vaeuumy itidtru*f mm wty
Total * ...
4 am!
^7
55
71
<*>, i
jei.s
6. a
Steam frr
The details of tin* tt*sts on tlu* V* S. Revenue 4 Hit
awl GuUatin nrr Riven in Table XVII, as made ab
a iKMtrcl of mivitl engineers to determine the advantti
pounding and uteam jat'ket^t. Thrtv <ther e
tested at the time, but they were of older tyj>es
interesting.
A of teg
to by M, F. are
XXX aid XXXI, are in 'I
ami i
in the
244
ECONOMY OF
The details of the tests on t
cinnati, together with tests on 1
Table XVIII.
TABU
DUPLEX DIRECTACTINO FIRE
INSTITUTE OK
TWO STKAIICYUNDRttS 1 6 INCH:
par
minute.
of fttrokii.
West*
length
01 utrokt*
KMC.
Httam
IMrtssure
by f*u.
W
u . 40
10, IO
^8.,
114
tt.70
11.07
55, ei
IK)
1 1 . 49
11.07
Si4
135
ic. fio
II . IO
5J,li
156
lo.go
ic.aft
47 J
193
lO.Ot)
10.31
45.6
175
11.77
u . 70
4^,6
'
11.74
u . 66
4ft. S
JWIWI
ft.;
u,,
u.
41.
TABt:
TKSTH OF AUXILIARY KTKA^
By P. A, Engineer W. W, WHITK,
OF IMPROVING ECONOMY
* The two on the directacting flrepumj
Massachusetts Institute of Technology are fr
XIX, and the on the few! and firepump on the M
are given In Table XX* Both sets of tests show the 1*3
consumption of by such pumps when running i
powers. The latter In Interesting on accoi
light that it on the way that coal in consumed
when at or lying in harbor.
Uttitods of The expci
of to build is the noncondensing engine 1
valve this type is only where economy
importance, or where* simplicity in thought to be it
Starting with this as the wasteful type of engine,
in economy may he by one or more* of the
devices;
i.
2.
3.
4,
5. Compounding.
6.
7*
246
ECONOMY
by the ideas that have be
of thermodynamics, and i
the steamengine; the four
in this category as a means
range effective. It has b
the cylinder of metal wh
energetic action on the ste
attempts to approach the
noncondensing engines, a]
to be gained by increask
devices enumerated (inc
jackets, and superheating
been applied to diminish
and allow us to take advai
appears at first sight tha
the first category, as it c
range between the steamp
but the steam in the cyli]
and it is better to consid<
cylinder condensation.
It is interesting to cons
steamjackets were used b]
he was limited in pressure
OF RAISING STEAMPRESSURE
that the theory has sometimes been misapplied, has
erroneous opinion that the steamengine has been d
without or in of thermodynamics. And further, I
all the then available has had a tendency tc
the.it importance, and It the more desirable to ;
as given above.
It Is now commonly considered that the steamen
been to full development, and that there is litt
to be expected; in fact, this <
was a or two ago, when the triple engi
at 150 to 175 pounds by the gauge, was perfect*
most is the use of superheated steam
now that effective and durable superheat
Experiment and experience have settl
well the for the various methods of improving
&ad of a fair conservative presentation to wh
will be few We will, therefore,
as briefly ai may be, ami give the
which they tie
In to out the to be obtained by
as we will only
of the with the best perfor]
the comoound beinff riven all the adva.nl
248
ECONOMY C:
If f is taken to be 100 F
300 ? and 400, the values of t
But the influence of the cy
Improvement unless we resort
studying Delafonci *s tests
Figs. 57 and 58 on 25
sumption is plotted as ordin*
cutoff, each curve lett
was maintained while a serti
resents without ii
steam in the jackets* Thos
with condensation! and thus
condensing. Inspection of '
tion in steamconsumption,
35 pounds by the to 6
without a Jacket, but i
to 80 and 100 pounds
sumption. The i
the limit for noncondenHinj;
on Fig. 58 are not quite KO
figures give the following a
simple of
TESTS
m the could be determined* The engine
with and without in the jacket, both condensing
condensing, and at various from 35 to i<
above the of the atmosphere. The effect
and the friction of the also obtained b;
frictionbrake on the
The piping for the* wits so that
drawn from a or from
boiler only the test. making
engine, which had been for a sufficient tim
to a condition of equilibrium, was supplied i
from the supply. At the for beginnh
the supply off and was takei
boiler during until the end of the test, an
from toiler The of tl
was at the end of the test the wi
boiler was its level be cl
At the end of a test the was to
noted at the The for f
the test for the
at the end was in a As
in the and In the spc
was the of tl
250
ECONOMY i
58 represents tests with ste
densation, at 50 pounds be
curves are the per cents oj
steamconsumptions in poui
HORIZONTAL COR]
CYLINDER DIAMETER 21.65 INC
BARREL (
BY F. DELAFON]
Number
of test.
Duration,
minutes.
Revolu
tions per
minute.
Cutoff in
per cent o
stroke.
i
a
60
105
60.0
58.6
6
3
7 !
594
9
4
36
5 H
12.5
5
73
58.8
55
6
7
II
61.5
599
6.7
8
39
58.1
12.5
9
120
598
75
10
IOO
593
83
ii
90
59.8
10.5
12
sss
58.0
14
13
50
591
18
14
94
596
5
15
102
59.6
55
16
40
59.4
it. 5
17
40
60
14
18
91
58.3
59
19
90
59.5
9
20
75
590
155
DKLA POND'S TESTS
results for individual arc represented by dots.
which or near which the curves are drawn. As there
a few in any a fair curve representing the
be drawn through all the points In most The <
HORIZONTAL CORLISS KNU1NK AT CRBU8OT
JIC*$ 4 j,jt INCIIVS
ONIVJ NttNKtWttPNXfttt*.
II? R im^AWNi*, lift Aft***, iKK$.
Number <*
Dumffoi
tut*
mlnuiM
I
7
3
SS
3
1 IJ
4
So
i
60
I
30
M
9
60
10
60
II
30
12
70
13
0
14
0
3
71
i**'?
lit. 4
61,1
ff ,4
6t.t
ir i rtnf til
17
jo
si
U
tf>
iH
aj 
.17
i
j
toi.o
IJ]M
717
76,7
77*5
77,0
7,
7*1,0
it, i
1,5
1.7
ii
47S
181.5
217
til
30Q
X
204
toi
radically from the
at so early a cutoff is u
probable error of
CONDENSATION
on Fig. $8. It not appear worth while to try t<
curve to reprencnt teats.
The complement of raising the steam
m
m
ECONOM
of either pair of results v
25 per cent, which would
of brake tests for this engi
ical efficiency when runn:
it was only 0.82 when ]
brake horsepower per h
indicated steam by the m
pairs of results became f 01
noncondensing 26.9, and
with steam in the jacket,
from condensation was
26.9 22.1 _
26.9
The gain from condens
and the conditions of ser
to twenty per cent. Cle
vacuum than with a poor
feature which should be <
pressure; when the condit
effective pressure is large
advantage of maintaining
when the mean effective
be best illusfrafeH wifh
OF
pressure for a pumpingcngine or millengine may b<
18 pounds per .square inch, ant! a difference of o
vacuum (or half a pound of harkprc&mre) will be
to nearly three* per cent in the power; on the other hai
engine is likely to have a redueed mean effective ]
forty pounds per square inrh t md compared with it i
of one Inch of vacuum LH equivalent to 11 little more th
cent In any the In economy due to a
meat in vacuum in approximately equal to the reduc
absolute in the divided by tl
A very important is out in this cli
the from namely, that the real ga
mined by the consumption for
The only for th<
power (as is clone) in that the bral
to and impo
was out on 144, a true of
of the in B.T.U.
per hour. But was not
by the are foj
of one the
obtection to it in
256
ECONOMY
In this case the larger cngin
capacity of the smaller one,
the absolute size of the
is little if any advantage In
limits of practice*
But the from
as will be apparent front tl
in Table X are for c
standards. '
and of the use of
from or s
and such are pos
engines*
Bipuaslofiu  There are
can be
is by the o
by the of
0'
which can be
mcnts; compound and tri
the tin
employed. The \
a triple, or
COMPOUNDING
The total for a compound or triple engi;
obtained In two ways: we may use a large ratio of
cylinder to the small cylinder, or we may use a short
the cylinder. The two methods may be
by the two Lcavitt mentioned In Table X; tl
the to the cylinder of the compound
Louisville, Is a km than four, and the cutoff for
Is a little less than onefifth strok
other hand, the triple engine at Chestnut Hill has a ]
than for the ratio of the cylinders, an
cutoff for the cylinder at a little more 1
So an ratio as eight would nc
for a compound engine, but ratios of five 01
used, not with the best results.
Marine utuially have comparatively little to
gion both for com{xmnd ami for triple engines, and coi
are unable to with an economy equal to that for
the type of valve gear which the feel c
to nut* fa little adapted to give the results.
question whether there is not room for impro
both direct if mH.
The efficacious method ^
258 ECONOMY OF STEA1
and two lowpressure cylinders was i
ships. Many triple engines have t
which with the highpressure and
make four in all. Again, some trip
pressure cylinders and two lowpr
intermediate cylinder, making five ir
Two questions arise: (i) Under \
several types of engines be used ? an
pected by using compound or triple e:
Neither question can be answered
From tests already discussed and
are given in Table X, it appears that
best results were attained with the fol
engines about 175 pounds by the gai
145 pounds, and for simple engines
for engines with condensation. Ne
obtained for a compound engine v
and on the other hand the simple en
with equal advantage. The informa
engine is sufficient to serve as a reli
least room for discretion concerning
pound and triple engines. There wi
,of serious disappointment if the follow
COMPOUNDING
pounds with a steamjacket ; with an allowable variation
pounds. For a noncondensing compound engine we
as the preferred pressure about 175 pounds, but our tes
include this case, ami the figure is open to question.
little, if any, occasion for using tripleexpansion nono
engines.
About ten ago aa attempt was made to introd 1
steam at about 250 p
marine in conjunction with watertube boilc
can be built for high pressures; but more recen
has to to triple engines even where the
has a highpressure for of developing a la:
per ton of machinery, or for any other purpose.
For convenience in trying to determine the gain f;
pounding, the following supplementary table has been <
f tea *4 kwaltt.
mmtitf* , .
Stenm fit*? ht
tt.TMf. iiMt*
.
twntr, mun<U .
Slmpit
il
III
ao
11,8
2 6p ECONOMY OF STEAME
Compound and triple engines have b(
to marine work, where for various reason
well be used. . Taking the engines of the
in the following supplementary table to i
we can determine the gain from compoi
Data and Results.
Revolutions per minute . 5
\ ! Steam pressure by gauge 6
f i. Total expansion
Steam per horsepower per hour, pounds .
Gain from compounding,
22 18.4
= 0.16.
22
Gain from using triple engine instead o
I
EXPERIMENTAL ENGINE
Properly the comparison for finding the gain from cc
ing should be cm thermal units per horse power pe
but the data for such a comparison are not given fc
engines, and as all the engines have steamjackets, the co
of steamconsumption* is not much in error.
StaamJacktts. As has already been pointed ou
of the influence of the cylinder walls, the
of a is to dry out the cylinder during
without unduly reducing the temperature of the cylint
and thus the condensation during admission. T
indeed supply some heat during expan
that Is of secondary importance, and the heat i
with a thermodynamic disadvantage. The principal
to supply which is thrown out in the exhaust
all lost in of a simple engine; in case of a compou
the heat supplied by a jacket during exhaust from
cylinder is intercepted by the lowpressure
and is not ll would clearly be much me
to the cylinder! of nonconducting rr
that A of the true acti<
has a tendency to prejudice
device, this prejudice has in many c
by the has come from indi
262 ECONOMY OF
the piping being so arranged
360
840
830
800
280
280
\
\
\
\
S\
V
\
s
\
\j
^
V N
X
\
4 "S,
\
EXPERIMENTAL ENGINE
steamjackets on the barrel and the heads, and <
supplied to any or all of these jackets at will. T
densed in the jackets of any one of the cylinders is c
pressure in a closed receptacle and measured. <
receivers were also provided with steamjackets;
provided with tubular reheaters so divided that c
thirds, or all the surface of the reheaters can t
steam condensed in the reheaters is also collected
in a closed receptacle.
The valvegear is of the Corliss type with vacv
which give a very sharp cutoff. The highpress
mediate cylinders have only one eccentric and w
"consequently cannot have a longer cutoff than hal
the control of the drop cutoff mechanism. Th<
cylinder has two eccentrics and two wristplates, and
valves can be set to give a cutoff beyond half
governor is arranged to control the valves for an;
cylinders. Each cylinder has also a handgear :
its valves. For experimental purposes the gove
control only the highpressure valvegear, when
running compound or tripleexpansion. The
used for adjusting the cutoff for the other cylinde
usuallv the cutoff for such cylinder or cylinders i
264
ECON01V
Clearance in per cent
Highpressure cylindei
Intermediate ' '
Lowpressure ' t
Results of tests on tto
order to form a triple
XXIII, and are represei
cutoff of the highpress
consumptions of therma
ordinates.
The most important
this engine is of the adi
steam in the jackets. 1
purpose: (i) with steal
receivers, (2) with steai
heads and barrels, (3) w
the cylinders only, and (<
The most economical
steam in all the jackets
the receiver jackets, as i
There is a small but dis
the receiver jackets also
EXI'KKIMKNTAh ENGINE
TABLE XXIIL
TRIPU>KXPANSION KXI'KKIMKNTAt. KMCUMK AT
rHUSKTTS INSTITUTE Of TKCHNOUx
TVtf'ff. .l
Aw.
.
' ! '4vittt ttwrtl 1ft pt i
n*
I 1 ti trill
1 1 J ^ **
I *;ii t & f i 1 i
*
1
j * s ^ ' 1 , 4 ! j ^ j g
1 ! * ^ r i ir , } ** * i 1 4 f l Ii
h/'r^ :(:,!*
Ctrl
I
i
1
o
a ti i iS , <* d* v , J; } A f
j
a
I i
f
i Hi l * 4*^ 1 t f# 4 * * ft
< i
1 1
j B
mi i* f ii  4 M 4 ; . i a A
** i
1 1
i
ft *j 1 11 1 1' 1 ii 41 >.* ft , ' H ^
? i
1 i
4 
tt %i / *' 14* l * i it i , I * ft
4 *
I ,
iff
uj (y % ^j M" W 1 * I . 4  IH 4 ,
if ft; i * * 4 ll t ' ' f li*<,
l 1
* ,
II
1st
r &
 M f 4 14^ i <* * ,<, i j t a ;
W ft' rf  ' / i t * t 4
5
II f
1 f 1^
M
7
KT ',1 4 ij *i* i fc * it < 'MI;
*
i?;;,,
4 III ii ij iif J ! * * i it i
** Mj << l s i  4 * 1 tr* t i " M *j
: ij
t
lt
ii* 
ttt A*\ it* ll lf <^ M , ' f f, , 4 / f ^, ,
i 41
lj
III *' M * I4 *,**. ,y  ^ ., , j f , , 4
1 MI( to ii in i * i l<f .  ; ^ /i f . j
It 4
f 
*4
Hi ii' 4? 4, i4^ 1 14 / <>. f I * 4 r 4 *l 
j i
t** 1
I? B
WiJ #*<ljif^% l* f * 4 *j* ! **'j
 1 1
iii
IMWWM*
^ I? *l * M< *' ** 1 H / * ft f. 2 i (
j * ^ f B
1 ,'
i
f ,i
4 w! o i f ^ fc ! , v t
4 /
i*

^4 i*t' M *ii <4I 1 * 4 , M i * ' , *
W ^'
*H
ill
*i ii; ** /' ! 1 M *' ' n * i * i ? r
J l! *! 1  i *< . ** , , ,!"
<,'
^
M4
ij
14 j*
*** rt*,i *i  14 1  ! i^ 4 ?i t   , , t j I
Ii t
$**!
*!_
1 ,'
I *j
4I
2
% (* S Ij *,,* 4 * # * v '
1
4$
* i
% to! i,* i til I III I , M fv , ,
1
U
IK*
266
ECONOMY
Table XXIV givtxs tests
In the jackets ami stea
the results of these wil
TA
TRIPLKKXPANSIt >N KXI'fcK
nilTSKTTS INS firm.
RFHKATI.RS.
!
n
10
it
i* i
GAIN FROM STEAMJACKETS
the most favorable conditions should be chosen wh
has steam in the jackets, and in like manner the
without steam in the jackets should l>e selected; a
of two such selected tests has more weight than a
comparison of individual tests, however great the
such tests may lie. An invcKtif{ati<ui of Dclafom
Tables XXI ancl XXII and represented by Figs,
gives such a comparison. The selected are th
Table X ancl two pairs, with condensation a
Thus the best result with steam in the jacket ancl w
sation is 16.9 pounds, ami without steam in the jac
the gain h
fX.i t6.)
 ~ " "< 
iH. t '
Without condensation the be*t results lire ,11,5 wi
the jackets find 4}.. without steam in thr jackets; the
JA,Jt " t.$
"* ' "** 0.1 I.
j 4 jfr
These results art* prolmhly ten* .small, us the strum
jackets* should he ftillrtlrcl and rtHirnrd to the botl<
a moderate reduction of tt*mH*raturi* below the tt*n
the Hteam in thr hoilrr. Hit* drip frtim the jiic'kcl.H
through a trap, ami m rrjinrttii in prtilmbly too sma!
the rnont ci!iHtIfiiiiililr rt*4iili the*
Data for a fur rittnpnttnd eng
at hand, but the i trtirrlbitl tin 365 to li
for the triple r ngir
268
ECONOMY
These heatconsumptions t
of steam per horse x>wer JM
consumption the gain from
appear to be only c> per ceo
cent. This large 1 different*
steam us<*d in the jackets, i
of the total steam consum;
vldual jacket is, however, n
in the jackets of the pi
the jackets of each of the oi
The etltvt of jacketing
surprisingly small, as Iron 1
B*T.u. per horse fwiwrr pi*i
result without steam i
only
174
The corre8[K>ndence
Callemlar and Nicolson ci
has already
From the
to MIV
INTERMEDIATE REHEATERS
are the Leavitt pumpingengines, for which results ai
Table X. The fact that these engines give the best
recorded for engines using saturated steam lead to the
that such reheaters may be used to advantage. The <
evidence, however, is not so favorable, for, as has be<
out on page 264, there was found a small but distinct dis
from using steam in double walls or jackets on the in
receivers of the experimental engine at the Massachusetl
of Technology. It appears that this engine gives
economy when steam is supplied to the jackets on the
and not to the jackets on the reheaters, and, further,
steam is used in the receiverjackets the steam in
pressure cylinder shows signs of superheating, whi<
considered to indicate that the use of the steamjacke
too far.
After the tests referred to were finished the engin<
nished with reheaters made of corrugatedcopper
arranged that onethird, twothirds, or all of the reheati
can be used, when desired. Table XXIV, page 266,
results of tests made on the engine with and withou
the reheaters; in these tests the entire reheatingsurfao
when steam was supplied to a reheater.
For some reason the heatconsumption when no
used in the reheaters is somewhat greater than tha
Table XXIV for the engine without steam in a
jackets; the difference, however, is not more than t
and a half per cent and cannot be considered of much ii
It is clear from the table that there is advantage from
reheater, and still more from using two. If the heatco
for the engine without steam in the jackets and wit!
in the reheaters (taken from Table XXIV) is assu
270
ECONOM
which is scarcely more tl
the jackets. These tests
they are too few and refei
Superheating. The in
the interference of the c]
engine economy is by tl
186364 a number of na
heaters by Chief Enginee
showed a marked advanfc
heated steam for stationa]
and in Europe. But th<
dry steam on one side anc
deteriorated, and after an
the use of superheated s1
pound and triple engines
More recently improv
introduced in Great Brii
endurance, and superhea
successfully for sufficient
the application of super!
Two series of tests will 1
on a simple engine, and s<
There appears to "be no i
DIXWELL'S TESTS
TABLE XXV.
DIXWELL'S TESTS ON SUPERHEATED STE
CYLINDER DIAMETER 8 INCHES; STROKE 2 FEET.
Proceedings of the Society of Arts, Mass. Inst, Tech., i8
Sati
irated Stez
un.
Supe
I
II
Ill
IV
127
83
63
180
Cutofi
0.217
0.443
0.689
0.218
Revolutions per minute
Boilerpressure above atmosphere, pounds
per souajre inch.
61.5
50.4
60.4
5O. 2
58.0
50.3
61.0
50.4
Backpressure, absolute, pounds per sq. in
Temperatures Fahrenheit:
154
302
IS7
3O3
158
303
152
478
In cylinder by pyrometer .
278297
279296
282300
313
Per cent of water in cylinder:
At cutoff
52.2
35.9
27.9
27.4
At end of stroke . ....
32.4
29.3
23.9
18.3
7.65
12. 7
1568
6.83
Steam per horsepower per hour, pounds,
B.TJJ. per horsepower per minute. . .
48.2
796 '
42.2
696
453
747 '
35.2
631
A metallic thermometer or pyrometer was place*
In the head of the cylinder. When saturated stea
this pyrometer showed a large fluctuation, but when
steam was used its needle or indicator was at rest
part of the apparent change of temperature with sat
is attributed to the vibration of the needle and th<
mechanism, it is very clear that the use of super"
reduces the change of temperature of the cylind
remarkable manner. The effect of superheating c
of the cylinder walls is also indicated by the per <
. in the cylinder at cutoff and release.
The apparent gain by comparing the amounts c
per horsepower per hour in favor of superheated
272
ECONOMY
we must compare instead tl
giving a real gain of
696 546
696
This same HarrisCorlis
consumption of 548 B.T.TJ
supplied with saturated stea
why the earlier attempts a
so easily set aside when it ^
pressure.
Though we have no test
condensation on engines o
it is probable that a very r
use of superheated steam u
heat were as much as fiftee]
consumption to a larger <
and would be likely to give
steam per horsepower per
The best results obtainec
steam in compound engine
in Table XXVI, for a
T^m'l* 1^1 STUckmf TTiTro f/aofc
SCHKOTKK TESTS
which places It a little beyond the performance oi
engine mentioned. But since the uncertainty of the
tion of power by the indicator is probably two per o
reasonably conclude that the effect of lining superh
in a compound engine is to place it on a level v
engine, and the* question is to be decided in prat
relative expense and trouble of supplying and using a
of a third cylinder and higher steampressui
It Is somewhat remarkable that steam was sup]
during the stijierhriiling but not at
Ing that for those the jackets had a small <
made evident by the percentages of steam c
them,
TAHI.K
COMPOUND HORIZONTAL \IILL KNUU4I
%Ntt jj witt't; j;,5
,
tt'ft f* Pi>4,
By Pwfijt*r M.
'' t > *
i }
*' ft ' ; . .
im iw p'i
Ktuwftf
re^jf 1 w
i
II , Hi IV ' V i VI
'*<*>*** *M. flirt, in 1*1 1
; f#* M' 17 V n 1 <i i
! lift Itfftltrt ftl II?' Hi U
'
y it V **
ft 1 ti * ti i, ii C
Vtt
I*, ? 11 D si
i i' i t i
i* 4
i i
274
ECONOMY
onethird stroke when the
about onesixth stroke wl"
tests on simple* engines sue
the small Corliss engine
Technology, confirm these
The term Mai expansion
can properly have only a a
taken to be the product ol
cylinder by the reciprocal u
for the highprmure cylinc
sion is ulx>ut 20 for all the t<
X, except those cm martin
poor economy. It may tfi
advisable to use much me:
and that km expansion sh
tions of service (for
expansion.
The stationary comjxnu
have about 20 expansions,
that for highest economy
quired. In practice
advisable.
Variation of Load. If
VARIATION OF LOAD
In the next chapter; and the second is evident from i
of curves of steamconsumption as given by Fig. 5
and Figs* 57 and 58, 352253.
The allowable range of power for a simple engi
than for a compound or a triple engine. Compi
simple and a triple engine may be made by aid of
59. The Corliss at Crcuaot when suppliet:
at 60 pounds pressure 1 * with condensation and w
the jacket, developed 150 home power and used
of steam, per horsepower per hour. If the increa;
to 10 per cent of the economy, that is, to it;
horsepower per hour, the horsepower may be redi
92, giving a reduction of nearly 40 per cent fronr
power. The triple at the Massachusetts
Technology with at 1 50 pounds pressure and
in all the cylinder jackets developed 140 horse* pen
233 B.T.U. per home power per minute. Again,
consumption to 10 per cent or to 354 B.T*
may be to 104 giving a
26 per cent from the normal power. The effect
power for be well fi
on them, but is to believe thi
would ill if a compari
Though the which we on comp
do not us to a investigation of
Is no that it is interim
the and the triple
When the by a
by the of the
of the te tt t
276
ECONOMY OF STEAM
cylinder is fixed, is likely to have a
indicatordiagram due to expansion \
the power is reduced by shortening the c
cylinder. Such a loop is always accon
economy; if the loop is large the engii
than a simple engine, for the high
nearly all the power and may have
piston, which is then worse than usele<
There is seldom much difficulty in n
any desired reduced power by shorteni
the steampressure, or by a combinal
But a compound engine sometimes g:
very low power (even when attention
the lowpressure cylinder), which usi
discussed; i.e., the power is developed n
cylinder. Triple engines are even n
way. A compound or triple engine i
power is subject not only to loss of <
action, but the inside surface of the
liable to be cut or abraded.
Automatic and Throttle Engines.
may be regulated by (i) controlling t
by adjusting the cutoff. Usually the
Al'TOMATK* AND THKOTTLK KNdlNKS
by gravity* When tin* engine is running steadily
speed the forces acting on the governor are in eqm
the hulls revolve in a certain hori/ontal plane. If
the engine* is reduced liir engine speeds up and the
outward ami upward until a new position of eqi
found with the halls revolving in a higher hori/<
Through a proper system of links and levers the upv
of the halls is made* to partially close a throttlevalve
which supplies steam to the engine and thus adjusts
the engine to the load.
Shaft governors have lar^r revolving weights whose
forces are balanced by ^tmng springs. They a
enough to control the distribution or the cut off \
engine, which, ho\vevrr must Ie balanced M that i
easily.
Automatic engines, tike tlu* (\rliss engines, ha\e
two for admission and two lor rxhaiist of ^team. Hi
relea.se*, ant I compression are tt\ed f but tlie cut otT i
by the ftovrrnor. t*su;tll> an ;ulmixsin valvr is att;
actuating mrcltanism by ,i lait It *r similar device, w
opened by the ^ovenor\ and then the valve is < lose*
by a spring or by some other independent device,
of the governor i* to ttmtroi ftie position of a *
which the latch strikes and by which il is opened I
valve.
Corliss and other automati* eiifjne^ have long h;u
reputation for cnonomy, which is commonly attrthi;
method of regulation. Il t true tltat the valve gc
enginc\s are adapted t< i*ivr an early cm oi'f, winch i
elements of the design of an rn*rni<'al simple rngti
ECONOMY OF STE
from the steam to the exhaust side
of similar construction.
Every steamengine should have
of its normal power; and again it
that a singlecylinder engine shoi
through the greater part of its stro"
lions, together with the fact that it i
a plain slidevalve engine to give ar
use of a long cutoff for engines con
The tests on the Corliss engine a
XXII, pp. 250 and 251) show clea
a long cutoff for simple engines.
out that a noncondensing engine
about onethird stroke. With cut<
pounds steampressure the engine
and used 24.2 pounds of steam pe:
running without steam in the jack
If the steampressure is reduced to
lengthened to 58 per cent of the si
is increased to 30.2 pounds per hor
power being then 173. The gain
off is
EFFECT OF SPEED OF RE^
Considering also that automatic en
built and carefully attended to, while
often cheaply built and neglected, th
the one and the bad reputation of tl
counted for.
It is, however, far from certain that ai
have a decided advantage over a throttl
latter is skilfully designed, well built and <
to run at the proper cutoff. Considerin
steamconsumption per horsepower per
is unduly shortened, it is not unreasonat
not better results from a simple throttlin
automatic engine when both are run for <
at reduced power.
The disadvantage of running a compc
with too little expansion can be seen by
consumptions of marine and stationary
hand, the great disadvantage of too mi;
evident from the tests on the engine in
Massachusetts Institute of Technology
265). Considering that the allowable v;
economical cutoff is more limited for a
engine, it appears that there is less reason
governor instead of a throttling goverm
triple engines than there is with simple
the most economical engines (simple, co
automatic engines.
Effect of Speed of Revolution. Thou
steam on the walls of the cylinder of i
rapid, it is not instantaneous. It would
an improvement in economy might be att
sfa
280
ECONOMY C
"surfaces exposed to steam in
fact, all engines which for \
to run at very high rotative
economy, in part from the r
fact that piston valves are co
to the kind of leakage descri
page 234, even when they z
monly the engine has a fly 1
valve to be very free with the
Willans invented a singleac
at high rotative speed, and si
passages without excessive cl
rod to carry the steam frorr
tandem. Tests on this engii
in this book) showed that a
200 revolutions per minute
from 24.7 to 23.1 pounds ;
further increase of speed tc
to 21.4 pounds; the engine
condensing. This engine use
power per hour, when develc
lutions per minute under 17
BINARY KXUINK
lottenburg give some insight into the possibilities of
The engine is of moderate si/e, developing about 15'
as a steamengine, and about .oo horse power as a 1
using steam at about 160 pounds by the gauge
superheating. The engine is a. threecylinder tri
engine, but can In* run also as a compound engi
probably is not proportioned to give the best eeono
latter condition.
The general arrangement of the engine is as folk
steam cylinders are arranged horizontally side* by
additional cylinder using the volatile tluid (sulphui
on the opposite side of the crank .shaft, to which it is
its own crank and connectingrod. Steam is supp
boiler and superheater to the steam engine, and
into a tubular condenser which acts as the sul
vapori/es; the condensed steam is pumped back in
and the vacuum is maintained by an air pump as usi
of 20 to ,; inches of mercury was maintained in t!
The vaporous sulphur dioxide at a pressure of uo t
by the gauge was led to thr proper cylinder, from
exhausted at about ^s; pounds by the gauge; this
condensed in a tubular condenser by circulating
temperature of about KO*' P, at thr inlet ami ab<
the exit.
The drips from tin* steam jackets of the steam t
piped to the steam condenser instead of being ret
boiler, but that cannot be of mwh importance
condensation in the jackets was probably le.ss than
of the total Meuni supplied to the engine, The pc
the engine is given in Table XXVIII in terms <
282 ECONOMY
TAJ
BINARY ENGINE, ST
By Professor E. JOSSE, Royal
Re volutions per minute i39
SteamEngine:
Pressure at inlet, h.p. cylinder
by gauge pounds 136.5
Vacuum, inches of mercury . . . 230
Superheating, degrees Fahrenheit 175
Horsepower, indicated 132.1
Steam per h .p. per hour, pounds . 12.5
Thermal units per h.p. per minute 244
SulphurDioxide Engine :
Pressure by gauge pounds: . . .
In vaporizer 132
In condenser 3 1
Temperature Fahr. at inlet to cyl
inder 1320
Temperature Fahr. at outlet from
condenser 66.2
of circulating water inlet ... 49 . 6
outlet. . . SO9
Horsepower, indicated ..... 45.3
per cent of steamengine power 34. 4
Combined Engine:
Horsepower, indicated . . ... . 177 4
Steam per h.p. per hour, pounds . 97
Thermal units per h.p. per minute 183
Mechanical efficiency 85.5
BINARY ENGINE
about 35 pounds in the sulphurdioxide cylinder a
ture of about 65 F. ? the efficiency would be
_
T 57S+46o '
n "55 ^
and ^  s2 = o.oo.
055
The results of the tests given in Table XXVIII
difficult to use as a basis for the discussion of the
the binary system on account of certain discrepancie
tests No. 3 and No. 7 have substantially the sam
steampressure, superheating and vacuum, and n<
vapor pressures in the sulphurdioxide cylinder
advantage appears to lie slightly in favor of No. 7
the latter test is charged with 189 thermal units pi
per minute, and the former with 176, giving to i
advantage of about 7 per cent. A comparison
horsepower per hour gives nearly the same re
parison of tests No. 2 and No. 4 gives even a
discrepancy, though the conditions vary more,
the total power of the latter is much greater.
If we take 200 thermal units per horsepower p
284
ECONOMY 01
Finally ii appears probahl
binary engine* could he obt;
compound engine, using sii]
good results might be expect
175 pounds gauge* pressure v
already been called to the f
but little with highly superl
unnecessary and illogical.
CHAPTER XIII.
FRICTION OF ENGINES.
efficiency and economy of steamengines i
cxl on the indicated horsepower, because tha
nlte quantity that may be readily determin
L*r hand, it is usually difficult and sometimes
ice a satisfactory determination of the power actu
the engine. A common way of determining t
led by friction in the engine itself is to disconnec
., or other gear for transmitting power from th
place a frictionbrake on the main shaft; the po^
hen determined by aid of indicators, and the po
pleasured by the brake, the difference being th
ned by friction. Such a determination for a
olves much trouble and expense, and may be i;
ce the enginefriction may depend largely on
nsmitting power from the engine, especially v
>es are used for that purpose.
M '
286
FRICTION <
cent of the indicated horsepo^
condition of the engine. The ;
pump (when connected to the i
the friction of the engine. It is
cent of the indicated power of
airpump. Independent airpui
best speed consume much less
States naval vessels used only o:
of the main engines. But as in<
directacting steampumps, mud
pointed out is lost on account (
tion of such pumps.
Mechanical Efficiency. The
an engine to the power generated
efficiency; or it may be taken 2
indicated power. The median
from 0.85 to 0.95, corresponding
above.
The following table gives tl
number of engines, determined 1
TABLE
INITIAL FRICTION AND LOAD FRICTIOI
pumping engines, by measuring the work done i
water.
Initial Friction and Load Friction. A part of th<
an engine, such as the friction of the pistonrings
stuffingboxes of pistonrods and valverods, may
to remain constant for all powers. The friction a
head guides and crankpins is due mainly to the th
of the steam pressure, and will be nearly proportional
effective pressure. Friction at other places, such
bearings, will be due in part to weight and in pai
pressure. On the whole, it appears probable that
may be divided into two parts, of which one is ind
the load on the engine, and the other is proportional
The first may be called the initial friction, and the
load friction. Progressive braketests at increasing
firm this conclusion.
Table XXX gives the results of tests made by Wa
ier and Ludwig * to determine the friction of a horizo
compound engine, with cranks at right angles and
wheel, grooved for ropedriving, between the a
pistonrod of each piston extended through the c)
and was carried by a crosshead on guides, and the ai
worked from the highpressure pistonrod. The cy
had four plain slidevalves, two for admission and two
the exhaust valves had a fixed motion, but the adm
were moved by a cam so that the cutoff was detern
governor.
The main dimensions of the engine were :
Stroke
Diameter: small piston
larere Diston
288
FRurnor
T\\\
FRICTION OK ('
WALTHKK MKUNIKK am! Luimiu
Hortr I*owrra
with l
air pump, j
Ml 7
7
iH
with
Sf, 
?i 7
ft^ *,
INITIAL FRICTION AN!) LOAD FRICTION
brake (numbers g, 18, it), 28, and 2oJ were irregular
tain.
The first nine tests were made with the engine wo:
pound. Tests 10 to 10, wen* made with the high pre.*
der only in action and with condensation, the low pn
nectingrod being disconnected. Tests ,o to <> were
the high^ pressure cylinder in artion> without t^ondensa
The results of thest* tests are plotted on Fig. Oo
effective horsepowers for abns.su* and the friction h<
for ordinat.es. Omitting tests with small power* (for
brake ran unsteadily), it appears that each series of t
2()0
FKICTI
normal net or brake horse j
to deliver, and may be rep
where a is a constant to IK
(>o. If 1* is the net horse
time, then the load frietior
when* h is a second consta;
The total friction of the er
/*'
so that the indicated powei
l.H.P. /' r /
The* mechanical efficiency
I
The compound ctntdeii!
sented by Kitf. 60 devcloju 1
power to the brake, so tl
friction. Thr diagram si
INITIAL FRICTION AND LOAD FRICTION
but at half load (125 horsepower) the indicated hors
I.H.P. = 0.07 X 250 + 1.07 X 125 = 151,
and the efficiency is
125. f 151 = 0.83.
TABLE XXXI.
FRICTION OF CORLISS ENGINE AT CREUSO'
By F. DELAFOND, Annales des Mines, 1884.
Condensing with airpump, tests 133.
Noncondensing without airpump, tests 3446
HorsePower Cheva
Cutoff Frac
Pressure at
Revolutions
tion of
Stroke
Cutoff, Kilos
per Sq. Cm.
per Minute.
Indicated.
Effectiv
I
0.039
0.64
64.0
27.8
16.3
2
0.044
2.40
68.5
60.0
376
3
0.044
2.90
65.0
672
452
4
0.065
4.90
64.0
117.0
88.7
0.065
6. 20
61.0
138.5
106.3
6
0.065
7.10
64.0
163.2
129.2
7
0.065
7.60
64.0
185.0
144.6
8
o. 100
.16
58.0
21.
10.6
9
0.106
55
60.0
6l.9
423
10
o. too
.82
573
82.7
61.0
ii
0.090
.80
58.3
1353
106.7
12
0.128
.82
58.3
1545
124.8
13
o. 142
76
62.0
42.3
28.4
14
0.137
7i
60.6
443
28.7
*5
0.132
50
540
795
598
16
0.147
.60
61.6
IOO.O
78.2
17
o.iSS
65
60.0
177.2
1450
18
o. 167
.22
61.0
40.2
279
19
0.197
55
572
no. 8
83.3
20
0.273
4
62.3
50.2
338
21
0.264
57
63.3
89.1
6r.8
22
0.240
.64
62.0
872
63.1
23
0.245
25
56.0
145.0
116.0
24
0.260
76
58.0
209.4
178.0
25
0.335
25
590
472
32.5
26
0.339
94
58.3
in. 7
90.0
27
0.338
97
6r.o
161.8
1330
28
I
47
593
81.3
67.2
29
I
47
61.0
80.8
67.9
3
I
.60
61.6
148.5
128.4
31
I
.70
61.5
216.5
191.0
32
I
.70
61.5
2155
191.0
33
0.50
.70
61.5
158
o.o
34
O.I2O
6.00
60.0
132.5
107.5
35
0.106
7.00
530
125.0 "
103.0
2<)J FkKTiO!
Table XXXI gives the rt
tests made on a Corliss en^
both with and without a
pressures and cut oil. The
on Fig. 01, and those withe
In both figures the abscissa*
the ordinates are the friclio:
are represented by dots; tho
most ^economical cut oft itn
40 1
lot
INITIAL KRKTION ANU LOAD FRUTK
friction than the other tests. The tests on this
clearly that both initial ami load friction are aff
cutoff and the steam pressure, and thai friction
be made at the eut otf which the rngine is expeeU
service.
tti
The initial frit lion w.i*. Hj,*!tt horsepower h<
without condensation* Hut IMJ;. 61 shows tlui
with condensation #a\r the ltv*t economy wher
160 horse power; the f rut ion was then ,<<* horse j:
the net horse power wsis i,<o, which will he taken f
hor.se power /*. ronsecjuently
i i $4 * H ! ; t^'* 1*47,
shows the Iir?4 eccjii
indicated IIOIM* JHW
i% leaving iKci fur the
In lik<*
condensation^ for ahout
the friction is , hcit^e
mm
I'h
I,
294
FRICT
in friction, when developi
sation it had 20; conseque]
(36
of the indicated power,
to the high vacuum maint
Thurston's Experiments.
tests on noncondensing e
with his advice, Professo
for engines of that type
load, and that it can, in
ing the engine without a
FRICTION OP 1>
STRAIGHTLINE ENGINE, 8
No. of
Diagram.
Boiler
Pressure.
Revolutio
I
5
232
2
65
22Q
3
63
230
4
69
230
5
73
230
6
77
230
7
75
230
niSTKlWTioN OK KRICTION
lubrication and other minor causes rather than c
of load.
Distribution of Friction. As a consequence of
in tin* preceding section, ProtVssor Thurston dec
friction of an engine may In* found by driving :
external sourer of power, with I lie engine in sul
same condition as when running as usual, hut witho
cylinder, and by measuring the power required t
aid of a transmission dynamometer. Extending
the distribution of friction among the several nn
engine may be found by disconnecting the scvt
one after another, and measuring the power requi:
remaining members.
The summary of a number of tests of this sort,
fessor R, C. Carpenter and Mr. (1. B. Preston,
Table XXXIII. Preliminary tests under noni
showed that the friction uf the .several engines \
the same at all loads and speeds.
The most remarkable feature' in tins table is
the main bearings* which in all cases is large, lx>th
absolutely. The coefficient of friction for the n
calculated by the formula
^ftftn H.jP.
ft n
is. given in Table XXXIV. p in the [iresHure <m t
pounds for tlu* engines light, ami plus tlte mea
the piston for the engines loaded; c is the circuit:
bearings in feet; n is flu* number of revolution
and IL P. Is flu* horse power required to overeor
*!$'* .
m\:.i
ffl^rt * 4 '.
i '% * r*i
: ll'^/l v : ',
296
FRICTK
TAB
DISTRIBU:
Parts of Engine.
\O rt
00
Main Bearings
Piston and Rod
Crank Pin
Cross Head and Wrist Pin
Valve and Rod
Eccentric Strap
47
32
6.
5
2.
5
Link and Eccentric
AirPump ....
Total
TAI
WSTKIW'noN OF FRICTION
The second and obvious conclusion from Tab
that the valve should be balanced* and that nine
friction of an unbalanced slide valve is unnecessary
The friction of the piston and pistonrod is always
but it varies much with the type of the engine, an
uncos in handling, it is quite possible to change.
power of an engine by screwing up the piston.ro<
too tightly. The packing of both piston and rod
tighter than is necessary to prevent perceptible le
more likely to be too tight than too loose.
ClfA
INTKKN'Al. <'
RECENT advances in the 
been found in the develop!)
and of steamturbines; the hi
When first introduced the oi
bustion or #ts engines was i
use to small si/.es, for which <
anee offset the cost of fuel,
horse pc nver was u larj.^' tin
time Mr. Dowson had stu'f'
eite coal and front i'oke in it
of 400 horse power were bit
as they had four cylinders tl
twice that of single rylindt
fuel used in the [imditrer \v
the present time, #asrn#inr:
'1C f t*/V\
STIRLING'S ENGINE
page 39) It was pointed out that to obtain the ma
ciency all the heat must be added at the highest prac
perature, and the heat rejected must be given up at
temperature. The hotair engine is the only attem
the example of Carnot's engine by supplying heat t<
drawing heat from a constant mass of working subs
An attempt to obtain the diagram of Carnot's cycl(
an engine would involve the difficulty that the aci
which the isothermal and adiabatic lines for air cr
very long and attenuated diagram that could be ot
by an excessively large working cylinder, with so m
that the effective power delivered by the engine woulc
ficant. This is illustrated by Problem 20, page 75.
this difficulty Stirling invented the economizer or
which replaced the adiabatic lines by vertical lines
volume, and thus obtained a practical machine,
engine is still employed, but only for very small pum]
which are used for domestic purposes, as they are fre
gcr and require little attention.
Stirling's Engine. This engine was invented ir
was used with good economy for a few years, and tl
because the heaters, which took the place of the boiler
engine, burned out rapidly; the small engines now
little trouble on this account. It is described
and its performance given in detail by Rankine
in his " Steam Engine." An ideal sketch is
given by Fig. 63. E is a displaccr piston filled ^
with nonconducting material, and working
freely in an inner cylinder. Between this
cylinder and an outer one from A to C is
300
INTKRNAI. C<
inner is pierced with holes t
displaced by tlu planter.
pipe through which rold wat
has free communication u
cylinder, and eonseifucitily :
l)c parked in tin* usual man
In the actual engine tlu
then* art* two displacrr rylin
cylinder.
If we neglect the action
cylinder // ami the loinimi
ideal eyrie. Supper the w
of the forward strokr, ami
its cylinder, so that \vr may
part of thai t ylintlrr or in i
perature T y the condition
by tlu* point /> *>f Kiit !
quit k!v
,K
strokr; \
litllr tlu
Ilir air ;
of thr ili
ratt*r, fr*
STIRLING'S ENGINE
stant temperature, as represented by the isothermal
completing the cycle.
To construct the diagram drawn by an india
assume that in the clearance of the cylinder H, 1
eating pipe, and refrigerator there is a volume of ai
back and forth and changes pressure, but remains a
ture jT 2 . If we choose, we may also make allowan
lar volume which remains in the waste spaces at 1
of the displacer cylinder, at a constant temperature
In Fig. 65, let ABCD represent the cycle of ope
out any allowance for clearance or waste spaces;
volume will be that displaced by the displacer pis
maximum volume is larger by the volume displaced
ing piston. Let the point E represent the maxin
the same as that at A ; and the united volumes of
at one end of the working cylinder, of the commu
FIG. 65.
of the clearance at the top and bottom of the disp
and the volume in the refrigerator and regenerate
of this combined volume will have a constant te
that the volume at different pressures will be repr<
hyperbola EF. To find the actual diagram A f
any horizontal line, as sy, cutting the true diagrar
302
INTERNA:LCOMBUSTION E
as Stirling's hotair engine. To avoid de
cant in the working cylinder Stirling foui
nect only i.
displacer cyl
cylinder, an
cylinders for
^^____ It has beerj
FIG. 66. mineral oil c
the displace:
hot end also of the displacer cylinder c
connected with the working cylinders, o:
Thus each working cylinder is connected
one displacer cylinder and with the (
displacer cylinder.
The distortion of the diagram Fig. 66
large clearance and waste space, and f
the displacer pistons are moved by a cran
with the working crank.
A test on the engine mentioned by 1
Johnson* showed a consumption of 1.66 o
coal per horsepower per hour; but the fi
large, so that the consumption per brat
pounds. This engine, like the original S
STIRUNcrS KNGINK
isothermal expansion, and />.<! and ,#(.' take
the constant volume lines on Ki#. (14. To six
lines are properly drawn, we may consider the eq
which was deduced <w page 07, Kor the lit
BC the volumes are constant, so that the equati
or transposing,
but this last expression represents the tangent of the
the axis (M* and the tangent to the curve. This a
(but with a dimin ishinj*; ratio} with the temperati
is constant for a #UN, the anj'je <lipends only on th
1\ so that the curve JIC is itlentual in form with 1
and is merely set oil further to the nght ; in cons*
like W X and ZY between a pair of constant ten
are identical except in their positions with regard t<
. SujJpose now ibal ibe material of the regene
temperature* 1\ at the lower end, and 1\ at tht* u]
that the temperature varies regularly from bottom
pose further that the air when &ivmK heat to tl
(or receiving heat from if i differs from it by only
able amount,. Then the diagram of Fi#. 67 will
ideal action correctlv, and it is eusv to show that
304
XNTKRNAI.~C<
Moreover, the small amount
ZY at the temperature 7'
heat yielded during the openi
so that. there is no loss ot ft
mentioned are represented In
It. can In* shown that onr u
at random, provided that tlu
tical and stl off further to
importance enough to vutrnt
In practice a regenmttor
temperature than the air frt;
!iiglu % r temperature than thai
of air is rapid. The loss of
of the original Stirling en^in
ten per cent. H may le pn
state thai regcnenitors ;irr r
at the prest*nt day.
GasEngines. The ihtH
to transmit, heat to and fro;
engines this dillirttlty is ret:
air (st that heat is develop*
and by rejecting the hot fi^
Tlie fuel may In* iltitnttmtfifij
GASENGINE WITH SEPARATE CO1
engine itself; the second type of engines,
engine is an example, is the only successful
time; the other type has some advantages wt
development.
GasEngine with Separate Compressor. 
a compressor, a reservoir, and a working q
as a gasengine a mixture of gas and air is dr;
compressor, compressed to several atmosphe:
a receiver. On the way from the receiver to t
the mixture is ignited and burned so that t]
volume are much increased. After expansi
cylinder the spent gases are exhausted at atm<
The ideal diagram is represented by Fig.
the supply of the combustible mixture to the
compressor, DA is the adiabatic compres
sion, and AF represents the forcing into
the receiver. FB represents the supply
of burning gas to the working cylinder,
BC represents the expansion, and CE the
exhaust. In practice this type of engine
always has a release, represented by GPI, fo
has reduced the pressure of the working subs
atmosphere.
This type of engine has been used as an oil
the fuel in the form of a film of oil to the a
compressed. In such case the compressor
and there is not an explosive mixture in
Brayton engine when run in this way could bu
or, after it was started, could burn refined '
defect appears to have been incomplete con
mip.nt. frmlmo of the cvlincler with carbon.
'^ !
mi
^00 1NTKKNAI,
U*mpiTatuiv> I'onvspondin
hrat added from A ti / !
*'v
and flu* htat withdrawn t'n
f i
M that thi* ftl'u itiu'v nf tin
Hut >inrr tin* r \pansi* n
,
1, //'""/
* lha! ihr rtfttatltiit f'nr rf!
'l*hU lllM tfv4Utt ill' ifltMl fl
lui* tin* uduittf.iftr nt M'Jilti
hy a Himjilr iiliMl uif'r,jli'i!
cllit'inu y, Ifu^v tar tht 4 i j
flit' rohuMf .tdi.mUn'r , n
<;ASKN(;INK WITH SKPARATK COMPRKSS<
above the atmosphere the eiliciency is
JL42ir:l.
/ 1.1.7 "*
e i
(T;^'^ 
When the cycle is incomplete the expression for t?
is not so simple, for it is necessary to assume cooling
volume from G to // (Fig. 68), and cooling tit const!
from // to />; so that the heat rejected is
< c'V nv ><, CA TJ,
and the eiTicieniy becomes
For example, let it he assumed that the pressure
pounds above the atmosphere, that the temperature a
F., and that Hie volume at G is three times the vohm
First, the temperature at A is
14,7
provided that. the temperature of the atmosphere is 6
j The temperature* at G is
i T T MiV"* /r \ 4 s
I and the pressure at (.7 is
\ MY
i ^'^i^l " f'^7 +
\ so that the temperature at // is
m
I
Mm,
308
INTERNAL
GasEngines with Compi
ful gasengines of the prese
in the working cylinder.
end of the cylinder only,
the cycle, so that there is o
working at full power. S
fourcycle engines. Some
of the cylinder accomplish
as twocycle engines; they
tion when singleacting. '.
have been made doubleac
stroke of the piston from
mixture of gas and air, wh
at the completion of this r<
the pressure rises very ra
working stroke, which is
expel the spent gases. In
are of equal length, for the
length, as required for th<
terbalanced by the media
strokes.
The most perfect ideal
GASENGINES 'WITH COMPRESSION IN 1
and withdrawing heat at constant pressure fr
with the adiabatic expansion and compressic
The heat added under this assumption is
c v (T a  T d \
and the heat rejected is
c p (T,  T c \
so that the efficiency is
c (T t  T f ) _
If the temperature at A and the pressure
then it is necessary to make preliminary
temperatures at D and at B before using equ
adiabatic compression from C to D gives
at D
T d = T c
in like manner adiabatic expansion from A
T b = T a
*)" .
pj
1 'lA^l
J< '
310
INTERNALCO
provided that the temperatui
2<OO
= 1047
nil
== (2500+ 460)
nc
1 ~ i 4os :
If th
atmosp'
shows *
as in ]
conside
heat as
by wit;
to can
F:G. 70. G > anc
stant
represented by GC. The he
and the efficiency is
GASENGINES WITH COMPRESSION IN THE CY:
For example, let it be assumed that the expai
when the pressure becomes 20 pounds above the
the other conditions being as in the previous examp
0.405
and
_ T I53 6  6 5 + 1405 ( 6 5 520)
__ I   
290O 917
Though not essential to the solution of the ex
interesting to know that the volume at C is
. 4
147
times the volume at D, and 'that the volume at B is
=5
times the volume at A.
When, as in common practice, the
four strokes of the piston are of equal
length, the diagfam takes the form shown
by Fig. 71; the effective cycle may be
7! 2 lNTKRNAIrO
The heat applied is
and the heat rejected is
so that the eflieieney is
M7'a  'i
Sinee the expansion and
the* equations
7V TV* * '/Via*" '
but the volumes at /! and /
at B and C; i'onseijtirntly It;
V
j
consecjuently
and the expression for elTki
GASKNGINRS WITH COMPRESSION IN THE (
pounds absolute, or 8iS.4 pounds by the gauge, '
efficiency is therefore not much less than the eflieiei
other examples; it is notable that the efficiency
same as that calculated on page ^07 for an engine
compression to <)O pounds by the gauge. For the
however, the pressure after explosion, which dt
temperature, may exceed 300 pounds per square i
The diagrams from engines of this type* re.s<
which was taken from an Otto engine In the lal:
Massachusetts Institute of Technology. I Hirh
stroke, the pressure in the cylinder is less than th;c
INTERNAL i'
of ;20tothi'inrh, ami iih *
pisttm; tlu upl*'*' pan i
appear In tlu' m^n. 'H^
pounds, and liuMvdtMiHiin
HI*
thrrr ami f*ur p*mml. l'
Ihr influriu'c' of Oi** riri^.i!
imUfutnl hursi* powrr will
Tin* i'uinin.sNin lin* *!*
or in rralicy from an ;iilitl
In* rXjHHlni to rtnrivv hr.it
llu lirst pan <f thr i ompn
during l hi" lattrr part, T
to I hi* ailialulir li* for *4
fur lart* rftiprtr%; hut in
jirr vrrv <lit'frrvnt f fr thr i
CHARACTERISTICS OF GASES
and, if the gas is to be used for generating power,
and adjuncts must be adapted to the conditions,
gas is made from coke, anthracite, or from noncakinj
coal,and consists mainlyof hydrogen and carbon mom
with the nitrogen of the air, together with live or i
of carbon dioxide and a small percentage of hyclroe;
dally when bituminous coal is used. Illuminating
commonly made by tin* watergas process, which yie
very unlike producer gas, hut that gas is enriched
carbons of varying composition; formerly illuminat
distilled from gas coal, which was a rich bituminous <
a large percentage of hydrocarbons when distilled.
The general characteristics of illuminating gas are
by the following analysis of Manchester coal gas <
the first edition of Clerk's Gas Engine, and used
investigate the effect of combustion on the volume c
ANALYSIS OF MANC'HKSTKU COAL <;/\S. (Hunsen j
Hydrogen, li ....... 45. >
455H,
Methane, C*H 4 i 34, <)  <xj,8 j 104.7,
INTERNA
COMPOS!
Hydrogen, H
Methane, CH 4 ....
Carbon monoxide, CO
Carbon dioxide, CO 2 .
Oxygen, O
Nitrogen, N
details are given on pag<
original paper, which ar
Rich noncaking bitur
larger proportion of hyc
In a paper on the use <
gives the composition ol
Scotland, and Germany,
following table were de<
COMPOSITIC
CHARACTERISTICS OF GASES
The amounts of oxygen required for the combustion
volume of any gas can be computed from the foi
resenting the chemical changes accompanying c<
together with the fact that a compound gas occupies tw
if measured on the same volumetric scale as the <
gases. Thus two volumes of hydrogen with one
oxygen unite to form superheated steam as represent
formula
211 +0  H 2 O,
and the three volumes after combustion and redact
original temperature are reduced to two volumes; in
to have the statement hold, the original temperature v
to be very high, to avoid condensation of the steam i
But in tlie application to gasengines this leads to no
ienee, because the gases after combustion remain at a
peruture till they are exhausted, and the laws of gai
assumed to hold approximately. A compound gas lik
can be computed as follows:
CH 4 + 40  CO, + 2H 8 O.
Since the compound gas methane occupies two vol
requires four volumes of oxygen, it is clear that each
of that gas will demand two cubic feet of oxygen; the to
INTKKNAl. ''<
hut in prartkv ilu pnuhuvr
volume of air, so thai thr f*
in J^o to .so volume, ami 1
contrail luii.
Clearly this ntultrr has 1
page ^;)(.H as to tlu* rt'tiaiu't"
whirh assumr lu'aiiiif! <t
Ft>r illutninatinit ^as that a?
and for proihu'cr ga^ tlu*
tlt'Stfoy flu* valur of thr nir!
Temperature after Explw
>
the iU'trrmtnatum uf thr t
cltlrrrniiiutitin is tlitlu tilt hi*
tun* and thr vrrv s!urt itiir
mum trmprraturr van hr it
A t j <imjarativrly siinplr t
rxpl<isitn tan l* mattr from
prrssion can IK* asstinirt! I
ju'rft't't ^a^i^s i an lr applini
Unr rnrasurrr! on an t^nlina
pH'ssurr, is 61 {Muttuls, *r
iHTHtUl'r of thr iSasrs ill thr
AFTKK BURNING
are and remain the same as those of gases at. orcli
tures, can he taken as a first approximation only.
In conneetion with tests on a gas engine (see pi
illuminating gas. Professor Meyer makes a careful
of the temperature which might he developed it
of a gasengine if the charge were completely bur
conducting cylinder. The results only will be
The composition of the gas will he found on jn
which it appears that it was probably coal g
Manchester gas, and not differing very radically
gas, by use of winch Fig. 7,1 was obtained. Tl
the end of compression was 6g pounds by the ga
explosion was 220 pounds, so that, the conditions
different from those of Fig, 7.1, except that the p
compression line is not on the ordinate for measi
imum pressure, and therefore the parallel caleula
made.
On the assumption of constant specific heats Pi
finds that complete combustion should give ,p5c
conducting cylinder, hut using Mallard and 1
equation for specific heals at high temperatures hi
Those experimenters report that dissociation of cai
begins at about, pocf 1 K M and of steam at about
320
INTK
time. The actual e:
for gas, and for lar
represented by the
1
but a part of this ;
carbon monoxide* an<
may reduce the expc
Water Jackets.
engines have the h
waterjackets; larjje
with water, and dm
stu fling boxes coole
engines are cooled,
cooling surface is [
chamber; the latU
former is in part fo
Primarily, water j
and to make lulirira
cooling devices has t
many inventors hav
it is only a (juestit :
water* iacket. or whe
ECONOMY AND EFFICIENCY
and oilengines have hern rated in pounds of fu<
power per hour. The variation in the fuel used for
makes the secondary methods less satisfactory than i
on steamconsumption, so that it should he employ
the calorific capacity of the fuel cannot he d
estimated.
Since the heatequivalent of a horse power is ,;
units per minute, the actual thermal efficiency of
combustion engine can he determined hy dividin
by the thermal units consumed by the engine per
per minute. For example, the engine tested by Pn
used about 170 thermal units per horsepower
and its thermal efficiency was 0.25, using tin* in<;
power. The ratio of the cartridge space to the ^
was , so that equation (187) gives in this cas<
3.84
nominal theoretical efficiency; consequently the
efficiencies is nearly 0.60,
By a somewhat intricate method Professor Me;
the efficiency for two tests on the engine for \vhi<
given on page 350, on the assumption that eomplel
occurred in a nonconducting cylinder. The ratio
222 INTERNAI^COMBUS'
heat, be taken as the basis of cor
the ratio of actual to theoretical efi
0.253 * 0.398 = 0.64, or
If, however, we take his second val
we have
0.253 + 0.297 = 0.85, or c
Professor Meyer uses these coi
importance of better knowledge of
substance in the cylinder of an
because, if the nominal theoretic*
basis of comparison, there appe;
improvement in the economy of
second set of computations is tak<
prospect of improvement. In co]
the fact that these tests were on a
only ten brake horsepower.
In the discussion of efficiency we
heatconsumption per indicated ]
because the fluid efficiency (or the
working substance) should for thi
confusion with the friction and
engine. For the same reason, an<
steamengine can be determined
KCONOMY
KFFK;.IKNC:Y
the indicator piston from rising too high which
effects of an idle cycle and other features. A po
expansion curve is shown, with oscillations due t<
suddenly leaving the slop. The exhaust of the sj
shown by the curve <//*, after whirh the engine dm
of air (without gas) and compresses it on the uppe:
c to d] on tin return stroke* the indicator follow
curve from d to r, so that tin* loop represents work
engine; finally the air is exhausted^ while the ind
the line cc. Tn explain the dtflVrenee between tin*
ab and ce with spent gas and with air onlv, it mav 1
INTERNALr
w :
1)5 rll } ' >
time considerable import
out spent gas, but it atte
engines.
In indicating a gasen^
the negative work of exha
allowance for the negati
Fig. 74 should be made f<
has only a few working c}
of the negative work ma
another reason why comp
power. As can be seen
mechanical efficiency ma}
depending mainly on the
continuous explosions, an
reduced if explosions are
Twocycle engines co
which supplies the mixtur
ten pounds above the atm
pression must be determi
measurement of the indie;
ValveGear. The suj
combustion engine are ;
least two valves (or the
STARTING DEVICES
remaining closed during the compression, exj
strokes; but very commonly the admission
and for gas (when the latter are separate)
trolled, and for very high speeds this action ;
From what has been said, it will be evid<
problem of the design of the valvegear for
tion engine resembles that for a four valve
daily that type of steamengine valvegeai
lift valves. The solution which is most evi<
monly chosen is some .form of camgear; us
held shut by springs, and are opened by a
either directly or through linkages. This c
iently placed parallel to the axis of the cylin
the main shaft through bevelgears; the f<
the gear in the ratio of one to two, so that t
one revolution for two revolutions of the
properly time the four principal operations
spring closing a valve must be properly d
give the required pressure to hold the valve
the proper "acceleration so that the valves
the control of the cam when closing. The
tion to the cams for the normal action of the
which facilitate starting the engine.
\ . '
if H ''
lii'V
326
INTERN
the operations of cha
formed, whereupon tl
for very small sizes, i.
into action, and whi
piston has completed
which the charge is p;
compression is much
this manner the ignit
past the deadpoint, o
ward. The disengag
and there is great dan
When electric or ot
handpower, this met
large size.
A very common de^
air from a tank at a
inch. This air is su;
the engine when nece:
disconnected tempora
and is worked like <
way, whereupon the <
action is restored. T
valves controlled bv 1
GOVERNING AND REGULATING
for controlling the power of an internalcombustic
by regulating the proportion of air and fuel, (2)
the amount of air and fuel without changing U:
(3) by <> nutting the supply of fuel during a part of '
delaying ignition.
(i) Regulation by controlling the supply of fue'
method for engines working on the Joule or Bray
compression in a separate cylinder, for which a t
cussion is given on page 305. For thus cycle thei
sion, but the gaseous or liquid fuel can be burned
sion in any proportion.
The Bniyton engine had a double control foi
load. In the first place* a ball governor shorten*
for the working cylinder when the speed increase
of reduction in the load; this had the effect of rai
sure in the air reservoir into which the air pump d
that, pump delivered nearly the same weight of ;
under all conditions. In the second place, there w
ment for shortening the stroke of the little oilpi
pressure increased; so that indirectly the amoun
proportioned to the load. A similar effect was p 1
the engine was designed to use gas.
For the Diesel motor, to be described later, tl 1
can be adjusted to the* power demanded for all
service.
But for gasengines it has not been found prael
trol the engine by regulating the mixture of gas j
within narrow ranges. This comes from the fact
or very poor mixtures of gas and air will not expl
menus at the "Massachusetts Institute of Technolc
INTERNA:
tures should occur befoi
that even though the ex]
the beginning of the woi
The tests on page 3Jc
varying from i : 8 to i
brake horsepower.
This discussion of tt
varying the mixture of j
for many purposes that j
a gasengine. Neverthe^
it was tried early.
(2) The common wa
vary the supply of the
There are two ways of <
charge may be throttled
lower pressure; in the se
closed before the end o
supply. The effect of tl
the reduction of pressur
sponding increase in ib
like that shown by Fig.
of closing the inlet valv
KiMTlON
small power the negative work of idle cycles ver
the brake economy of the engine 4 . Now, a sin
cycle engine has only one working stroke in four
nish between times the work of expulsion, filling
sion, and even with a very heavy fly wheel will <
lurity in speed of revolution that is very objectio
purposes. This difficulty is very much increase
is governed by omitting* explosions on the hit or i
(4) Delaying ignition is one of the favorite w
the power of automobile engines on account of i
it is little used for other engines, and is very \s
as there is not time for proper combustion.
Ignition. The ignition of the charge may
one of three methods: f i by an electric spark, {.'
or (3) by compression in a hot chamber.
(V) The electric spark may be produced in o:
,,, ],y the make and break method, or by the jum]
For the first method a movable piece is worked.
der walls, which doses a primary circuit some t
tion is desired; the slight closing spark has no
proper time the moving mechanism breaks tin
good spark is made between the terminals, wl
with platinum. A coil in the circuit intensifies
opening spark. The spark obtained by this n
to be better than tin* jump spark, but there is 1
venience of a moving nurhanism in a cylinder <
high pressure, and the motion must be comr
piece which enters the cylinder through a stuflm]
The jump spark betm'een two platinum termu
lated spark' plug, screwed through t lie cylinder
~ , INTKRNAl.
Tin* divtilt may la* MIJ
generated by a small dyn
supplied from any tonvri
plied* the engine is usuall;
The rlrtlf'ti' nirthoil ol
history uftluKa* niittn*\ a
now iriuLs t> iwvomr univ
1 M * ! Thr hot tubr tnjl;
krpt rrd hot lv a Hun 11
Illln* turiirs ont luli oltt,
IH ftirnr'it upwani I HI n
timr tit* 1 rxpl<M\i nii\ < n
tuln* by a valvr \\hi h i
tht* luin* has an inlrt \.i
tubr with air *lra\vn in d
has IHTII \vittrly y^nl if
mtlhud has ttiri \viih lift
if is passing aw;iy.
Usrd r\f IllNlvrly III *il rli
taking utivantaK** *( a u*t
Illii
GAS PRODUCERS
same way. Premature explosion in a small e
started may be an inconvenience, but in a larj.
lead to an accident.
GasProducers.  A gas producer is essent
which burns coal or other fuel with a. restriele
that the combustion is incomplete and the prod
tion are capable of further combustion. In iu
gasproducer will deliver a mixture of carboi
nitrogen together with small percentages of earbo
and hydrogen. If a proper proportion of steam
the air, its decomposition in contact with the i
will yield fret* hydrogen, and the gas will give u
when exploded, and develop more power in the
When gas is produced on a large scale in a
intricate* devices may be used to rectify the jj
byproducts, which are likely to be so import*
the methods employe* 1. The most iwporlan
the present time appears to be ammonium si
used as a fertili/er, and for this reason u coal h
has a relatively large proportion of nitroget
station a coal containing three per cent of n
crude ammonium sulphate that could be sold
of the coal. This branch of chemical engineer
lij:
f
N :
w
j' I
^/
1^
51ft
>f?f
iNTKKNAI,
tin* prvst'iH time tin Hirl.
caking hituminou, ial. .
tion, at St, l.oui*. in tu^t, a
raking bituminous i'o;il and
pla.nl, ami if is likrly thai
ustd in prartii'f.
Ilg. 75 fjvrs fhr srt lint
i .1 i 4 " tlir i',ratr t ;irr\!f
rfnf ';':
if. 11
i ; r
ri%mrit f'ttr tiitti" /,. f* fl
OTHER KINDS OF GAS
cite; those that burn bituminous coal must have
of dealing with tarry matter. Sometimes this is
by passing the gas through a sawdust cleaner
centrifugal extractor is added. Some makers r
by care in cooling before the gas comes in conte
Others pass the distillate through the fire, and
into light gas or burn it; with this in view, some j
with a downdraught. It is probable that diff
fuel will need different treatments.
Blastfurnace Gas. From the composition o:
gas on page 316, it is evident that it differs fror
only in that it contains very little hydrogen, an
like the gas that would be made in a producer w
steam. During the operation of the furnace tl
is liable to vary and the gas may become too w<
this difficulty, it is desirable to mingle the gase
more furnaces. Since the gas available from ;
be equivalent to 2000 horsepower, it is evident th
to develop power from that source must be 01
scale.
The gas from a blastfurnace is charged with ;
of dust, some of which is metallic oxide, and re
and the remainder is principally silica and lime
fine and light. To remove this fine dust the
passed through a scrubber, which has the additl
of cooling the gas.
Other Kinds of Gas. Any inflammable gas tl
nished with sufficient regularity can be used
power. The gas from cokeovens is a rich :
producergas in its general composition. Natui
of 90 to 95 per cent of methane (CH 4 ) with a SE
of hvHrncyp'n and rntrncmn anH trarpc of nther 0*;
334
INTKKNAI, t 1
Gasoline. Thr lighter <
Iim\ an* mulily vapori^nl
the must rratlv means if M
uf several hundred hotse
have been built for small
of gasoline has bent littntt
i' raft ami tt aut>nu*bilr^;
for husini'ss nthrr thin> r ,N
tion of thr rnj'int's. Tin
tivrly .small [u\\rr IIMI! f*!
Tltr m*>t uta! fVaturr
or farbuivtnr, ami ihi*' <
t'spiH'ially for autnnjtbilf
SjHH'll.
ThtTt* an thtvt' tyjt*^ t*
thcisr that tr 'it'Ilt S Mit a 1 ^
clt'jit'iiflin^ on asftif.iijMft
d***fiidi'ti tin ilitrt ! vi ri
mass uf the fluid, !' flu HI
fart* of \vifr *;i!I,/r; MHiii" *
a rt'^ulati*n of frnl that i
Hiij*itlrti s Iraving only a
in any CUM" thrrr \\as a 1 1
roultnl in ihr *r<tiut ji<
Ihtitt,
llir Ilitift* rrtrnt i arht
supply lit'ing drawn fwJ
lint* i.s stippliril itit! IIMH
ninrr or IH^ in riiurti
KKKOSKNK OIL
A third form of carburetor is illustrated by
the gasoline is supplied by a pipe K to a valve t
to give good average action. Below Is a fine c
the end of a vertical rod which is
held up by a light spring; at the
middle of tin* spindle is a disk
valve which lit slooscly in a sleeve.
At aa are air inlet valves, and at
A is the entrance* to the cylinder.
During the suction or tilling .stroke
the spindle is drawn down, opening
the valve at the top of the spindle
and allowing the air ft* draw
gasoline by aspiration, Some* of
the hot products of combustion
from the exhaust are circulated
around tin* aspirating chamber to
prevent undue reduction of tem
perature. This type of carburetor
works well enough at moderate l
speeds, but at very high speeds the inertia
and disk valve cannot be* overcome rapidly enoi
which is consequently throttled, so that there is r
vapon/ri
itolteil !
em! i.
of this engine i> MIUUII in j
of the cylinder head '
the eitFJ
fniu a
the **u.;im* is running. T!
tltis Itiif mi! nf the vaj
with thr Iit! .spent jaM" ; !
Mrokr thr i hari'r f ;iii i
n'ssfd rut ITS lin* vapiri/i
the* va
nn i*" 1
tltr fulfil ailhrfritl tirptrat
ad is put on for a *
y i utilrulliii^ if;
hypuss valvr oil thr ctil sitp
t* tlir lank, Thr hli *r ni
\"iJHri/.rr Wiitilil brromr IH
THE FOUR CVCLK KN r (;iNK
appears to be no reason why there should bo troul
of some form of carburetor like those used for gas
The Fourcycle Engine.   Fig, ;H gives a verticil
Westinghouse fourcycle gas engine built in various
horse power with one cylinder, and up to 300 with th
Massive engines of this type are horizontal
acting pistons, Having
two cylinders tandem
or four twin tandem.
It is somewhat curious
that while massive
steamengines tend to
wards the upright con
slruc'tion, large gas
engines appear to be
all horizontal; it may
bo for tin* convenience
of the tandem arrange
mcnt. In Fig. 78 the
frame of the engine is
arranged to form an
inclosed crank case,
which is somewhat
unusual for #as
engines. The piston
is in the form of a.
plunger,, so that no Kll4> y(i
crosshead Is needed;
a common arrangement for all except massive
The cylinder barrel and head are wulerjurket
3.;S
IN '11' KNA1
thai ran le moved !<;, 1
to t !?j\r any desired nil
areas for t f a> aiul air
areas remain niuhani^
piMon valve to *i\r ih
clrniandri! h\ tin l*ad *
ihr r\hati>l vahr 1 A" ,ttv
iiulicatctl. I In tains in,
rwulntiun <*t % thr tn^iti
Lar^f ri*rs haxr ihr i
liiiniiii!*, the valve, an*l !;
lliri'e is a handle tni %hij
mint r,s t eilliliri.'lMii \vhi
IH\V tellsiull lit.ike aJitl }J
thrown intn ai ti**n; tttr>
uperate^ the vahr ,/,
Twc>cycl Engines*
\v!iir It e\liati'".? I lie ,irli!
perfViniieti \\ lih a irt\.tj.
lm\rr than th.it  thr ,
atlvanta^f *i'utini the
nihir uay. The iir^i /
\\UN that ly Inii^ili! <*!
TWOCYC 'I,!'*. KNCHNKS
regularity of rotative velocity. The engine could
twice us much power for its si/e as a four cycle er
certain tests by Mr. Clerk, shown! a slightly bet
than the older type of engine. But the operation
the remnants of the spent charge by the fresh char
of this type is rather delicate, there being a chance
the spent charge will remain, or that some of the
will be wasted; it is likely thai the charges mingle
engine experiences both defects. Eventually the (
was withdrawn from the market, but the principles
two types of engines: ( i ) small gasoline engines for
other small craft, and (!) large engines built for b'
furnace gas.
Gasoline engines of small power and moderate r<
have been made on the two cycle principle by e
crank and connecting rod in a casing, so that the pi:
,as the compressing pump. On the upstroke a r]
and gasoline is drawn into the crank rase, and it. is
pressed on the down stroke. There are two sets <
through the cylinder walls near the em I of the dow
are opened by the piston; these an* on opposite*
cylinder; one set, which is opened slightly earlier th;
forms the exhaust ports ami the other the inlet 'ports
communication with the crunk case, and therefore
and gasoline to replace the spent charge. A barri
the cylinder head which prevents tin* fresh charge
directly across from the inlet to the* exhaust, but ne\
action Is probably much inferior to that of Clerk's t
had the charge supplied at thr cylinderhead. Then
340
INTERNALCC
engines have been introducec
Two German engineering fir
especially for burning blasti
as 1500 horsepower in a sin^
The Korting engine (bu
Company) is a double actin
as long as the stroke of the (
of the cylinder is a ring of
the end of each stroke, an
one end of the cylinder and
enginecylinder, and arrang<
driven by one crank (which
one for compressing air, ai
of the two pumps are des
burned.
The airpump compresses
phere and delivers air to the ;
cams at the time when the ]
controls a bypassvalve TA
pump in communication i
stroke of that pump, whid
the first place the compressi
THE DIESEL MOTOR
plungers In a long openended cylinder; these
connected to cranks at 180 so that they appro?
from the middle of the cylinder simultaneously,
has a crosshead at each end of the cylinder to it
thrust of the connectingrod, so that the engine
great length on a, horizontal foundation. Towai
end of the cylinder there is a ring of exhaustports
the inner (or crank end) piston, and toward the cm
cylinder there is another row uncovered by the 01
part of these outer ports supply air, and a part gas
and gasports may be controlled by annular valve,
by hand when the engine uses blastfurnace gas.
conditions the engine is regulated by a governor, M
the pumps that supply air and gas. These pum
driven from the outer crosshead, have bypass
connect the two ends and begin to deliver o:
bypass valves are shut by the governor, so that
adjusted in amount to the load. When the engir
gas that has a wide* explosive range, the governor
annular valves at the gas ports and varies the mix!
The Diesel Motor. A new form of intern*
engine was described by Rudolf Diesel in 1893
away with many of the difficulties
of gas and oil engines, and which
at the same time gives a much
higher efficiency. The essential
feature of bis engine consists in
the adiabatit: compression of
atmospheric air to a sufficient
temperature to ignite the fuel
W '
f'01
} f L'v
m\':{
i H
m,
342
INTERNALCOMB
ger. Atmospheric air is drawr
pressed from b to c to a p:
square inch and a temperature
is injected in a finely divided
excess it burns completely at
by the injection mechanism,
is petroleum or some other oi
interrupted, and the remainde
is an adiabatic expansion. The
at e and a rejection of the proc
The cycle has a resemblance
differs in that the air only is c
the combustion is accompaniec
his theoretic discussion of his
of combustion shall be so regul
not rise during the injection of
therefore be very nearly an isot
the fuel is added during the o]
cd, the weight of the material i
physical properties change, so '
isothermal. The fact that then
THE DIESEL MOTOR
rise of temperature, or that there is any great advj
a regulation if the temperature is not allowed to ris
The diagram from an engine of this type is sho^
which appears to show an introduction of fuel :
or oneseventh of the working stroke. It is prol
compression and the expansion (after the cessatii
supply) are not really adiabatic, though as there i
dry gas in the cylinder during those operations
may not be large. The sides and heads of the c
the engines thus far constructed are water jac
the use of such a water jacket and the consequent
was one of the difficulties in the use of interr
engines that Diesel sought to avoid by controlli:
combustion. The statement on page 39 that
efficiency is attained by adding heal only at the
perature has no application in this case. The r
are that heat cannot at first be added at a temp
than that due to compression (about 1000 F.), b
tion proceeds heat can be added at higher ter
with greater efficiency. The fuel may be regul
avoid temperatures at which dissociation has an
after burning can be avoided.
The oil used as fuel is injected in form of a sp:
344 INTERNALCOMBUSTI
engines, by the necessity to form a
discussion of the theoretical efficienc
the efficiency increases as the time of i
In practice the engine shows a slig]
light loads, due probably to the los<
waterjacket, which are nearly constc
In the exposition of the theory of
that all kinds of fuel, solid, liquid, 2
in his motor. As yet oil only has bet
leum or other heavy oil has probabl
of such oils. It is evident that gas
of engine; the gas can be compress
somewhat higher than that in the i
air is which is used for injecting oil.
sary to cool the gas after compressio:
supplied with air.
There appears to be no insurmoi
ing powdered solid fuel to this enj
ash from such fuel in the cylinder
to give trouble. Diesel claims that
(for example, a hundred pounds of
the ash will be swept out of the cy
iinrl will rr>t orivp trmiKlfV "hut that
TUK DIKSKI. MOTOR
A theoretical discussion of thr efficiency of th
simple engine us represented by Fig. 70. may 1
considering that heat is added at constant tern]
to d and that heat is rejected at constant volun
bearing in mind that be and dc represent adiabat
From equation (75), p*W u k i? the expressioi
supplied from c to d is, for one pound of working
Q,  At> f v f \w,~t ART, }<>&
1 1 . 11 e
The heat rejected at constant volume is
Since the expansion </r is adiabatic,
(i
^.
t' r
but since the compression be 5s also adiabalic,
and consequently
'
mK'ratutv /'? I ' lr *
prrssuiv at tu '* *
ill !' :
jlr l
lip;
li;
ZnjirtrtL llut i>, lv rrilu
liy it writ's uf i.tlruLiffM
Tliis JN a MTV impnt'Lini
will hau' in prat tin litiU
It>atl^
[I is 11 pnM* *l !ha*.
i rill i*' .t J *a'* f? '
m
'v
.ii thai ill* Iraian*
KNG1NKS FOR SPECIAL PURPOSES
The equation for efficiency gives in this case
( I f \ a jin e
778 X 0.2375 X 530 (^^~) '  i
( \o.07<)6/
e ' J ~x^___
1.405 X 53.22 X 1480 log, ^iLZli
0.0796
Engines for Special Purposes.   Small engines <
to give any required degree of regularity for elect]
purposes, by giving a suflicient weight, to the i
large power the same object can be attained by usi
of cylinders, by making the engine double acting,
struction of twocycle engines, or by the c.ombinati
more of these devices.
Thi fourcycle engine has not as yet been ma
and even if the complexity of valvegear for run
directions could be accepted, it appears likely t
starting device would be required for every reversa
launches and automobiles is done by aid of a rnecli
ing gear, except that for some small boats a rever
is used. Such gear for large* ships appears to be
well as impracticable.
Twocycle engines would not require much co
xvhulr .,>sum. Su.h .
*i 1114
t'll ihr ^
fti.r runnim*.
Alt if iHi' mMii^
lilir vr!iidr'M,ill 1
not itir t.u iliU t
am
ihr
Economy
ECONOMY OF GASENGINES
(5) Time of ignition.
(i) The influence of compression is indicated the
equation (187), page 312, which shows that the effici
expected to increase progressively with increasing <
To exhibit this feature and to compare it with the resi
in practice, the following table has been computed f
and 7 of Table XXXV, page 350. The composition o
atinggas used was similar to that on page 315;
detailed report of these tests shows little variation in
Number of tests ... 2 5
Ratio of compression .4.98 459
Theoretical efficiency . 0.479 0.461
Thermal efficiency . .0.270 0.264
Ratio 0.564 0.573
Such a comparison is commonly considered to si
actual efficiency follows the theoretical efficiency,
being based on the indicated horsepower, and be
by dividing 42.42 (the equivalent of one horsepow<
units per minute) by the thermal units per indicated
per minute. But if the brake horsepower is taken
of comparison, as has already been shown to be ]
appears to be practically no advantage in the higher
,^ a INTKKNAt.
kintls of {{its the ft* h''t
basing the * fmijun^n MI
*F!u* tir.Ht trin ut t n 't^ *.h'V
(JASKNiUNl 1 WITH t! I
ta\i a i '" '
1*1? if I ;;* a* M t *?' U >'fr j
4 J
4 >'
4 ^
4 ( * ! '
ECONOMY OF GASENGINES
eight to one will give the minimum per brake horsepower,
remainder of the table is less conclusive, but it appears
that a ratio of eight volumes of illuminatinggas to one v
of air is proper, and that for powergas the ratio should be
what larger than unity.
(3) A committee of the Institution of Civil Engineers *
three gasengines of varying size, but all having the same
of compression, and tested under the same conditions,
results that bear on the question of size are as follows :
Brake horse power 5.2 20.9 52.
Thermal units per horsepower per )
minute t 159 1S * 4
It is to be remarked that the results just quoted are re ma
low, but that the composition of the committee and the p
tions taken, place them beyond cavil. It is somewhat difii
account for the difference between the results just quote*
those given in Table XXXV, though part of it is due to the
mechanical efficiency of the former. This was estimated
about 0.87, while that of the engine tested by Professor
was about 0.72; allowance for this difference may be esti
to reduce the results of the first test in Table XXXV :
thermal units per brake horsepower per minute. This
trates an inconvenience of using the brake horsepower
*M,
Ml
35**
ivrt R%
l'rotVMr \tt \ i in i
thr infill* m ! tin tifttf
llit'iinal unii  }*i in*!!
tMtt'il h(J l <* }tV*rl ,n l
jninuti
Tlti * *tj*t i .u i .hurt
thi arnr ir nil Int la
Illliti !! ii*!i',
Tffr Ut 4i*fl a > f> 1
rniiirs has JMVU tHir.ii
rsl rrMlU ttut i.
r tif l)ir lli.lift)
tiHikr !iti',r JiMttrl. 11
VtihilUr ,"
Hvill'i'M 41 I*HN
MrtltiUlr CH*
A PRODUCERGAS PLANT
development of power by the combination of a Taylo]
ducer with necessary adjuncts, and a threecylinder Wes
gasengine; a detailed report of the tests is given b;
Parker, Holmes, and Campbell,* the committee in ch<
The gasproducer had a diameter of 7 feet inside
lining, and at the bottom was a revolving ash table
diameter; the blast was furnished by a steamblower
from a battery of boilers used for other purposes; t
made to determine the probable amount of steam tak
blower, but the variation of steampressure acting at t
during tests made this determination somewhat unsa
The cost of the steam in coal of the kind used for any
be estimated closely from boilertests made with the sa
The gas from the producer passed through a coke
and then through a centrifugal tarextractor using
amount of water. From the extractor the gas passe<
.a purifier filled with iron shavings to extract sulphur,
way to the engine the gas was measured in 'a meter.
The enginecylinders were 19 inches in diameter ai
inches stroke. At 200 revolutions the engine was rat
brake horsepower. The engine was belted to a dire
generator, and the energy was absorbed by a waterrhe
The results of a test on a bituminous coal from Wes
354 INTERS
TEST
Duration, hours . . .
Total coal fired in prod
Coal equivalent of stean
Coal equivalent of powe
Total equivalent coal .
Thermal value of total,
Total gas (at 62 F. anc
Thermal value of total \
Efficiency of producer .
Electrical horsepower .
Mechanical efficiency, e
Brake horsepower . .
Gas per horsepower pe
Thermal units per horse
Thermal efficiency of bi
Coal per brake horsepc
Combined thermal effici
It is interesting to co
plant with the tests ;
from which the results
TEST AT CH
Duration hours, . . .
Coal required by plant,
Thermal value of Georj
Heat abstracted from 01
Efficiency of boiler . .
ECONOMY OF A IHKSKL MOTOR
correspond to one pound per brake horsepower pi
of a pound per indicated horse power; the makei
powerplants are now ready to guarantee a eo
one pound of anthracite per brake horsepower
Economy of Oil Engine.  An engine of the typ
page 335 was tested by Messrs, A. E. Russell and
of the Massachusetts Institute of Technology,
had a diameter of 1 1.22 inches and a stroke of 15
220 revolutions per minute developed ten brake
the mechanical efficiency was about 0.72, so that
power was about 14; the clearance or charging sp;
0.44 of the piston displacement.
With kerosene the best economy was 1.5 pom
horse power per hour; this kerosene weighed
per gallon, Hashed at 104 K M and had a caloi
17,222 thermal units per pound.
The engine was also tested with a crude d
comes from petroleum after the kerosene, weighin
per gallon, with a. Hash point at i.S F,, and hav
power of 10,410 thermal units per pound; of this
used 1.3 pounds per brake horse 'power per hour.
The thermal units per horse power per minute
l*Mtv%L'i*n** in*! 1 tn fVir tin* fHcftlhiti*" flu thfmi?l i^lVi
I
ml
ffi I
IIP;' 1 
ill
Ife
356
INTER*
quently 0.32. At an
power, the oilconsui
(34.4 horsepower) th
Since oil for lubria
together with the fuel
of this type that erro:
eating oil is to be gua
Distribution of H(
matter in the discussit
of the heat, and espe
work. It cannot be c
because any heatengi
retical cycles, which
major part of the hea
The following tabl
Clerk.*
Dimension
of Engine.
6.75 X 137
9.5 X 18.0
26 X 36 ?
WASTEHEAT ENGINES
first question to be determined is the mean ef
that is desired or can be obtained. This must
fuel and its mixture with air, and on the degree
There does not at' the present time appear to
that will serve as the basis of a working theory
the mean effective pressure even when thes
determined.
It is desirable', in order that the engine shall li
compart, that the mean elTeetive pressure shall b
engineers commonly make use of go to 100 pound
pressure; but German engineers who have had
very large engines for which pre ignition is dange
content with 60 pounds or less.
Wasteheat Engines. *( )n page 180 attentioi
the fact that the exhauststeam from a steame
used for vaporising some fluid like sulphur di
thereby the temperature range could be extern
tests quoted failed to show the advantage that mi
when this method 5s used with steamengines. ',
from a gasengine is very hot, probably 1000 I
there appears to be no reason 'why the* heat sh<
as it could readily be used to form steam in a bo
Durt)oses.
1; W i I' 1 '
I ii ( [*:.
4,;.;
COMPRESSED air i
energy, and for pi
pressure, produced b;
of iron and steel; an<
than that of the
blowers) are used to
for producing forced
be given mainly to th
production and use <
ceptible of but little
be reserved for anotl
A treatment of the
involves the discussi
through pipes, and c
storage of energy difi
the compressed air,
FLUID PISTONCOMPRESSORS
which receive air at atmospheric pressure, con
deliver it against a higher pressure. They are sir
pact, but are wasteful of power on account of frictio
and are used only for moderate pressures.
Fanblowers consist of a number of radial pL
fixed to a horizontal axis and enclosed in a cas
axis and the vanes attached to it are rotated at a 1
is drawn in through openings near the axis and
centrifugal force into the case, from which it 1
deliverymain or duct. Only low pressures, suital
tion and forced draught, can be produced in tl
little has been done in the development of the
determination of the practical efficiency of fanbl
ventilatingfans have their axes parallel to the di
aircurrent, and the vanes have a more or less h<
so that they may force the air by direct pressur
effect the converse of a windmill, producing ins
driven by the current of air. They are useful ratt
air than for producing a pressure.
Fluid Piston Compressors. It will be shown ;
of clearance is to diminish the capacity of the cor
sequently the clearance should be made as smai
T^itTi thie in tnATxr tVA valxr^c r\f rrrrmrp>ccrrc an/
hoil ^ ii* ,!
i'i,iu ,; t<
'n a : * i
illi itidjn! 4
ail ! i .
V. iv
it* u 1 t
ot v, i*i i n,
lfn t*!*u ;i*i
i if> 3 ' ,
i II* i f ? ai* i
MOLSTURK IN THE CYLINDER
ing water into the cylinder, but experience has
work of compression is not much affected by :
only effective way of reducing the work of coi
use a compound compressor, and to cool the ;
from the first to the second cylinder. Three stu
are used for very high pressure 1 ,,. It is, howe^
air which has been compressed to a high pres
density is more readily cooled during comp v cssior
Moisture in the Cylinder.  If water is not ir
cylinder of an aireompres^r the moisture in the
on the hygroscopic condition of the atmosphere
the air were saturated with moisture the ubsolut
tive weight of water in the cylinder would 1:
Thus at 60 P. the pressure of saturated stean
fourth of a pound per square inch, and the weig
foot is about o.oooH of a pound, while the weig'
foot of air is about o.oK of a pound. It is pn
only effect of moisture in the* atmosphere is to
the exponent of the equation (77), page 64.
sion probably holds when the cylinder is cook
jacket.
When water is sprayed into the cylinder of
of operations rrpivsriHt
tlu* air is rompivssrd,
,
If
sll*i 1
' I
ffhrr
VUlfl
cif tin 4 otmprtssor vvl
that tlir !'iiiiinvs>itiri i
nrntial i iirvr haunt; il
thru
rk {' * ujj
Thr \vtrk ff
%rlL '
,
EFFECT OF CLEARANCE
in which the subscripts refer to the normal proper
freezingpoint and at atmospheric pressure.
If, instead of the specific volume v v we use the \>
air drawn into the compressor we may readily transfc
(189) to give the horsepower directly, obtaining
n l
H.P. = I44 v % <[)  i
33000 (n  i)
where p 1 is the pressure of the atmosphere in pound
inch, and n is the exponent of the equation repr
compression curve, which may vary from 1.4 for <
pressors to 1.2 for fluid pistoncompressors.
Effect of Clearance. The indicatordiagram
compressor with clearance may be represented
The end of the stroke expelling air is at a,
and the air remaining in the cylinder ex
pands from a to d, till the pressure becomes
equal to the pressure of the atmosphere
before the next supply of air is drawn in.
The expansion curve ad may commonly be
represented by an exponential equation having the
nent as the compression curve cb, in which case tl
M/'XT'I ntrrii/^ri
the* pns.siuv /> r aruL .1
l;tw rxprt'sM'i! by tilt" r 1
iu \ulumr will U*
part of th' pistim di.spl;
I
anil thi . t i
without t
lit
f.n tor l*>
aiur 11111%
Tfinpemture at the I
tin t omprr*> r yliiiitti
Ijtouf hi in willi tt it w.i
vupur Ci>lli*\v,s ihr li w o
VOLUME OF THE COMPRESSOR CYLINI
pressor to the plan* where it is to he used. The lo
will ht k discussed under the head of the flow of air
it should not he large, unless the air is carried a ]
The loss of temperature causes a contraction of v
ways: first, the volume of the air at: a given pressi
as the absolute temperature; second, the moistu
(whether brought in by the air or supplied in the <
excess of that which will saturate the air at the lowes
in the conduit, is condensed. Provision must
draining off the condensed water. The method
the contraction of volume due to the condensatio
will be exhibited later in the calculation of a specia
Interchange of Heat. The interchanges of
the air in the cylinder of an air compressor and th
cylinder are the converse* of those taking place bctw
and the walls of the cylinder of a steamengine, <
less in amount. The walls of the cylinder are ne
the incoming air, nor so warm as the air expelled:
the air receives heat during admission and the
compression, ami yields heat during the latter
pression and during expulsion. The presence <
the air increases this effect.
Volume of the Compressor Cylinder. Let
360
If thr
will to
the rlraramr
rxprrssrtl in uli ^
HI
thr air i' r\rll'i! it
i! is iirltvi'frt.1 I'IMII
fill" I ilfflfifyv.Mt ill
fiitfii it*. tiiiftf"f!:,SHit^ t .
as i.ili ulatol, vJiriln
i rra^nJ l?y m .un**M
COMPOUND COMPRESSOR
The work of compressing one pound of air fr
p i to the pressure p' is
n I
The work of compressing one pound from the
is
n_ 1
M ( //>
TF,=
ll
w  i I \p f l ) n  i\ \p'
because the air after compression in the first c]
to the temperature t^ before it is supplied to the
and consequently p f v' = pj) r The total work c
\_
 rif JL
and this becomes a minimum when
becomes a minimum. Differentiating with re
equating the first differential coefficient to zero,
Threestage Compress*
iTfftiifvtl, as \\hnr air *
to UM ;t t
whit h flu aii' ' pa^
vva\ frtni uiu*
an* /, ami /,
in
way:
Thr \vurk of iomjrr
it**, ftil'il ttiil'i iif ii
FRICTION AND IMPKRKKCTION. 1
and l "._!
Equations (206) ami (207) k*ad to
from which by elimination we hav
/
and
Sinrt* the temiH*rature is the sanu* at the ad
of the three cylinders, the volumes of the eylr
inversely proportional to the absolute pressures
As with the compound compressors, this meth
a threestage compressor leads to an equal disti
Ix'tween the cylinders. For, if the values of t
equations (210) and fn)arc introduced into e
(204), taking account also of the equation (t<>o{
tlu* total work of compression
37o c
engines; compressors dr:
to a like extent by fricti
The following table
effect of imperfect valv
as deduced from tests
had a diameter of 18 in<
RATIO OF ACTUAL
fe
Piston speed,
feet per
minute .
So
1 60
200
240
280
This table does not
nor is the clearance fc
EFFICIENCY OF COMPRESSION
would be
2
but pjV t = p t v t for an isothermal change, and const
w = ^ 10 ^;
Some investigators have taken the work of isot!
pression, represented by equation (214), as a basis o:
for compressors, and have considered its ratio to the
of compression as the efficiency of compression,
together into one factor the effect of heating during
and the effect of imperfect valveaction.
Professor Riedler * obtained indicatordiagram
cylinders of a number of aircompressors and drew
the diagrams which would represent the work o
compression, without clearance or valve losses. A
of the areas of the isothermal and the actual diagn
arbitrary efficiency of compression just described. 1
table gives his results :
ARBITRARY EFFICIENCY OF COMPRESSI
HYDRAULIC AiRCOMPRESSOl
temperature. The essential features are an asp
ing the water with air, a column of water to g
pressure, and a separator to gather the air from
compression. The water is brought to the com]
stock, its it would be to a water wheel, and below
away in a tailraee; the power available is detei
weight of water ilowing and the head in the pel
tailraee, in the* usual manner. Below the dam
vated to a depth proper to give the required
2.3 feet depth per pound pressure), and then a <
vated to provide space for the separator. I
plate iron pipe or cylinder, down which the \v
passing the separator the water ascends in the
away at the tailraee.
The head of tin* pipe is surrounded by a \
drum into which the penstock leads, so that i
to the head all round the periphery. The hea<
of two inverted conical iron castings, so formt
into which thr water Hows at first contracts ai
the changes of velocity being gradual, no ap
energy ensues. At the throat of thr inlet, wh<
highest, then* is a. partial vacuum, and air is j
numerous small pipes sn that the water is char
of air. The upper conical casting can be set b
the supply of water and air.
As the mingled column of watrr ami airhu
the pipe, the air is cumpressed at appreciably
of the water. At the Icnvrr rml, the* pipe rxpu
velocity, and delivers thr air and water into
the air gathers in the top of the bell, from u
AirPump**.
*r*
\ufti tin
itM.tiii i
tump,
lilt mri,ii! *4 tft jr ?s
liy tilt" f ftf tip. fit Mil J'.itfr
irtil it i 1 * t u*<ft*m.tr* ?*+ :
DRYAIR PUMP
Seaton * states that the efficiency of a vert:
airpump varies from 0.4 to 0.6, and that of
horizontal airpump from 0.3 to 0.5, dependii
and condition; that is, the volume of air an
discharged will bear such ratios to the disp
pump.
He also gives the following table of ratios o
pump cylinders to the volume of the engine cyli
discharging steam into the condenser :
RATIO OF ENGINE AND AIRPUMP C
Description of Pump.
Description of Engine.
Single
acting vertical
Doubleacting horizontal .
Jetcondensing, expansion
Surface " "
Jet
Surface "
" compound
Jetcondensing, expansion
Surface "
Jet
Surface " "
" " compound
Dryair Pump. In the recent development <
ing, especially for steamturbines, great emp]
obtaining a high vacuum. For this purpose tt
pump which withdraws air and water from t
been replaced by a feedpump which takes wa
condenser, and a dryair pump which removes
is necessarily saturated with moisture at th
the condenser, and allowance must be made fc
770
If ih<
an 1
tn i*
;,! / I ,,
!U t tli^ *
i iti Ml ,!, n
t ulltlrliNlHi*
II
CALCULATION FOR AN AIR COMPRE
85. J Lj.8s
X 7 7; 2080 e
51.9 0.878
Assuming the air pump to be singleacting
nected directly to the engine which made abo
per minute, the effective displacement of the
should be
2980 : (50 X <>o)  i.o cubic f
To allow for the effect of the air pump eleara
of valve action, and for variation in the temper;
ing water, this quantity may be increased by 50
The engine had 3! feet for the diameter ar
stroke of the low pressure piston, so that its <
nearly 50 cubic feet; the air pump had a diam<
a stroke of one foot, so thai its displacement
feet; the ratio of displacements was about sixtee;
ancy shows that the conventional method of des
provides liberal capacity.
Calculation for an Air Compressor. Let. it b
the dimensions of an air compressor to deliver
air per minute at too pounds per square inch 1.
also the horse power required to drive it.
If it is assumed that the air is forced into
at the temperature of tin* atmosphere, and, ft
is no loss of pressure between the compressor
pipe, equation (ic.)j) for finding the volume
compressor will be reduced to
r,  v. & joa < w OT , M4J ( . u
If now we allow five per cent for imixTftrt
37*
If thr
if thr r\rnl "< *'*'
the uir in ihr tlrif^ 1
whivh ihr lUlfirira^n
/4^l
t \t H:) trVfilll!i' %
Will tir
thr i Mini*!"*"'^ 1 *'* &
tit > ii.:
CALCULATION FOR AN AIR COMPRES!
The calculation has been carried on for a simple
but there will be a decided advantage in using a coi
pressor for such work. Such a compressor should
pressure in the intermediate reservoir
X 147 = 4i.o6 po
The factor for allowing for clearance of the
cylinder will now be
m\pj m ioo \ 14.7 / ioo
The loss from imperfect action of the valves an
of the air as it enters the compressor will be less foi
than for a simple compressor, but we will here ret
2464 cubic feet, previously found for the apparen
the compressor. The volume from which the dime
compressor will be found will now be
2464 * 0.9784 = 2518 cubic feet,
which with 80 revolutions per minute will give 15,
for the piston displacement, and 755.5 square ii
effective piston area, if the stroke is made 3 fee
Adding 16 inches for the pistonrod, which will b
pass entirely through the cylinder, will give for th
the lowpressure cylinder 31! inches.
Since the pressure p f is a mean proportional be
p 2 , the clearance factor for the highpressure cyl
the same as that for the lowpressure cylinder, and, a
are inversely proportional to the pressures p 1 and
pressure piston displacement will be
(15.74 X 14.7) 5 41.06 = 5.64 cubic fe
iiMins will U 1*'^ than
piv;,Mvf, Ai'ain, ihr tin
>waH l'i.''in may tr rr
tthit h ilij*nl >u tin* i
mvivr niiu It uHmtiMn a
Tin*  **! iT{uirnl I
frtn rjualitli i t*^ * t' r
ills .ipl'atvnt * aa !!^ *
a}]ai**tit * aja iH' alrra
H.r.
{"fir !r!Sl]*f!4f?4l'r 4! ft'
will !* i'^r ;>" I 4 '. a!ui**,
FRICTION OF AIR IN PIPES
which last term is obtained by dividing the a:
by its perimeter. For a cylindrical pipe we ha
m = ircd 2 nd = id . .
The expression (215) represents the head of lie
overcome the resistance of friction in the pipe w
of flow is u feet per second. Such an expression
be applied to flow of air .through a pipe when th
ciable loss of pressure, for the accompanying inc
necessitates an increase of velocity, whereas the (
the velocity as a constant. If, however, we cc
through an infinitesimal length of pipe, for wh
may be treated as constant, we may write for 1
due to friction
P u 2 dl
2g m
This loss of head is the vertical distance throu
must fall to produce the work expended in ove]
and the total work thus expended may be founc
the loss of head by the weight of air flowing tl
It is convenient to deal with one pound of air, so
sion for the loss of head also represents the wor]
The air flowing through a long pipe soon '<
perature of the pipe and thereafter remains at a <
ature, so that our discussion for the resistance oi
made under the assumption of constant tern
much simplifies our work, because the intrinsic <
remains constant. Again, the work done by t
ing a given length dl will be equal to the work
when it leaves that section, because the produa
But tlu* vrlwifv f ;iir
ian !> n
Thr ai
Irngth ill if pij 1 *, anil
work must lr
tiihtT r
f liriitl i> rtUiil lei thr
Bui frttttt lli' * hir;u i
FRICTION OF AIR IN PIPES
But from equation (221) the velocity at the entrai
where the pressure is p l will be
WRT . rrr
MI= __ and w
so that equation (223) may be reduced to
gRTm p, 2
Equation (224) may be solved as follows :
The first two forms allow us to calculate eithi
or the loss of pressure; the last form may be us<
values of f from experiments on the flow through ]
From experiments made by Riedler and Gut
fessor Unwin f deduces the following values for f:
Diameter of pipe, feet.
0.492 0.00435
0.656 000393
0.980 0.00351
with ; !
?  ,,,,,,, s .
FINAL TEMPERATURE
steam was used in it. The full line ah is a hypcrb
line ac is the acliabatie line for a gas; both lines are dn
the intersection of the expansion lines of the two dk
Power of Compressedair Engines. The prol
effective pressure attained in the cylinder of a cot
engine, or to be expected in a projected engine,
may be found in the same manner as is
used in designing a steamengine. In Fig.
85 the expansion curve i 2 and the com
pression curve 3 o may be assumed to be
acliabatie lines for a gas represented by
the equation
and the area of the diagram may be found in the usi
therefrom the mean effective pressure can be determ
ing the mean effective pressure, the power of a give
the size required for a given power may be determii
The method will be illustrated later by an example
AirConsumption. The air consumed by a given
air engine may be calculated from the volume, pi
temperature at cutoff or release, and the volume, t
and pressure at compression, in the same way that t
consumption of a steamengine 5sealculated; but
the indicated and actual consumption should be the
there is no change of state of the working fluid.
intrinsic energy of a gas is a function of the tempc
the temperature will not be changed by loss of pro
valves and passages, and the air at cut oil will be
in the supplypipe, only on account of the chilling a
wn.ll*; of tht* rvlindrr rhirim*" jiHminKion. which ;rrfm
jtvs>urt' in v.th> .U'
found bv thr r*juuiin
if thr r\{;WMtn
nit! if r\pitMsit>n fi
in ** hit !i T, ;> ?hi ^
i*!i4 <, / r j. ?hr ,;*
iiiil / i . th* !rn$'
:tt thf vijtjK I'M'*"
jtii'*Mtir tins in th
i**f Ilfii ll t/ f l< 4 !h
iii* fin!* h 4 . il i *
th*' frWJtiM"jJ< III
In i'i
ii mj t.tMa* in
MOISTURE IN THE CYLINDER
the walls of the cylinder of a compressedair engine 2
working therein are of the same sort as those taking pla
the steam and the walls of the cylinder of a steamei
is to say, the walls absorb heat during admission and c<
if the latter is carried to a considerable degree, and
during expansion and exhaust. Since the walls of tl
are never so warm as the entering air nor so cold
exhausted, the walls may absorb heat during the be
expansion and yield heat during the beginning of com
The amount of interchange of heat is much less
pressedair engine than in a steamengine. With a
expansion the interchanges of heat between dry a:
walls of the cylinder are insignificant. Moisture
increases the interchanges in a marked degree, bu
make them so large that they need be considered i
calculations.
Moisture in the Cylinder. The chief disadvant
use of moist compressed air and it is fair to a
compressed air is nearly if not quite saturated whe
to the engine is that the low temperature experie
the range of pressures is considerable causes the i
freeze in the cylinder and clog the exhaustvalves,
cultv mav be overcome in Dart bv making the valves ar
CALCULATION FOR A COMPRESSEDAIR EN
automatic valvegear the actual mean effective pi
be 0.9 of that just calculated, or 38.7 pounds per squ
For a piston displacement D the engine will de^
revolutions per minute
144 X 38.7!) X 2 X iso ,
6 horsepower:
33000 F '
and conversely to develop 100 horsepower the pist
ment must be
n IPO X 33000
D ~ 144 x 38.7 x 2 x i 5 o = T  974 cublc i
and with a stroke of 2 feet the effective area of the pi
1.974 X 144 T 2 = 142.1 square inches.
If the pistonrod is 2 inches in diameter it will hav
3.14 square inches, so that the mean area' of the p:
143.7 square inches, corresponding to a diameter of
We find, consequently, that an engine developin
power under the given conditions will have a diai
inches and a stroke of 2 feet, provided that it runs
lutions per minute.
In order to determine the amount of air used b;
we must consider that the air caught at compression i
CUMi'KKSSX!) AIR
of the putton displacement, If the lompresMim omirred ufl
dently early t raise the prtHMire to that in the supply.pig
More the admlsMtn \alvr ttjtened, then only o.jj of the pista
displacement would ! used j*r .stroke ami a saving of about i
JUT cent would lie attained; in MK h tae the mean cffecth
pressure wouttt l MnalUr um! lltr ni/r uf thr cylinder would t
lurgrr,
1'hr airrtnsuipton for thr
cttlnr frrt rr minutr. 1'lir afttutl air consumption will I
sttmewhat \v*& tn anotint *l l**' of prrt.tirr in thr valves an
fiiiH^igrs; il may b fair to avutwr ifio miu fi KT minute f(
the urttial ti*nstmtfiiit.
In order Ir* niiikr oiu complete i ;di ul.it ton f*r the um of con
pn?)Wi i d air for tran<*tiiilfiic jmHrr, thr ittt*i fr the rampnwc
air engine imvr Ittrfi nwde to iorrr^jxmtl with the re^uiu of calci
tatins fur an air rumpre^Mr cm jMit*' ..177 tnd fr the lew <
pressure in it pte tii .,!*4 ^in* there i^a f pressui
In (IciwinK tltrtifit thr piji at *siaitt smii^rjitwrr^ there
a nrrr%iiiti$ri.f tnrrraitr t! volume . : that the pijic delivei
tuhir frrl ftrr minute, Our takttkfit*ii for the aircc
of in engine to drlivrr too horw power given itlwut 160 cub'
f?t., frtim which It appear* that the ^y^tem l TOWftrtwr coi
d urt ing= pin.*, und tMmpre:**.rd *isr engine should deliver
X jJ^.ft * i*#j f htre j*ower.
If the frictitm of the comprevMrd air engine i* to I
ten frr cent, thr HWrr drlivrrrtj liy il to the (or I
lite mat him* driven directly from in will l*e
'*; ,t itsiif%r }HtWer<
The straiti Kiwrr renjuirrtt ifi drive 4 %ifiilr rmirfr wi
fount! to l*r huriejHwer; it .fi%wtirniiy ?
of the .ir*mpMWrr i
fr doing wos
compound compressor is used, then the indicated steampower
is 444, and of this
1 80 T 444 = 0.40
will be obtained for doing work.
If, however, we consider that the power would in any case be
developed in a steamengine, and that the transmission system
should properly include only the compressorcylinder, the pipe,
and the compressedair engine, then our basis of comparison will
be the indicated power of the compressorcylinder. For the
simple compressor we found the horsepower to be 442, which
gives for the efficiency of transmission
180 4 442 = 0.41,
while the compound compressor demanded only 377 horse
power, giving an efficiency of ^
180 4 377 = 0.48.
It appeared that the failure to obtain complete compression
involved a loss of about 13 per cent in the airconsumption.
It may then be assumed that with complete compression our
engine could deliver 200 horsepower to the main shaft. In
that case the efficiency of transmission when a compound com
pressor is used may be 0.53.
Efficiency of Compressedair Transmission. The preced
ing calculation exhibits the defect of compressed air as a means
of transmitting power. It is possible that somewhat better
results may be obtained by a better choice of pressures or pro
portions. Professor Unwin estimates that when used on a large
scale from 0.44 to 0.51 of the indicated steampower may be
realized on the main shaft of the compressedair engine. On
the other hand, when compressed air is used in small motors,
and especially in rockdrills and other miningmachinery, much
less efficiency may be expected.
Experiments made by M. Graillot * of the Blanzy mines
showed an efficiency of from 22 to 32 per cent. Experiments
* Pernolet, L'Air Comprimg, pp. 549, 550.
i I
AIR
madr by Mr. Daniel at lards gave an Hl'tnisicy varying from
0.355 to 0.455, W M  ( r*^wes wrung from ,,75 atmospheres
.$ atrt!tttlirfr>, An r\Hriwent made by Mr. Kraft * gave
an efhrienry of 0. ij; for a Muutl mat bine, lining air at u pressure
of live atmospheres without e\panMon.
Compressed air ban turrit u.ed fur Manumitting j HI WIT either
whrrr jHiwer fur fompre.*Mon i'* iheap ami abundant, or where
thrrr an nttwrns why it i< ^Hiully de \able, as in mining and
tunnt'lHng. It i^ now >i to a on*ileiable extent for driving
hamlloul*. smli a* drill*, t Unifying c hmt, ami talkingtools,
in mat him* and Uiler ^Si*". itml in hbtpyards. It is also used
for oHTalin# trane and other imuhtiu 1 . where wrr is used
only itt interval*, M thai tht tondrnratiort of steum (when used
dirttlly) ** fwrft^ivr, ami w here bytiratdu j*tiwer i* liable to give
trouble from fmvjrig.
Ci.iii*i*oi air ha? trrii ii^nl to a MTV i niiiilrrii bit? extent
fur tratisfttlititti? JHWT in IVix Ilir '.vsinii ajiH*An to be
v,xK*nMvr and It* i. tr%rt mainly i*n aft*utnt of tt ctinvtjinicncc
for {U*livi*rint !*itiiill iwrf% m in 4ii"** where ilir eoUl t'^htusl
fan iit usrtl fr frlfigrraliirti, 1'lir trouble from fretting oi
mttUturt* in ihr tylimlrr haj* lrrn jtuitilrd by allwing the all
tt IliiW thntugh <  il 4 ir wltitli i% hrttitl rxtrtmlly byi
rlwrrtiiil firr, I*rfr%M$f I'mvm ^timatrH tlutt tin tikirncy ol
if 0.75 may t* e attained under favorabU* t'onditfoiu
tlir lir is r,if Ihr tim*rn?rf*r, but In* nol
includi* ihr c*t.l l IwrS f*r rrhriitinu In ilii% rsilninlr,
of by Air, MtsrrvIw or
fur driving ,*lrrri tar**. A n^ttem dri,rhjctl by Mrlariki WK
air nl 'i)o to HP itifiis MT *jUitfc intii in rr^trrvtiim having 2
rafittify tl *^ fubir frtl, Utr tar al?* iiff1ra a of ho
water at a temHTaturr of A!HWI i?;rf" I*'., through wtiirh theaii
,i*i cn the way to the motor >md tiy wits* It it i* liratttl aw
ram. Tlii'i utc of hot water give* a
method f stwfini? !**W*T, ^mi al'vo A\n^i trouble from
used lor driving streetcars in New York City, but the particu
lars have not been given to the public.
The calculation for storage of power may be made in much
the same way as that for the transmission of power; the chief
difference is due to the fact that the air is reduced in pressure
by passing it through a reducingvalve on the way from the
reservoir to the motor. By the theory of perfect gases such
a reduction of pressure should not cause any change of tem
perature, but the experiments of Joule and Thomson (page 69)
show that there will be an appreciable, though not an important,
loss of temperature when there is a large reduction of pressure.
Thus at 70 F. or 2i.i C. the loss of temperature for each 100
inches of mercury will be
o.92 X
= o.79 C. = i
Now 100 inches of mercury are equivalent to about 49 pounds
to the square inch, so that 100 pounds difference of pressure will
give about 3! F. reduction of temperature, and 1000 pounds
difference of pressure will give about 35 F. reduction of tem
perature. The last figures are far beyond the limits of the
experiments, and the results are therefore crude. Again, the air
in passing through the reducingvalve and the piping beyond
will gain heat and consequently show a smaller reduction of tem
perature. The whole subject of loss of temperature due to
throttling is uncertain, and need not be considered in practical
calculations for aircompressors.
For an example of the calculation for storage of power let us'
find the work required to .store air at 450 pounds per square
inch in a reservoir containing 75 cubic feet. Replacing the
specific volume v t in equation (213) by the actual volume, we
have for the work of compression (not allowing for losses and
imperfections)
W  3 X 4647 X 144 X 75
20520000 footpounds.
I
394
4 lit
If thr prrssiirr i% rrtliitri IM >i* j*ufnl." bv ttu g.aii'i' before it
usttl, thr voiumr of iir will !
75 * *4r : fs .i' >ijiulh frrt.
The work for ruittftlrtr cxjtanMon of onr {Htttmi to ihr
of ihr atmo>jhrrr will t*r
am) thr work for >.tu riibti frrt will lr
144 ^ 04.7 * j 5,* 8 ^ "" I % I I  5*^7'
foot {MUt mis without allow ing for t, t r, *i iittfMrtfrrfbnj*,
maximum rwYirmy of 'Coring ami rritoring rnrrgy by
usr f rctfiiirrwrtl air in ittb t;t::*r it thrrrfofr
. ^*.
In ir<iSltr llir rlluiriift t.itlim! ! ittufr than 0.^5, If
Suddtn It tiu> nut In: out tf 4a
lion lo M danger that niay arrir if air ;it high rr^urt* it sudden!
It'l Into a filfie wliii It ii,i* oil mmgtr*) wiilt thr air in it or eve
ittihtTing to llir tiilr of thr i 8 **. '1'hr ;iir iff thr iv mill bccott
its triiiit*raiiirr l#*.*iite riiniigli i ignite Ih
nil J4ncl i'AUnf an r*ii'tsn, Thiit iftth tlangrr IH nut imaginary i
slttiwii by nil rsfiltt'titsft tvhuh mturrcvl urulrr nt
it lfit* wltklt WHH .ftiritiig rtiough ! willtil^ttit thr airj
LlqttW Air. Thr irwfki!l way of It*jtft*fviftff ilr oft
litrgr jtiatlr ii that tlrvisnl l Uinlr *irrmtiftg MB flic RfliJCtio
of thr Urmwriitllfr 111 lif!ii*, I Ift *,agr C, U tfe
empirical r*rrvii*n ttntutrti hy Jimlc iimt K^tvtn for th
rtt)uc'ttn in trtfificTjiitifr f ilr fhming through a rtB plu
with m diffrfrrtrr *if fr*%nrr riw.r^irr*! ly it Ittilir* til
freezing, and T is the absolute temperature of the air.
A modern threestage aircompressor can readily give a press
ure of 2000 pounds per square inch, and if the above expression
is assumed to hold approximately for such a reduction in pressure,
it indicates a cooling of
. 92X a22_ =37 o a
y ioo X 0.491 "
or about 67 F. By a cumulative effect to be described, the air
may be cooled progressively till it reaches the boilingpoint of its
liquid and then liquefied. Linde's liquefying apparatus consists
essentially of an aircompressor, a throttlingorifice, and a heat
interchange apparatus.
The aircompressor should be a good threestage machine
giving a high pressure. The throttling orifice may be a small
hole in a metallic plate. The heat interchange apparatus may
be made up of a double tube about 400 feet long, the inner tube
having a diameter of 0.16 and the outer tube a diameter of 0.4
of an inch; these tubes for convenience are coiled and are then
thoroughly insulated from heat. The air from the compressor
is passed through the inner tube to the throttleorifice and then
from the reservoir below the orifice, through the space between
the inner and outer tubes back to the compressor. The cumu
lative effect of this action brings the air to the critical temper
ature in a comparatively short period, and then liquid air begins
to accumulate in the reservoir below the orifice, whence it may be
drawn off.
The atmospheric air before it is supplied to the condenser
should be freed from carbon dioxide and moisture, which would
interfere with the action, and should be cooled by passing it
through pipes cooled with water and by a freezing mixture.
The portion of air liquefied must be made up by drawing air from
the atmosphere, which is, of course, purified and cooled.
The principal use of liquid air is the commercial production of
oxygen by fractional distillation; several plants have been installed
for this purpose.
C'HAITKR XXT.
.KVri.\i;M. \rlUNIs.
ftr producing k
e ir ^nrr. It ni
>i lw lrnijHrature
A Ri?rw<u:*ATtxis.\c*itWK N ;i
tmH*ruturfH or for tliiit '*we
la? umi (or making UT r fr mtiitt
a cellar or *torehou*e.
Refrigeration on A *ftiitlt ^ale wav t*r obtained hy I hi* sol
lion of ttrtiiifi iall; a familur iliis%!i',titi! is thr stilutiun
immn Mil with kr, ;inuthrr i* ilir inhiii<m f sal ammoni
In walrr. (Vrtain rdr !} ting ttt;u Itiiir^ tr*riiil n the raj;
jttrilori nf miir uttafiir liwiI, fr r\sti{r, t ummtmia
walrri If tin* mathinr ! i* wrk iiiti*'K ilutv rmt?t litsoi
lirriiriicrmrtit fr rrtitsistling il litii! fr**m tlw uhnnrlK'nt. T
mm! rrrrnl ani t*wrrfiil frffi*rf;i!siit nut ltlitr% jirr revew
llt'iil rngiiirA, lliry illiiif,$w list vnrrl# .'aitiHiantT (air
amftwniiil fruiti ihr t**l*l r**iim r t*Isni mil, imfirrii h, a,
drllver it It* a imlif r on*Im'trf. "Iliii's Uuy lakr hrat from
t'tilt! utliiiit'r, ! w<rk am! ii*il Iir4i, sinl itnaity nJiTt then
of the in ami ittr h*4i rui\iili*ni of tbr work dot
Thrsr ri*wr'*t tirni rtiitr% 4 lsi*rvrf , urr wry far from btfi
r**vrr%llilr tnitinrH, not Jy * ai mim f iiHrfn ilwns imi Iw
but litT4li* they * si irvrf.'sillr ryrir,
f rft liifir! art in tmnmon ., i
sulphur <lto%ii* ur snmr oihr volatile Iliiltl fa Uii
tf affit*i!ii;$, C*arlsn tltutiifr Iwi Iwrft iisnl, but there i
dilikiilltr !* l itiult ri"^'tifr .tn*l thr f..n! tli.il the rritkmi le
{irrAturr k M a ,
Air "Hit' general arwft^rmeRl
i,itlBr ! t htMin tv i ; 'ii?. *. ft ttiftsf
oi u. c.umju.mwu<.,yuHu<u /i, nu expansioncyimaer & 01 smaller
size, and a cooler C. It is commonly used to keep the atmos
phere in a Coldstorage room at a low temperature, and has
certain advantages for this purpose, especially on shipboard.
The air from the storageroom comes to the compressor at or
about free/,ingpoint, is compressed to two or three atmospheres
and delivered to the cooler, which has the same form as a sur
facecondenser, with cooling water entering at e and leaving at /.
The diaphragm mn is intended to improve the circulation of
the cooling water. From the cooler the air, usually somewhat
warmer than the atmosphere, goes to the expansioncylinder B,
in which it is expanded nearly to the pressure of the air and
cooled to a low temperature, and then delivered to the storage
room. The inletvalves a, a and the deliveryvalves b, b of
the compressor are moved by the air itself; the admissionvalves
, c and the exhaustvalves d, d of the expansioncylinder are
like those of a steamengine and must be moved by the machine.
The difference between the work done on the air in the com
pressor and that done by the air in the expansioncylinder,
together with the friction work of the whole machine, must be
supplied by a steamengine or other motor.
It is customary to provide the compressioncylinder with a
waterjacket to prevent overheating, and frequently a spray
of water is thrown into the cylinder to reduce the heating and
the work of compression. Sometimes the cooler C, Fig. 86,
tlt;KKATlM; MAl'WNKS
is replaced ly .m app.ir.itti. HwtftUiin* ,i Meant engine jetcon
denser, in \\hith thr ;iii i t4r*S 1\ a pray uf uater. In any
cast it in essential flul tlr mnttlwe in tin air, as wrll as the
water injeitrd. should ! ellii uwly removed Ufure the air ii
delivered ti the expansion cylinder; otherwise snow will form
in thai cylinder an*} inierfrre ttiih tlu iiciion of the machine,
Various mechanical dcviers tt.m l:rrii tHt'ti in tulUrt ami remove
water frni tin* air, luii air nuy S suturatctl with moisture aftej
h 1ms jiitMitd >IKI a ilruir, Thr lUH C'tilrmiin Company UM
u jrl itHlrr with prnvitiun fr ti4!rjiin^ and withdrawing water
and ihrn ii s * ilir uir ihrounh JMJHS in ihr citldrtKim on th
way tn ilir rxansun i>ltmU"r. 1'isr n44ri!i
at a trnifK'riilW't* a tilth iiSt**%r frrr/itii? jinl, M ihsii the
ture in the air i* tmlrii%fd uj**n ilw sidr^ tif the iH i a anc
drains bat'k intt* ttir tmtrr.
an air rrffiiirwliiig nun Iitnr i
tit ilw rM rim i mtin*fily
and the skr f iln tna* hint i Utrnr '*
ftrmam't'. Hi*' itTfrm,nur ituv U
fhr nuu him n i t, Itrnil i y Ir %uih
{fir MId air may t*f
Kill Huhtticm* friifti wliitli
Wftlln uf llir iin alisl lltrfi
iiMtl its tlmTtbed, thi
hai n( fttr itlrncmphare
t.n!is;ifr*l with Its per
imrtiiMtl hy runnto)
jrc"urt"s; lr example
i* n u*t! 4 ij* in a iionfreeanj
r >$ir <ti*'tir<ni'* liriti through thi
Mri  ilir t tifif*"%.fif>r ftt be UW
vt*r Thr mathtne then i wti in produce ice,
thr lirlftt? lie used for otisling in* or Ittjititb, A rotcftlni
his been ftr (irtw)tnitt^ in nil n small 'iilr without cooliaj
watrr, n the reverse of ilt prtmiple; i' a!nitiheric ai
is tif"%! rsfafitloi tltiilnt delivered to a toil of plpt* U
a Hitlt solution, thru the ir in lr*i from thin toil, after absorb
Ing heal from the brine. * ompfrr&Md to itmtspherk
Proporttont of Air Tht? pcrfor
f a iiiiitltlflr fiwi) l*r .*tttted In tCTtft
of the nutntirr l iltrrma! tn * unit of time
or In of the f iir *fiiitTi, Thr Intent hat o
of kc Ic tn l*c fe t a brie* or 144 .T.W,
cylinder be p v that at which it leaves be p 2 ; let the pressure at
cutoff in the expandingcylinder be p a and that of the back
pressure in the same be p, let the temperatures correspond
ing to these pressures be t v t v t s , and / 4 , or, reckoned from the
absolute zero, T v T 2 , T 3 , and T 4 . With proper valvegear
and large, short pipes communicating with the coldchamber
p t may be assumed to be equal to p t and equal to the pressure
in that chamber. Also ^ may be assumed to be the tempera
ture maintained in the coldchamber, and 3 may be taken to
be the temperature of the air leaving the cooler. With a good
cutoff mechanism and large passages p s may be assumed to
be nearly the same as that of the air supplied to the expanding
cylinder. Owing to the resistance to the passage of the air
through the cooler and the connecting pipes and passages, p 3
is considerably less than p r
It is essential for best action of the machine that the expan
sion and compression of the expandingcylinder shall be complete.
The compression may be made complete by setting the exhaust
valve so that the compression shall raise the pressure in the
clearancespace to the admissionpressure p s at the instant
when the admissionvalve opens. The expansion can be made
complete only by giving correct proportions to the expanding
and compressioncylinders.
The expansion in the expandingcylinder may be assumed
to be adiabatic, so that
(231)
Were the compression also adiabatic the temperature t 2 could
be determined in a similar manner; but the
air is usually cooled during compression,
and contains more or less vapor, so that the
temperature at the end of compression cannot
FIG. 8 7 . be determined from the pressure alone, even
though the equation of the compression curve be known.
RKrKI'ifcKATISti M.\* HtM.S
It* ihr nir paving through ihr tHstifrr.tting. machine p
minutt* U* J/; thru ihr hr.si wiihtiruwn from ih? n>ttiroom
Tht* work *f compressing M {mimd* ui ur from the pre&urc
to ihr prom i! re ft in *i fomprr^ur wjtltntsi ilriiraritr is (Fig, 8
W f  vll f p.r. *
f
it*  ^ ? f
t t I* a '** I "
* i
Vlf
"r I
ir ii *.
, * f .* . , , <
s I \,f
I Ihr
In*
fi snii * An **
If ill* t%]4n*oM til Ihr i^.t^M,
lU^% U Ihr ,,% ittr ff lltF d 1
by ihr ut will h* lh* 4* riti4iiititi fijj) or fi t *
l t ^ trt i ( />, f , .a*l f, by Ij ft; to tA
it; ~
I
H  1 t
w
me auierence between the works of compression and expan
sion is the net work required for producing refrigeration; conse
quently
or, replacing M by its value from equation (232),
W = 2i *i + ^ Ji ~" V
/ t / 4
(237)
(238)
The net horsepower required to abstract Q t thermal units
per minute is consequently
778Q t < a + fr  *,  <.
33000 /, / 4
. . . (239)
where ^ is the temperature of the air drawn into the compressor,
and t z is the temperature of the air forced by the compressor into
the cooler, and / 8 is the temperature of the air supplied to the
expandingcylinder, and U is the temperature of the cold air
leaving the expandingcylindcr. The gross horsepower devel
oped in the steamengine which drives the refrigerating machine
is likely to be half again as much as the net horsepower or even
larger. The relation of the gross and the net horsepowers for
any air refrigeratingmachine may readily be obtained by indi
cating the steam and aircylinders, and may serve as a basis for
calculating other machines.
The heat carried away by the cooling water is
Q, Q l +AW (240)
If compression and expansion are adiabatic, then
Q z  Me, (I,  / 4 + /, + <4  /i  < 8 )  MC P ('
Q z  Me, (/!  /< + / + U  / t  /,)  Mc p (t,
or, replacing M by its value from equation (232),
. (241)
Qi
^1 ~ ^4
(242)
If the initial and final temperatures of the cooling water are
4O2
REFRIGERATING MACHINES
tt and t t) and if <? and q k are the corresponding heats of the*
liquid, then the weight of cooling water per minute is
G  ^7. = <2t (t oifo gi ) ' ' ' (243)
The compressorcylinder must draw in M pounds of air per
minute at the pressure p t and the temperature t v that is, with
the specific volume v t ; consequently its apparent piston dis
placement without clearance will be at N revolutions per minute,.
Mv, MRT. , ,
D =M7^ (244>
for the characteristic equation gives
Replacing M by its value from equation (232), we have
, }
e 7T .... 1,245;
2Nc p p 1 (^  I*)
Since all the air delivered by the compressor must pass through
the expandingcylinder, its apparent piston displacement will be
(246)
If p v the pressure of the air entering the compressioncylinder
is equal to p^ that of the air leaving the expandingcylinder (as
may be nearly true with large and direct pipes for carrying the
air to and from the coldroom), equation (246), will reduce to
D. = D c p ....... (24?)
* i
Both the compressor and the expandingcylinder will have
a clearance, that of the expandingcylinder being the larger.
As is shown on page 363, the piston displacement for an air
compressor with a clearance may be obtained by dividing the
apparent piston displacement by the factor
complete, the same factor may be applied to it. For a refriger
ating machine n may be replaced by K for both cylinders. To
allow for losses of pressure and for imperfect valve action the
piston displacements for both compressor and expanding
cylinders must be increased by an amount which must be deter
mined by practice; five or ten per cent increase in volume will
probably suffice. In practice the expansion in the expanding
cylinder is seldom complete. A little deficiency at this part
of the diagram will not have a large effect on the capacity of
the machine, and will prevent the formation of a loop in the
indicatordiagram; but a large drop at the release of the expand
ingcylindcr will diminish both the capacity and the efficiency
of the machine.
The temperature / 4 and the capacity of the machine may be
controlled by varying the cutoil of the expandingcylindcr. If
the cutoff is shortened the pressure p 2 will be increased, and
consequently T* will be diminished. This will make D e , the
piston displacement of the expandingcylinder, smaller. A
machine should be designed with the proper proportions for its
full capacity, and then, when running at reduced capacity, the
expansion in the expandingcylinder will not be quite complete.
Calculation for an Airrefrigerating Machine. Required
the dimensions and power for an air refrigerating machine to
produce an effect equal to the melting of 200 pounds of ice per
hour. Let the pressure in the coldchamber be 14.7 pounds per
square inch and the temperature 32 F. Let the pressure of
the air delivered by the compressorcylinder be 39.4 pounds by
the gauge or 54.1 pounds absolute, and let there be ten pounds
loss of pressure due to the resistance of the cooler and pipes and
passages between the compressor and the expandingcylinder.
Let the initial and final temperatures of the cooling water be
60 F. and 80 F., and let the temperature of the air coming
from the cooler be 90 F. Let the machine make 60 revolutions
per minute.
With adiabatic expansion and compression the temperatures
; MAi JUNK
til
of thr air rowing i'mm ih uiitrrs^t*r ami
tlimUr will l
/, 
7*4  Ufo *
Tltt rortt Stif*
. U
VM;
gitl from tfc
.', /,a54l
i i "
ir
tt
}nr minuir; ruH'*rtiiriitSy tin itri hni*.r JO\VCT if ihr machin
s i
^54 U
II.J II, I*,,
iint ltr fsi
lit tr s. h*r^i
By rtjutiitttti
rn fi in m*i
r aisfrfii ii.%in
tvill lr
j,,yeii ft.
11
of th
f I 1 4 * t '1 ' * i
IV" '* ^ ^.'li * " * .jo rittiic f?t,
/, W
If lilt* tlruriimr tf ll$r iiSll*frw%t.if i yiiftt)rr i* of it
tiw4*nrflit'itl, t!sr ittr fat I*r f**r i. SrafiiSiif liy tt)U4ttoR (ifl) f
t t
,l *
f .1 i * * r * 1. 1 f
i
J v r % f
2.33 * 979 ~ 2 3 8 cubic feet.
If, further, the clearance of the expandercylinder is 0.05 of
its piston displacement, the factor for clearance becomes
0.963,
100 \i4.7/ 100
which makes the piston displacement
i\9o * 0.963 s= 1.97 cubic feet.
If now we allow ten per cent for imperfections, we will get for
the dimensions: stroke a feet, diameter of the compressorcylinder
15^ inches, and diameter of the cxpandingcylinder 14 inches.
Compression RefrigeratingMachine. The arrangement of
a refrigerating machine using a volatile liquid and its vapor is
shown by Fig. 88, The essential parts are the compressor A,
the condenser B, the valve 1), and the vaporizer C. The com
pressor draws in vapor at a low pressure and temperature,
compresses it, and delivers it to the condenser, which consists
of coils of pipe surrounded by cooling water that enters at e and
leaves at /, The vapor is condensed, and the resulting liquid
gathrrs in a rr*>rrvou in thr !Uont, from wht'iur it is led
small i}K having a trgttbiiui* uilu* /> to thr va>oriw
rrfrigrr.tlor, 'Hu rriViijri.iiu*!' > ^M mutlr uj of rwls of
in whiih lir xol.tlih" liquid v.n*orut"u Thr toils nuiy be
dirrrtly for i**liit *>*f.s r thrv may Ir iiiiiurrsrd In a
uf hrinr, wlittlt rtuiv lr ist*l Cor II!IIIK *afrji or fur itiakin
Fig. KH *htWH ihr iimjn*str with ittr sin^lr ailing vc
cylintlrr whu h ha.s hr.il t^hn, !**! \.iIvr.H, ;ml vjilvt*s ii
jnHltm. SmstU nuihiw% tr'twlly h.ivr ! il*ui4riiclirig
jmHMir tylttuSrr, L.uifr m.ihif. Iwir vrrtinii
which may S" sinjjlr iutiiiK nr ii*ul>U iicimi;.
Tin i u U* whiih It.i". Sw'tfi 'Siiitnl fur llir
rrfri^rritifiig iiwt hM ! im*mI*tr, S*i,ni s <* iltr working
is itlli%vr*t to !lntt l!!f*ii*l tli r%.4ii!t".t>ii i ot I, itiin sht* rspan
toil* without UinK work. '!' itwlr ihr u It tomftMe,
ftlilllli U *$ 'tilll r\julitj^ %lilrt' ilt ttliiili hr liquid
t)o work * ttu* kiv ff*i ilw i hirrt in i h v4)HrUing<
fitil lltr vvttrk ftaiiinl tit H* Ii * yhmlcf *t$!i! lit* in^tgnif
ailti ii WJ>I*1 Irail lo i n!liilii rtliO" iIl iliilu *iUtr,
Proportion* f EtfrigtrttingMichlttw, 
IpjttttS *nlrfrr*S in llir *ih l ihi * im!rnj'r flows* l tht? i*.
k wilh llir trfstfw'fsilisfr / 4 4fil !ii* s t til it ilir liral ,
ihrou^h lltr r%ifisirt * k ilinr i% A ifliai VAJK
tittn. but m hrjii itiiiiri r l*'i. lltr \ft<t*r llttwing froi
y dry
thr
Irwttt llir ctf;ilftf *il by it
i s _ j >//,. ^ (S ......
Ttti* u*tnirrw*r ivlintlrr t* .aSmai"* tiri hy a Wittrrji
hul It is ni*I *rni4#ii4r llwil wti i j^rkrl tuin inttrli rflitl c
1i:C% ffilrfft llir i Umdrf *lfV lifl<i If !
ilcifl, \W i
equation (80), page 65, giving
* 1
k
This equation may be used because it is equivalent to the
assumption with regard to entropy on page 121. The value
of a is i for ammonia and 0.22 for sulphur dioxide as given on
pages 119 and 124.
As has already been pointed out, the vapor approaching the
compressor may be treated as though it were dry and saturated,
each pound having the total heat H 2 . The vapor discharged by
the compressor at the temperature t, and the pressure p l will
have the heat
r ft f \ 4. IT
p v i/ ' ^ r
The heat added to each pound of fluid by the compressor is
consequently
c f (t,  t,} + H,  H v
and an approximate calculation of the horsepower of the com
pressor may be made by the equation
P = 778M \c v (t,  Q + H,  HJ
33000
or, substituting for M from equation (249),
7780 \c (t t } { H H \
33000
(251)
The power thus calculated must be multiplied by a factor to
be found by experiment in order to find the actual power of the
compressor. Allowance must be made for friction to find the
indicated power of the steamengine which drives the motor; for
this purpose it will be sufficient to add ten or fifteen per cent of
the power of the compressor.
The heat in the fluid discharged by compressor is equal to
the sum of the heat brought from the vaporizingcoils and the
heatequivalent of the work of the compressor. The heat that
408
REFRIGERATINGMACHINES
must be carried away by the cooling water per minute is co:
sequently
<2 2 = M (H 2  ?1 ) + M\c p (t s  g + H, HJ;
where r t is the heat of vaporization at the pressure p r
If the cooling water has the initial temperature t w and the fin
temperature t' m and if q w and q' w are the corresponding heats
the liquid for water, then the weight of cooling water used p
minute will be
If the vapor at the beginning of compression can be assum
to be dry and saturated, then the volume of the piston displae
ment of a compressor without clearance, and making N strok
per minute, is
D ^ (25
To allow for clearance, the volume thus found may be divid
by the factor
as is explained on page 363. The volume thus found is furtt
to be multiplied by a factor to allow for inaccuracies a:
imperfections.
The vapors used in compressionmachines are liable to
mingled with air or moisture, and in such case the performar
of the machine is impaired. To allow for such action the s:
and power of the machine must be increased in practice abc
those given by calculation. Proper precautions ought to
taken to prevent such action from becoming of importance.
Calculation for a Compression RefrigeratingMachine. I
it be required to find the dimensions and power for an ammoi
refrigeratingmachine to produce 2000 pounds of ice per he
from water at 80 F, Let the temperature of the brine in t
DC 05 r. Assume mat me macmne win nave one uouuie
acting compressor, and that it will make 80 revolutions per
minute.
The heat of the liquid for water at 80 F. is 48 B.T.U., and the
heat of liquefaction of ice is 144, so that the heat which must
be withdrawn to cool and freeze one pound of water will be
48 + 144 = 192 B.T.U.
If we allow 50 per cent loss for radiation, conduction, and
melting the ice from the freezingcans, the heat which the machine
must withdraw for each pound of ice will be about 300 B.T.U. ;
consequently the capacity of the machine will be
Q 1 = 2000 X 300 T 60 = 10000 B.T.U. per minute.
The pressures for ammonia corresponding to 15 and 85 F.,
are 42.43 and 165.47 pounds absolute per square inch, so that by
equation (249)
.. t t = 668  460 = 208 F.
The horsepower of the compressor is
p _ 77301 \c 9 (t s  Q + H,  H
33000 (H a  ft)
^ 778 X loooo {0.50836 (20885) + 556  5351 =4I>
33 (535 ~ 58)
If we allow 10 per cent for imperfections, the compressor will
require 45 horsepower. If, further, 15 per cent is allowed for
friction, the steamengine must develop 53 horsepower.
From equation (248) the weight of ammonia used per minute
1 'M = <2i + (H 2  Q t ) = 10000 * (535  S&) = 21 pounds;
and by equation (254) the piston displacement for the com
pressor will be
N
_
X 80
_
v
feet
4io
If 10 prr rtnt i
action* tin* piton li..plarrmrt wilt } M  mic
elutmrfcr may t* nuulr t^ im hi irul ihr *
Pluidt Af Thr ihiuh ituti tuvr t>
won frfriH'ralifiiiiiii'titftrs iirr rilur, tjlhi
ami a rtiislitrr f nulphur li\i>U* am) *iirU
I%tr e S fltilfi, Thr pfrvtlirr'i  ifir 4,i**r'i i
r:n, ,iiii *il**t* jjir pfrvtiifr *f ll
rarlwn fiii%iilr, *tfr unrn in stir I
imperfect vaJ
ir fmit, and t
n eomptf
!.* known
table:
t ti
HP
MHi I 74;
Klttcf it'irtt ill ihr raflv Mmjrrv>t*tt fitl!tnri, but It I
ill llsr frfrirr4l? I hi*
ihr fifwfiln %4tiftir larifc, si ituf I tic
fttf ttrfr rilfirf f bully, Mtt
OVrf, alf !. Jfiil, IIM lllr itiiii liiitr rtfi
4it*'.tr liii*
fully, bill if ltii;i llir tii'*atfvaftitgr ift^l 'Hsl4!lirk t
feffnri! jy iltr f muniurt* n!* ihr in wW
ct.ifftwiwft tctuf's, Aflrfiiii Is4'i
Ifi ihr frtrft! m.a< Iwfsr j *AJh ff*tjitJ, Wl
ilfl riicti!i* MIiili?i i! tn Iwliir l Ci
A* n *5lw in Itsr fil4i% I^lrt's 1
ill iw Icftwfa!iifr til?rftitrli*iir turlwrrn
of Jiiitl iimntunk. am! ihr
hr It li,r* lr tunl by till*
ammonia.
Absorption Refrigerating Apparatus. Fig. 89 gives an
ideal diagram of a continuous absorption refrigerating appara
tus. It consists of the following essential parts: (i) the gen
erator B, containing a concentrated solution of ammonia in
water, from, which the ammonia is driven by heat; (2) the con
denser C, consisting of a coil of pipe in a tank, through which
cold water is circulated; (3) the valve V, for regulating the
pressures in C and in 7; (4) the refrigerator 7, consisting of a
coil of pipe in a tank containing a nonfreezing salt solution;
(5) the absorber A, containing a dilute solution of ammonia,
in which the vapor of ammonia is absorbed; and (6) the pump
P for transferring the solution from the bottom of A to the top
of B\ there is also a pipe connecting the bottom of B with the
top of A. It is apparent that the condenser and refrigerator
or vaporizer correspond to the parts B and C of Fig. 88, and
that the absorber and generator take the place of the compressor.
The pipes connecting A and B are arranged to take the most
concentrated solution from A to B, and to return the solution
from which the ammonia has been driven, from B to A. In
practice the generator B is placed over a furnace, or is heated
by a coil of steampipe, to drive off the ammonia. Also, arrange
ments are made for transferring heat from the hot liquid flow
ing from B to A to the cold liquid flowing from A to B. As
thr amnumia is Ir!ilW h**m ,iir in II ilir v.ifw driven
contain* MIW mui.nir. whi h i.uri* 411 unavoidable lots
rtlit irnry,
of in 4ir An a
atiriic m*u'hifU' itm^trmtnl tifmlrr thr Ilrll Culrmi.
" * * JM;
W*IH IrslrtI ty l*fifr>H<ir S hn'iltr * 4! .tn iait*ir in Hambtl
wlirrr It Wits tjM'tl in tn4iniiit ;i low tr}n{H*raturi* In a stota
t, "Ilir in;ti liiiir i ; li^ii^iifS^iS, ,ind tt.w ilir *btortt for
rtiin i yiifttlrr U*t fir.irrf ilir itaiii, l*nwrr k furniit
by a ^ir.ifii rtiifir iii lini* on i ruik 4! lltr i0ur rnd of
main ,sliifi utit) it it:i*tit Am^lf. !* ilir t. r^nk driving the i
ii<*tifl.t% 8 Ili.ilSi lltr 'If;iin i \ liiiilrr iUis.1 ilu" riian,itijjeyjfl
littVr (Iblfililiitiill ilir Viihrj, wilh tntlrftrftitrnl tlfl=ff Vl\
Tlir ilimrm *' ,trr j*iiin in ih fi*i
itr 4
It
III ilir tiT%!b, $l
i'f'iiiiiirf's, il
! flit ff*ft
it
it i' by
ft
Ufj rfr nH4* lir4 1u c4i ll rll f
B*rf4iWfr f llir ,f %'a. 1 * it
ill r4 ill* ijf vhn*trf, 1
fitt flic 4 ir i %iiirn *h<w for lite ci
llt?lft .! *frfjiifr *lir$f i
rtlil'si1t, 4l fwf lilt*
and compression, though neither is complete. No attempt
was made to measure the amount and temperatures of the cool
ing water.
The data and results of the tests and the calculations are
given in Table XXXVI.
TABLE XXXVI.
TESTS ON BELLCOLEMAN MACHINE.
Number of test
Duration in hours
Revolutions per minute
Temperatures of air, degrees Centigrade :
At entrance to compressioncylinder
At exit from compressioncylinder
At entrance to expansioncylinder
At exit from expansioncylinder
Mean effective pressure, kgs. per sq. cm.:
Steamcylinder: head end
crank end
Compressioncylinder: head end
crank end
Expansion cylinder: head end
crank end
Indicated horsepower :
Steamcylinder
Compressioncylinder
Expansion cylinder .
Mean pressure during expulsion from compressioncylinder, kgs.
Mean pressure during admission to expansioncylinder, kgs. . .
Difference _ .
Calculation from compression diagram :
Absolute pressure at end of stroke, kgs
Absolute pressure at opening of admissionvalve, kg.:
Headend
Crank end
Volume at admission, per cent of piston displacement :
Head end
Crank end
Weight of air discharged per stroke, kg.:
Head end
Crank end
Weight of air discharged per revolution, kg
Calculation from expansion diagram :
Absolute pressure at release, kgs. :
Head end
Crank end
Absolute pressure at compression, kgs. :
Head end
Crank end
Volume at release, per cent of piston displacement :
Head end
Crank end ._ . .
Volume at compression, per cent of piston displacement:
Head end
Crank end
Air used per stroke, kg. :
Head end
Crank end
Air used per revolution
Difference of weights, calculated by compression and expansion
diagrams, kg
In per cent of the former
Mean weight of air per revolution, kg
Elevation of temperature at constant pressure, degrees Centigrade.
Heat withdrawn per H. P. per hour, calories
I.
6
65 os
19.3
27.3
19.00
47.0
2.263
2.230
I. OCXS
1.869
1.502
1.615
85.12
128.85
60. 10
335
2.82
0.53
1.04
0.783
0.765
6.15
8.50
0.2744
0.2716
0.546
1.32
1.45
1.14
1. 20
104.65
106.1
16.5
19.8
0.234
0.254
0.058
10.6
0.514
66.3
371
n.
i.6 3
61.2
17.5
26.8
16.6
47.0
2.336
2.294
1.861
1.825
1.589
1594
8235
118.55
56.12
325
2.83
0.42
1.04
0.788
0.749
S.os
8.41
0.2764
0.2742
0.551
1. 14
1. 19
104.7
106.3
16.0
rg.6
0.233
0.254
0.487
0.064
n.6
0.519
64S
354
III.
2.92
63.5
19.1
27.2
19.1
47.0
2343
2.301
1.870
1.906
1.626
1.624
85.71
126.01
5946
340
2.84
, 0.56"
1.04
0.764
0.765
6.03
7.91
0.2750
0.2730
0.548
1.33
1.46
104.8
106.4
16.6
20. 6
0.238
0.255
0.493
0.055
10.0
0.520
66.1
363
TABLE XXXVII.
TESTS ON REFRIGERATING MACHINES.
BY PROFESSOR SCHROTER.
Number.
System of the machine.
Dimensions of the steam
cylinder.
Dimensions of the
compression cylinder.
3
31
10
5<:
4
3.
8.
ii
Diameter of
piston, mm.
Diameter of
pistonrod,
mm.
a
a
!
c/3
Diameter of
piston, mm.
Diameter of
pistonrod,
mm.
eS
I
Linde.
t
Pictet.
37^25
1?
330
45
55 S
'if?'
68
800
602
740
poo
325
250
43
ft
#
4
54.0
420
poo
3
g
7 ' ..
a::::::::::::::::;::
o
I<J
12
Number.
Revolutions per minute
compressor.
Indicated horsepower
of steam cylinder.
Indicated horsepower
of compressor.
Absolute pressures of vapor,
kilos, per sq. centimeter.
Initial
temperature. 8_
u
'W
In compressor
during
expulsion.
In condenser.
In compressor
during
admission.
In vaporizer.
64.8
598
54.7
551
53.6
66.1
2.76
459
26.27
27.30
9S8
9.31
1366
2.50
2.64
4.85!
4'S5J
4.90
453
4.91
455
427}
4.8 3 J
2.63
3.24
0.82
1.03
''S
i. 06
ii. ip
It. 2
II. 2
II. I
III
10 15
10 I
10 15
10 3
3 *
4
s
59. i
2p,23
14.11
6
7
49.6
65.15
65.8
64.2
64.7
64.S
26, i
345
91.2
945
99.2
24.49
18.1
258
52.01
61.70
66.42
75.02
8.13
10.68
377
4.11
423
58i
I378
787
10.41
3.22
35
362
S ii
2.36
2.07
045
0.63
0.73
0.67
8. .......
IO .........
12
Number.
Ice formed.
Temperature of
water or brine
cooled.
.
'
t
Temperature oi
water supplied,
degrees C.
Per compressor
horse power,
per hour,
gross, kilos.
Per compressor
horsepower,
per hour,
net, kilos.
At entrance.
At exit.
i
a ,
9.0
8.3
34.8
3i7
~44
59
li. ip
II. 2
II. 2
II. I
9.5
18.2
IO.O
9.7
6. 05
4.4
S.9
a95
2,38
9.24
4.71
9.97
=^ 3
IO.O
9.7
6,05
6 .... ... . .
7 . . ...
1
Q
"3
ir.s
ii. 3
ii. 3
16.8
25.0
28.2
20. 6
152
22.6
25.9
I8. S
10
II
12
the data and results of tests on three refrigerating machines
on the Linde system using ammonia, and of a machine on
Pictct's system using Pictet's fluid, all by Professor Schroter.
The tests on machines used for making ice were necessarily of
considerable length, but the tests on machines used for cool
ing liquids were of shorter duration.
The cooling water when measured was gauged on a weir or
through an orifice. In the tests 3 to 6 on a machine used for
cooling fresh water the heat withdrawn was determined by
taking the temperatures of the water cooled, and by gauging
the flow through an orifice, for which the coefficient of flow was
determined by direct experiment. The heat withdrawn in
the tests 7 and 8 was estimated by comparison with the tests
3 to 6. The net production of ice in the tests i and 2 was deter
mined directly; and in the test 2 the Ioss 4 from melting during
the removal from the moulds was found by direct experiment
to be 8.45 per cent. By comparison with this the loss by melting
in the first test was estimated to be 7.7 per cent. The gross
production of ice in the refrigerator was calculated from the
net production by aid of these figures. In the tests 9 to 12 on
the Pictet machine the gross production was determined from
the weight of water supplied, and the net production from the
weight of ice withdrawn.
A separate experiment on the machine used for cooling brine
gave the following results for the distribution of power :
Total horsepower 57.1
Power expended on compressor 19.5
" " " centrifugal pump 9.8
" " " waterpump 3.6
The centrifugal pump was. used for circulating the brine
through a system of pipes used for cooling a cellar of a brew
ery. The waterpump supplied cooling water to the condenser
and for other purposes.
4 it*
nNti MAt'IttXKS
A similar fr4 <n tltr l*i ui nut him
rr of
r iinm ...... ....... 7.9 H,
am! inirnnrtjiitu* gr.ir . . . . . 16,6 "
** grar, ami puwj .
In t.sHH comparative* tr*r %trrrc made !y i*rtilr,Mor Schrfitc
tm a Ltfifir and on a i*uui rrfriRcratinii ittarhtm*, in a aped
building provide! by tm* l.imlr C*uany whit'h had eve
ronvrriiriiiT ami fiitiltiy (r r\ai **rk. Tlu following tab
gives llir riiitiil iSIntc'fi5.ii'* *f ilir
A,\! Mf'TKT
.i illt.i.ff, \ll\, M It
tf
if, i
y 8 MI
S
44
Thr Limit* u.w*l 4ml *4' alltiwrtl to rlra
at nil^Iitrr wf liquid v;tr ifii lh* iiffi*rr%%f , so
water Jiirkrl itiis rr*uif*<t, Thr i*iifii madum*
fl will , tt'li itli Is 4 ftii%ttjrr if *ut}hitr !tt**id* and i arlMift tliuil
tiHif llir rftifi"*.tf ti*i*rtl liy a Wiiirf i*krl,
TliriiIlii jiiml fri%n! nf !l$r Sr%li .trr givra in Tiililr XXXVI]
Five irsi% wrrr iiMiir tm ra* h m>t him*. Ttic irmprratunr
tltr % it iiiiiift *r iriwr whit ft ftrat Wiin withdrawn by t
r Sit rtil, Tlif rnif.ifl* r irftifiw'ffitttfr'i
TESTS ON RKFRIGERATINGMACHINES.
By Professor M. SCHKOTER, Vergleichende Versuche an Kallemaschinen.
Piclet machine.
One vaporizer.
I
II
III
IV
V
Steamengine :
S7o
21. 8r
16.82
0.771
399
1.47
6.10
3o8
0.850
6.09
3.03
6. 1 1
3 os
9fiS
19 72
IS.J
957
19.71
9.67
IQ.7I
+ 0.6
3S07
56.8
20.88
16.10
0.771
39t
1.05
1.96
4.98
0.847
2. 02
4.99
2.O4
4 .08
9.6O
19.70
15.6
9.64
19.72
9S7
19.64
+ 0.6
2SS6
57.1
18.75
14.26
0.761
3 84
0.68
9.92
13.01
0.845
9.91
T2.9I
994
12.88
9.61
19.59
16.8
958
1937
9.61
1935
+0.4
1852
57.6
1593
11.83
0.743
425
0.17
1793
20.96
0.841
18.00
21. OO
iS.OO
21. OO
9.68
19.51
l6.7
968
I9'52
973
1959
13
1075
59.3
27.56
22.91
0.831
6.39
i.5
2.04
5.01
0.846
1.99
5.02
2.05
4.96
9.68
35i8
18.6
9.73
35.o8
9.72
3501
+ 8.9
1708
Compressor :
Mechanical efficiency
Pressure in condenser, kilograms per square
Pressure in vapomer, kilograms per square
Vaporizer :
Mean temperature of brine, entrance . .
Mean temperature of brine, exit ....
Initial temperature of brine, entrance . .
Initial temperature of brine, exit
Final temperature of brine, entrance . . .
Condenser :
Mean temperature of coolingwater, entrance
Mean temperature of coolingwater from
Mean temperature of coolingwater from
Initial temperature of comlensingwater,
Initial temperature of condensingwater, exit
Final temperature of conclenningwater,
Final temperature of condensingwater, exit
'Refrigeratlve effect, calories per horsepowe
Linde machine.
Steamengine:
44.9
18.14
15.53
0.856
9S2
38p
6,00
a 89
0.850
5 9
2,89
S97
2.94
95*5
19.76
9S6
1974
9S7
19.74
1.8
4308
4S.I
18.26
15.20
0.833
934
3. 95
2.02
5.02
0.846
2.05
502
2.04
5.04
9. 54
19.63
9SS
19.42
9S4
1945
1.8
3182
451
1703
14.31
0.840
9.00
2.13
999
12.91
0.843
995
12.94
997
12.89
9.61
19.84
9.61
19.82
9.60
19.89
1.9
2336
448
1570
12.63
0.805
8.89
1.56
17.92
20.82
0.840
17.97
20 . 83
17. 96
20.83
9.61
19.72
9.64
19.79
9 5$
19.88
2.1
1711
4So
24.41
21.86
0.895
1403
a.95
2.03
5.01
0.845
2.03
5.00
2.03
501
9.68
3533
9.68
3545
965
3544
+ l
2O2*
Compressor :
Mechanical efficiency
Pressure in condenser, kilograms per square
Pressure Jn vaporizer, kilograms per square
Vaporizer :
Mean temperature of brine, entrance . .
Mean temperature of brine, exit ....
Initial temperature of brine, entrance . .
Initial temperature of brine, exit
Final temperature of brine, entrance . . .
Condenser :
Mean temperature of coolingwater, entrance
Mean temperature of coolingwater, exit. .
Initial temperature of water, entrance . .
Initial temperature of water, exit ....
Final temperature of water, entrance . .
Error in heat account, per cant
Refrigerative effect, calories per horsepowe
Kl' HilUI'KATIMi MAt'IHNtCS
hi CitV ;"C. t !."('., ami iK" ('. The coolb
watrr wa.s ^uttplird ! ihr tomlrnnrr at aUuu </*. C fnr
a* ^' *( &VIJ, 
trsts, ami for all but otir ii Irft tin lomirfttrr with a trrnperatu 1
of nrarly xfC,; ihr iilili trtt ** rai h mat htnr was made wtl
thr r*il Irtttfirralurr of thr t*milit \valrr ;tl alUt J5*> C.
Tltr firrswiiirr in ihr tontjrr%or drjtrmlrd, of runrse, on tl
trmH*niturr? cf tltr brim* and ihr itiiti watrr. For all tl
txtt'jpt ihr fjfili iti nuh itiiu htitr, ihr nmximum prenoi
t*f ihr working ^nb^lani'r W4' nrarly i on*)ant ; Jtimtif  kibgraD
IHT <iiafr frittimrirr fr ammonia and alut ,j ktlograms f(
l*utn\ fluid. Thr Siftti ii"t hatj tofuidrrably highrr prtssur
ttrrrsMmling ii ihr highrr trinjKraturr in llir (ontlrnn^r. Tl
mi fit in ttft i jrr*>urr f ihr tv(*rkiri ailiitm r of tnirj*r diminbhe
ihr lirilir Iffiirr*itiifr frll.
Thr hrat yirldrt) jrr httr lo thr ammonia in ihr vaporis
ritli'MlalfiJ by iiiiiiij4%ifti, ii*i*cfltrr ihr amount f hrine use
in an hour, ihr *jirriik hrai of ihr btmr, and iu increase c
iritiirr*tiiifr, Ilitt ihr initial *ftd fifirfl i.'fiit*r*tiurr.A were n<
atbMrattrit from ihr Ammonia in ihr tondrttHrr w*i* a
front thr watrr tinnl *rr hour and tl*i im rrair *f
Thr ralr it lai ititi fr I*ttirtS ma* htnr tnvolvr4 akit the jacte
water 4 nd its tmrra.nr of trntjirraiurr. A trrllon is ipplfg
fur ihr vArkiiuni of intital *ind itnil trttiirriiuir of ti
ttwlifigWiiirr, If ihr hrat rtjimalrnt of ihr of the eon
frr*f4r in aiiiinl to ihr hrai yirhlrd by ihr I'ajMirkrr the sui
should I* rttiiii to ihr jibitratlrd by ihr riwilingwtte
Till* Jrf Wit f ijiifrfriii r lnlWrrti lhrtr I* inirulalloflS t
thf hral iillr*iti by Ihr niii walrr t? at iiira,tirc of tl
if Ihr
Thr frffiffrftttivr cill in ilItifirt S\ diitdtng tin* hrat
by fltr by ihr lirifsr tf ihr *!ram ry Under,
first ftiitr lr%i..% iii tiifi^irffii irmjirralurr in ihr rundrnser
a iirtrrii.w in llir rrfrtKrriaittvr rfl I for rarh rotcWta
a* ihr i4 ihr lit* i
the s* ftfliitrtf, Thf fifth tmt, with
effect than the second test, which has nearly the same brine
temperatures. These results are in concordance with the idea
that a refrigerating machine is a reversed heatengine; for a
heatengine will have a higher efficiency and will use less heat
per horsepower when the range of temperatures is increased,
and per contra, a refrigcratingmachine will be able to transfer
less heat per horsepower as the range of temperatures is
increased.
TABLK XXXIX.
TKSTS ON AMMONIA RKFRKJKRATnSTGMACHINR.
By Professor J. 1C. DKNTON, Trans. Am. .S'c. Mcch. Kngr., vol. xii, p. 326.
1
II
in
IV
Preatuira above ntnionplmrn, poiuiibi por Hqunro lunh :
Iftt
aH
H.a
ay ,H7
Temperature, dugrucm Fnlirnnholt :
jH.80
ao^
a .ao
38.4?
,, .6^
0.6*f
S4 ,OO
outlui ...,,,,.. ,.,,,,......
8? ,ftft
^,4'
Hi ^6
Ba.86
Jack^twtvtart Inlaid, ,..,.,,,., ,..,,..,.....
,\,\ ,6 j
<s6.7
S*t J
t .0
^y .a
si?
irf
313
a 60
ttnterl UK tutndonBttr .,,....
910
108
Brino, paumlN per inhiuCw, . , .
aaHi
tua H
Specific ntutt.. ,....,.,..,...,,,.,..,,.....,........,
o.Ba
a. To
0.78
Q*?H
T46H
16.67
aH.ia
from <H>fii]>rti;ie>r clinplm'iHmwi, ,
Heat aooount, H.T.W, per minute ;
14776
918^6
HH^4
97800
351:8
140
tAT
ift?
6oK
6^6
jHa
rtH
a;o
Total t.ako.n from tumiHwin.,
jH*> (a
10160
108 s^i
18017
3. c
Power, ota. :
17.88
sB.Sy
H<(.tt
7' 7
7t .d
8 .6
OB. 7
54 7
<i*O, A
Tr t a
O.Ht
o,tt,i
IM
Q.HI
Kefrigerativo lfot:
74.8
3^^J
44.64
74. "j6
B.T.U. abBtraatfed from brine pnr nriKjwr minute .
74
34 . I
107
14. x
97
106
aj , ^7
Table XXXIX gives the data and results of tests made by
Professor Denton on an ammonia refrigeratmgmachine. The
only iums mjuirmi; rxplaiuiimi an ihr rrfrigrnttivo effet
am) thf i,tl liiilnl Umi<rraturr i>? Ihr Uif*ir leaving the COB
tlrn**rr; thf iaiirr was tulfiitatrt) ly iln
am) smw* l*th ihr tutulin^ r!ir*! >l tltr Jarktt and ihr error i
a*siiminK un ait I hi tali*' ii*ns*fr%"4j*n, Thr (\Nim*nt usttl her
I\ ,1 irsllr '.iii.iiirr Ihaii tli.tl f <jii} t t!>Mf} u.ji/l iigr r o* r ^
rrfriirr*illv ritVii W4S *ii!,itiifil In sli\tiiit* thr tt.T.f. i
lit tint amntiitti.l in .t ftlsIitlSr !y llir li*r' fmiVrr iif llif H
iUitilrr, llir ttii' r h'fM jMttr in ,r hnurs Wits
!iV I1Illlli>Hili* llir frfiirl',diu* rSln  tft thtTftMl
tiiJnwir by llir nuinUr *f iiitjiwir, i 4 f,iv ami itnn tlividin
ihr {trctim t ly ^r,:> i flu M*ufsi'i In 4 i!$*t'i tun I arid by u
Cllii* lira! f iwll$H 4 *s,5ii! *4 !*?, "*lsr hil'i f iff w
MM! l%'4'5 I^I'rf'fl *>l ,,i ^'.iJJJWij I fi*Jif of {{jf{
f n*iil r ls*si''M' j'nttrr frr hf, ami Wj* ntk'iiltle
ty i!!l!ihiti* llir ii.i.r', jr hr>* jnvnr *t niinutt 4 by 6
ami tttuslJfif* In j, > 144,
Thr main fi'a<stn i4 lltr 11141 lists* %%rfr
f Udt
f tl *{*hr tftftifMsI
litr n^lill'* i*f a !r^I HM!r liv *r*fr*'>Mf J, E, t * OH
II hm if I ilii.fi i$ittifii4 fr<fi'Jrfdlitil tllii* liifir tfr given in
XI,. Thr Iliiii liilir it 4*4lrti IM Iwll 4 f **! 
fiiliir frrS (<*}! if y 4! a tfl (ulpg riidlII'lifr!fit at Ne
Havm, t*tnn, In mnfirjii^ti *ASII !hi ir*,! thr **rcif
ihr ilfilll'. Will* li 'rff%ri ;ii ji s;tsri r< hr.it ffi*fll llir I'Cllf
ttl ihr MRintuttU. Wii'J ilrlrfltiillrrf .% slifn I r%*rlllt"fit,
SEVEN DAYS' CONTINUOUS TEST, SEPT. 1118, 1888.
fGenerator I S77
Average pressures!
above atmosphere^ Cooler
inlbs.persq.in. [ Abgorber 23 . 4
Atmosphere in vicinity of machine ...
Generator 2 7 2
^ . (I nlet 2I ' 2
Bnne {Outlet 16.16
_ , (Inlet S4i
Condenser Qutlet 8o
Average tempera j let _ _ 8o
tures in Fahren< Absorber JQ ^ ' ' II;t
heit degrees. rU ppe r outlet "to generator .... 212
Heaterl Lower " " absorber .... 178
llnlet from absorber I3 2
Inlet from generator 2 7 2
Water returned to main boilers from steam
coil 26
Average range off Condenser 2 5z
temper at u re s"j Absorber 3 1
Fahr. degrees. LBrine _i S I 3
Brine circulated per ( Cubic feet I >^337
hour. JFounds 119,260
Specific heat of brine  8o
Cooling capacity of machine in tons of ice per day of 24 hours . 40.67
Steam consumption per hour, to volatilize ammonia, and to
operate ammonia pump pounds 1,900
. . ,. j ( Per pound of brine 41
Ellimnated i Total per hour 4^,260
Of refrigerating effect per pound of steam
consumption 2 43
.(At condenser, per hour .... 918,000
British therm a l] Re J ected JAt absorber "   1,116,000
units: "j ' f On entering generator
... J coil i> 2 3
Per pound of steam^ Qn leaying generator
. coil 2 7i
Consumed by generator per Ib. of steam
condensed ' 93 2
Condensing water per hour, in pounds 36,000
Equivalent ice production per pound of coal, if one pound of coal
evaporates ten pounds of steam at boiler I 7 1
Calories, refrigerating effect per kilogram of steam consumed . . 135
Approximate c o i 1 C Condensing coil b 7
surface in sq. ft. } Absorber " 35
I Steam " * 20
432
KKKKlM'KATINliMAl'ltlNKS
brine chilliti am! th M4titK w.tirr usetl were measured with
mt'tfis, which were afterwards ie>ir*t umler ihe conditions of
the exjK'rimem.
It k intcrrsiing uftmiwr** tlu* rrfrirraiivr rflrris expressed in.
pitinei.s l kr IHT jHumtl *! ru4l. On ilir* lianU ihr c
machine Iralttl by !*roCrvor t**ntn h;t.* an atlvanuigc of
* tow ' 1 1 j jwrf ft'fll,
But lilt's tttirffift i realty unfair to the on
machine, for if steam nt^ine ii <i vat met I IM re<utre a ronsump
tion cf three jKUintb f *'al l^'f hr* jH%vrr JUT hour,, while the
calculation fr tin* al?ir>iinm4i'hine it Ita.^rrl cm the ussmmptloa
that a jHrtjnil f ctwl can evajnr4te irn ]tmmh nf wntrr; but an
automatic cmening engine **f the utirti itrr tlinki be able
tti run on *to or a j f irmi jnr twir^rjitiwirr fcr hour,
CHAPTER XVII.
FLOW OF FLUIDS.
THUS far the working substance has been assumed to be at
rest or else its velocity has been considered to be so small that
its kinetic energy has been neglected; now we are to consider
thermodynamic operations involving high velocities, so that the
kinetic energy becomes one of the important elements of the
problem. These operations are clearly irreversible and conse
quently the first law of thermodynamics only is available, and if
any clement of computation involves reference to equations that
were deduced by aid of the second law, care must bo taken
that such computations are allowable. It Ls true that all prac
tical thermal operations are irreversible for one reason or another;
for example, the cycle for a steam engine is irreversible, both
because steam is supplied and exhausted from the cylinder and
because the cylinder is made of conducting material. But all
adiabatic operations in cylinders (which serve as the basis of
theoretical discussions) are properly treated as reversible and all
the deductions from the second law may be applied to that part
of the cycle. In particular the limitations of the discussion of
entropy on page 32 have been observed.
Three cases of continuous thermal operations have been
discussed (i) flow through a porous plug, (2) the throttling
calorimeter, (3) friction of air in pipes; to which it maybe well
to return now. In all, the velocity of the fluid has been so small
that its kinetic energy was neglected; in none of them was any
reference made to equations deduced by the aid of the second
law of thermodynamics. Rather curiously, all the operations
were adiabatic, using the word to mean that no heat was taken
from or lost to external objects ; in the case of transmission of air
in pipes, this comes from the natural conditions of the case
423
44 ri."v <*' M
ami in thr othrr two uHMitMit% thru was lurrfttl insulatii
from hrat. Ninr *f ihr uirraiu>ns an iatrntrojm ; forinstaiu
ihr rntroy of slraiu Mliri In thr t alofiturlrr till Mgg j
is about t.oo ami ihr riiin'V of ihr Mijtrtltr.ilnt steam in t
utiorimrirr i* aUut 1.7 j', 1! this ijor*. mi iuur into
f lltr pnlIrm ami i** nurr i uriotts than IIM
rvrit tif riiniT iftijmilaiirr than lt*riiirti) iti at't'ount of thcckvelc
mrnt of ^trittii turinnr**, Th% far ill Mitittt*itlns have be
bit?iI tn itii'.iS*iist *u lion, ami whrn ,ilirtiijt i% nuide to all<
fir friftion it i'* !** ly ihr a('t*iitaiton tif an rxperimen 1
fiifitiatttrliliil r*U.ilio. Stj*i.;r llwf a fhtti) i> flawing fn
I hr hir^rr jtH ,1 initt tin '
iHttittfil l ihr i tiiiftffr in
%ritju il wish ** rrtlist liiifi In pressu
Tlir lit ! Ui% of iiirratpdjmaw
il'i r%'fi"*'srst i% riji;iiiift (ifi), 'Slge
ilir MI U ill uft *f it trfSII lei ti
rfirf?y, ami br writ
11* * i/A'i;
fririi!* ih im of kl
thr k%l trrm in ihr 
t*l it br l!u! lltrfr i4 4 If it iiiiir ittin In a
,, ..jttrr ; tltr in ,1 rtrri* lltr ^rvmwv J t tm the flukl
ttf it, ihr in If fcui iii it ilir
F*itlt *f 4 illiiif jprtsaiitH Ifiifti *i the Olii
ihr l^i'j, it, iiitli ftttttmi
H tU*rH ihr I*! 1 *!' Thf i"^lfli*liwll til
;t Ifcillrf f i it%"ifiiirftir, <in*i if ihry 4fr ^Wpl
iitfiili!ifi'i wilh IM r; iiiil wiiJ huit).
If ihr vritK'ily i A ii I", ihr kinnn. rtirfgy of one unit
T * , '
in rylititlrr i ;  * ; lltr In & is 
for a r,,
is no heat communicated to or from the fluid the sum of the
intrinsic energy, external work, and kinetic energy must remain
constant, so that
V 2 V 2
R i + ^ l 'i + ~^~ " 3 + PM + ^ ; . . (255)
this is the fundamental equation for the flow of a fluid.
If the walls of the pipes are well insulated there will not be
much radiation or other external loss even if the pipes have
considerable length, and in cases that arise in practice that loss
may properly be neglected. There is likely to be a considerable
friclional action even if the pipes are short, and the logical method
appears to call for the introduction of frictional terms at this
place. Such is not the custom, and a substitute will be dis
cussed later.
Usually the velocity in the large cylinder A is small and the
term depending on it may be neglected. Solving for the term
depending on the velocity in B and dropping the subscript,
we have
~ EI  EI + p i v l  p a v^ .... (256)
Incompressible Fluids. There is little if any change of
volume or of intrinsic energy in a liquid in passing through an
orifice under pressure, so that the equation of flow becomes in
this case
(257)
If the difference of pressure is due to a difference of level or
head, h t we have
p l p^  hd,
where d is the density, or weight of a unit of volume, and is the
reciprocal of the specific volume; consequently equation (257)
reduces to
*,
(258)
ft us
which w lh* iMi
small orituc.
Flow of
i\r
Thr imrititu mrrgy of u unii of
which clrprrol* only * ilir tt.fniiituft tf the ;aH and not on
that flint* takrn *r uy lair filtfr, The
flow f 'A grt' llirft'ltifr lij *tnri
' rf I'v jv s 5 
Jf * S
thin plut* if is i M.jMin.il % }. ** i!n '*jif,ili
for llw* rt*ffiitiift if llir rtii'i!issfi j;Ai jifii a% though We
lin with *in aitittMiu r%*ifi^is*n i 4 ftunfunilutling d
Xi* ihr f*4i ! tliaf lh sftrf.*si : Itflr Jtnti the
ittrrnifll line itfr *fsiiiji,sll% iilmiii ?i <JM^ ftj! *how$ tli
jurrfrtl UAH tia** m ii%ifr,f,ilin rn*ff% it mi ttin^rtjiiriilty fc
all ill* *hini?r in ifiifiiisti' rnrrgy I*
fur (itiisiiir mlii* It in ilii r4.w i<s. iilii to iaerei
thp til lllr if,!*, inirat til 1C
of i n$f moi<ir. If iliii ti ill
JWfiiifi C^5*l'
SO
i* *
_s
'?' I "" JV >  ,  * *' 9
 "*u vvjwu.i.iv.u. 1110, y cUSU UC UCU.UC.eCl JLOf
work of air in the cylinder of a compressed
air motor (Fig. 91). The work of admission
is A v i> tne wor k of expansion is by equation
F ' G  " (81), page 65.
to.
and the work of exhaust is
so that the effective work is
iV,'
* 1 1
which is readily reduced to equation (261).
For the calculation of velocities it is convenient to replace the
coefficient p t v^ in equation (261) by RT V since pressures and
temperatures are readily determined and are usually given, thus
7 2
p
If the area of the orifice is a, then the volume discharged per
second is
aV,
and the weight discharged per second is
aV
w =
when v 2 is the specific volume at the lower pressure and is equal
to
H.oW !' H
I* from npuiiMit I^,H ani i', from
anc
miming
" " j;, v 1 1.
Thr rqualitms tlrtltitrti for iltr tlmv nf air apply la the flov
from a largr iylimlrr r rrsrrvoir ifii. .1 nuitl straight tub
through at r*umlrl rilur, Thr l\vrr n%>airr i iht premtm
in thr small tuU* ;uul tiitf*'^ itutrrt.tUy from llir *rrs*urt' af thi
(4jtir int witii It ihr hjU iiwy Mivrr, In trrr that tht? to
shall mil U* inu* It ullninl In fri. iitn iif,.iiti4 ihr s?i of thi
Hib it *hmthl In *h*rt mi mir llt.nt mt r r iv\ii r tUtHametet
Thr flow cUt Mii .t,if ! U ;iln tr*I 1> iiwkiiig the tub
vwy shrl, ami sSir ilirn of mutitUtiK i mi imixtrtnnt; th
i*cUti(rbi fr Ihr lUw f iilj ir anl iram nwy b* appliet
with it fair ttt'tcrrr tf Apn>\imitit*n ! ntiiitr.. in lliin filtto am
It* irrri*iii;ir uriiwt*.
i*rIriMr Flwgfiir * mat* 4 I*iri* numUr *f rs
Iliw f uir from n rrfv**ir into ih iiiMit'itirfr, with
in Ilir rr*rrvoir vdiytnu ttnm J4*M IMW. f mr wry to 3366 mn
Hr iiM'il two tliilrrrnl unfit r*, ur i.tiHs; iilttl tltr clhrf 7,314 mtt
III liiiilttflrr, tmlh Writ runt*l Hi tlw rlllriilirr,
fir fiHifiti ihr prrviun i ihr r$lisr ukrn by c
a ;%ilr rtlwi% *'^^ ?*. ! ;T ? ' **f ihc ;i.!nlulr jirr^urr In tfc
rrnrrvuir ?* a* ihiit *fr:t'Hirr %i ; 'a.% mrr ilt4H iwki* tht* atma
jihrrir jirrHHurr ; tindrr '^< h Mimliii*n ihr In the orific
I.i tn()r{**nt!rftt of Ihr prr>.itirr of ihr iilltlxiilirrr,
tf lltr r.ii i ** i' rrjUr*l by I he nutnUr a.^fij ami if *
/'
rrtkr by tin Vitlur t,,O in rtuali<>n ,*h we ttiull have ft
ttlf riiiitiH lii lltr of i$ !4'i
/**
II.
pressure .less than twice the atmospheric pressure Fliegner found
the empirical equation
iv = 0.96440;
4/W
v*
 A.)
(266)
where ^ is the pressure of the atmosphere.
These equations were found to be justified by a comparison
with experiments on the flow of air, made by Fliegner himself,
by Zeuner, and by Weisbach.
Although these equations were deduced from experiments
made on the flow of air into the atmosphere, it is probable that
they may be used for the flow of air from one reservoir into
another reservoir having a pressure differing from the pressure
of the atmosphere.
Fliegner' s Equations for Flow of Air. Introducing the
values for g and R in the equations deduced by Fliegner, we have
the following equations for the French and English systems of
units :
French units.
t > 2p a , 10 = 0.
t < 2p a , W = 0.7900
a (Pi  Pa}
English units.
pt > 2p a , W = 0.5300
Pi < 2 A> w 
p l = pressure in reservoir;
p a = pressure of atmosphere;
7\ = absolute temperature of air in reservoir (degrees centi
grade, French units; degrees Fahrenheit, English units).
430
In thr Knj?U*h nytrm /, and fa ar pound* JHT square inch,
and <t Is. thr arra of tttr orit'ur in Mturc inrhr*, while w is the
flow of air through thr uriiiir in (Huinth JHT .Hivond. If dcsircdj
thr arra may !; gtvm in %iii*trr ftrt ami ilu pnssurfit in pounds
cm ihr .st{urr ft, t i i hi iutiimnn umvinimn in thermo.
dynamic's.
In thr Frrfifli system *<' i >s tiw lUuv in kilogmmH prr st*cond,
Thr jinKMiivH nwy U i*svrii in kiliigraiiit, JHT Mjuure metre
and the ami ti in stjnitri imifr*; r lltr arru tniiy Iw given In
httiiir' rrfiliinrirrs, and llu rrH.4Hrr* in kiigrsns tn the
unit of artit. If thr .r^nr" nrr in mtllttnrtrfs of mc?rcuty ;
multiply by 13.5(15*12 if iiiim'*plu*n.. multiply by lojjj,
Tbaonrtieai i''nm a dU uv k in **f tin* m.an vtlodtj
tif ttwlrriili'.* of a H4^ i''l*r?rirr drdmf> for tlir maximum velocitj
thrttugh an oril
in ittrirsr unit:'*, ili f * ratio of prr^wtr ^.s^f** iii"4t*rt In efjuatloi
I * ^ %1 *'
Thr aiffrltralf of rqualion f^i) tKTUrs for th<
it* ^ 8 4 >  o,5j;,i, but t hi figure pr*tmbly km no phytlca
of Fr *i of liqukl and It
Ciio! a n s giiT
s
* %pi,
r lir
it In wttltli llir vrlmitv i*
i
!' v
p + Apu r;
 /> 2 ). (268)
The last term of the righthand member is small, and fre
quently can be omitted, in which case the righthand member is
the same as the expression for the work done per pound of steam
in a nonconducting engine, equation (143), page 136, except
that as in that place the steam is assumed to be initially dry, x 1
is then unity. The intrinsic energy depends only on the con
dition of the steam, and consequently reference to the second
law of thermodynamics first comes into this discussion with
the proposal to compute the quality oc 2 in the orifice by aid of
the standard equation for entropy
x,r
I'JU 4.
T,
X
rp "I"
* 2
the acceptance of this method infers that the flow of steam
through a nozzle differs from its action in the cylinder of an
engine in that the work done is applied to increasing tho kinetic
energy of the steam instead of driving the piston.
Values of the righthand member of equation (268) may be
found in the temperatureentropy table which was computed
for solving problems of this nature.
The weight of fluid that will pass through an orifice having
an area of a square metres or square feet may be calculated by
the formula
w
(268)
The equations deduced are applicable to all possible mixtures
of liquid and vapor, including dry saturated steam and hot
water, In the first place steam will be condensed in the tube,
and in the second water will be evaporated.
rm'pUu'lr, anil ruinr* f* IT**!, ihr itin>:> f iiuiim will U? turned
into hr.it ;til will MijKrhr.u tltr strain. Straw blowing into the
air will IK wri orar tltr triinr, Mijtrrhratnl ,it a link distance
ami if tin air U 'tl will %lunv a 1 * a iluml nf ttiUt further from the
oriiitr.
Raoktae'ft Equations, Afnr ;n invrMtKution of the expert
nunts mail*' by Mr, R, I). X.tisr m tin iSw of strain, Rtnkine
l fliJi! ihr prcssurr in ihr urii'ur IN nrvrr Ir:",s ihnn the
whirh gtvrs iltr nt4 \iittum uright i*f *iiltiirgt\ and
that llir tlini hiiri in {Htiifuh r Miin*l may U ritlnilatwl by
the folbwitifl rmiriitl ni
.t
thr* atnimftftrfr, Instil in {Htutuit *n lh* '^juarr im It, aritf ii i
arra in wjiiarr im hrt.
Thr rffr if ihrir riiiiliiiri' i>* li*ililr In l* at
bill ihr llfiw tiirisiigli a uivrn orthtr itw% U kfi
if te%ts are n it *il r nrat* ihr *rrviiirf!
HltI Ii .ii*rii,l ittitatil i% l*iiflt fsir Ihal rilHr.
Fr
tif tlit* external of bark prr,?*urr (**
IttriiHlla ftir thr *It"'hariCr f Mriiftl llit?i*i t c
n*r Ct*flt;
nwrr i1im*ly
iht* flow,
ihr following
ihr ftrigiii ln*ifi in fffifa *f r*iml, thr iirra Iti siUire Cti
iiirifrs itm! ihr irr%stifr in ktlonrum^ frf
F*r KnglUh unii* ihr
the II1iarir t*<ing in unh *r? i%ctjnl thr In
terlit^ thr prr^ttrr in ftiiffi% dlt%*4iiir fwr %cWfi* inch*
I hi* fiifftftiisi i 1 * wrlf wfifiril by Itis
FLOW OF SUPERHEATED STEAM
rOO
on the flow of steam, and that when the pressure is less than
that required by the formula the flow can be represented by a
curve which has for coordinates the ratio of the back pressure
to the internal pressure and the ratio of the actual discharge to
that computed by the equation on the preceding page.
The following values were taken from his curves :
Ratio of back pressure
Ratio of actual to computed discharge.
to internal pressure.
Converging orifice.
Orifice in thin plates.
095
o4S
0.30
O.QO
0.62
0.42
0.85
73
oS 1
0.8o
0.82
0.58
Q7S
0,89
0.64
0.70
0.94
0.69
0.65
0.97
73
0.60
0.99
0.77
o55
0.80
o.45
0.82
0,40
0.83
He further gives a curve for the discharge from a sharpedged
orifice from which the third column was taken.
Flow of Superheated Steam. Though there is no convenient
expression for the intrinsic energy of superheated steam, and
though the general equation (256) cannot be used directly, an
equation for velocity can be obtained by the addition of a term
to equation (268) to allow for the heat required to superheat
one pound of steam, making it read
2
= cdt
The accompanying equation for finding the quality of steam x 2 is
r cdt + it. 4.  *i 4. o
J ~7p ~r ~r i j, T 2
A * * i * 2
Here ^ and T are the thermometric and the absolute temper
atures of the superheated steam, t l is the temperature of saturated
steam at the initial pressure, and / 2 the temperature at the final
434
pressure. ami the letter. r, and r f and I 1 , ami <i, represent the
t:orresKmling heal* 4 x'apuii..aiion ami entropies if the Ijqm^
lictlh equation* Jtpply oitlv if ittr Meant Unomrs rnolsi at the
lower pressure, whit It is the usual ta*.r. Tttry tnuy obviously
IK modified to apply to Miam that remain^ superheated, but
.stu'h <i form *!** iii npjuar i havr pr;t(tua) apftlication.
Thr iiirtliiii if rnliu linn of tin* inlritrab In ftuation (369)
iiml (jyol IN pvrii un MK' ti i; ailrrttttui i rulfnl to the fact
ttmt tht lrmHralurr nil ropy i^lU allfnriK rratly solution of
rttiiiti<n ? jfHj f ai^ of ihr vt!mi!y U*w liurtn^ which tht*
remain* sujwrhraleit.
Flow to TwtMW tnd l ! ,tt*,
(lowing through a Iu1 *r nov.ir w
i> very high, rraihinj; #!<*.* fns
Hi* velmity tf air or steam
h a i.it*r iiiieremr in
%r mul in \riir fi
rtotjiirrttiy the enV* t of friitinn K mailed even* in short tuba
by Iliii liitrf * tit* sit straight tuhe j,i
long ami o.t5X of an in h internal diameter, under an
pressure of t'l'j jMiund** to ihe *uttare im It delivered onlv
<;*.! of the amount of 'iearn ral ulaieti b\ ihe adiahulif miihod,
and ihe pressure in the ttit*r fell gradually from tji {Hiundn neai
tin entrance to 14,^ Hunth near the rtii when delivering to i
ritndrii*rr at ;iiul ittminpherit' pre^ure. If there were tnj
tliir ffr *Uth tlevue in enginerring the prottlem would
li fall ftir it tiirtliwl of dealing with frit lion re^emhling
jte for f air in p". *ni r*killy nurc Uifficult)
wuultl be found In ;i ^tii^fatlory ireatment.
Friifll ihr inve^tij^tltont llial liavr ttrrw itwilr tii ihr flow 0;
^teitm through no^le^* II ap^ar** thai they should have i well
rounded entriince, the fadiu* of the i urvr of the t titui at t?ntnme
mil lit thrre fmirili^ *f litr didinetrr f the
or iltrtnif; from ihe tltrwi! the t*o//lr sliuu
to the estit, avoiding any rapid t iwifigr of vc
is sijcii a ttmnge t* likely to roughen the 'tttrfate where it occurs
The iciRgiiycliniii *ettin ntay well tr a siraiglil linr Joloeci t<
the witilisfi ly a i urvr f ratlins. Thr taper
FRICTION HEAD
435
the cone may be one in ten or twelve; this will give for the total
angle at the apex of the cone 5 to 6; if the entrance to the nozzle
is not well rounded there will be a notable acceleration of the
steam approaching the nozzle and this acceleration outside of
the nozzle appears to diminish the amount of steam that the
nozzle can deliver. The expansion should preferably be suffi
cient to reduce the steam to the pressure into which the nozzle
delivers; otherwise the acceleration of the steam will continue
beyond the nozzle, but the steam tends more and more to mingle
with the adjacent fluid through which it moves, and a poorer
effect is likely to be obtained.
If the expansion in the nozzle is not enough to reduce the
pressure of the steam to (or nearly to) the external pressure into
which the nozzle delivers, sound waves will be produced and
there will be irregular action, loss of energy, and a distressing
noise. On the other hand if the expansion in the nozzle reduces
the pressure of the steam below the external pressure at the
exit, sound waves will be set up in the nozzle with added resist
ance. This latter condition is likely to be worse than the
former, and if the pressures between which the nozzle acts
cannot be controlled it should be so designed as to expand
the steam to a pressure a little higher than that against which
it is expected to deliver, allowing a little acceleration to occur
beyond the nozzle.
Friction Head.  In dealing with a. resistance to the flow of
water through a pipe, such as is caused by a bend or a valve,
it is customary to assume that the resistance is proportional to
the square of the velocity and to modify equation (258), page
425 to read
where C is a factor to be obtained experimentally. The term
containing this factor is sometimes called the head due to the
resistance or required to overcome the resistance, and the
equation may be changed to
Kl.ti\V
A'
it bring understood ikti of the available head A, a certain portic
A* ij. UM'd  in tiviu tuning reMsuuurs ami the remainder
used in prodming the vrSmtiy I*. Thin t.f*rii y well e
by shifting A' to the tiher *tde nf ihe equation nd writing
A i
 n v).
' '
r* nn .sttam turbines t
Thi* fitrllstnl ha** Urn trtl .y
aiiiiw fur fiidiitiil ami *slsrr n
l* lififiiiltrti thitt it i a rujh nfut u'*..iii'4*iUry nirthocl bi
*rrlwi? it will srrvr, I'lu i.tltii if v fi4lly \'iirirs lirtwee
o.df; ami e.t$ for flim thrxu^h .1 ninglr mu^h r i uf guid
tiliwlrs tr Itwniiig hm kcI> in a strain Iisilifir,
Tlttfr Is tnr tlilfrrrmi* Utwtrn thr )Hhaviur <f water an
an rbslir Iliiiil lilt* air r ^!t'*ii that fiiimi J clearly undmtooc
iiiifl krjit in miml. t''ruiu<nal IT ".1441111 and oihrr resistance
lt ilir flow tf waitr, transform rnirj?> inn* hmi anil that ha
i l*st *r if il in kri lv thr water s> mil available afterward
fur prtttlm in;; %! tiy; tn llw ihr )tand the rurrgv whic
i\ t"XKmlrtl In ovrri uming fruittitutt ir ilirr resistances c
like nature by straw r air. i* nhan^rd into Juat arsci rematnn I
llir llwitl, nwy I* a%itiUit*le fnr ii& i rnSing tijrrnllcift*.
en Flow of Thrrr r* fivr c
ftcrrimrntinK n ii>* <K*w f Mriim through uriturn ami
thai Itii'i' litvn iiiilil to tr*i ilir thrnry f lhw, Kinr of then
il Hepariitely *r sit (tmbinann t .an 1 made l value
if the fririitifi fai ttr y.
Ill Steam tinging through an tri!Hr ir a ntt/,/le may b
rtifKlrllwti and weighed,
fj) *t'he prepare at one t*r several iini;% In a mmik mi
IIP measurer! by ^idr orifjiei r by a ^rarrhin^ tuljr; lln* tatti
be l* ifi%'cn!igalr llir frrt4tire in lltr rrgbtl f th
Ii llir enframe, r in ilir rr^fiun Uyint the exit, aa
IMI in* Hint willi an i.tsf^r,
BUCHNER'S EXPERIMENTS
437
(3) The reaction of steam escaping from a nozzle or an orifice
may be measured.
(4) The jet of steam may be allowed to impinge on a plate
or curved surface and the impulse may be measured.
(5) A Pitot tube may be introduced into the jet and the
pressure in the tube can be measured.
Of course two or more of the methods may be used at the same
time with the greater advantage. It will be noted that none of
the methods alone or in combination can be made to determine
the velocity of the steam, and that all determinations of velocity
equally depend on inference from calculations based on the
experiments.
Formerly the weight of steam discharged was considered of
the greatest importance, as in the design of safetyvalves, or in
the determination of the amount of steam used by auxiliary
machines during an enginetest. The first method of experi
menting was obviously the most ready method of determining
this matter, and was first applied by Napier in 1869, and on his
results were based Ran kino's equations,
Since the development of steam turbines much importance is
given to determination of steam velocities, though it is probable
that the determination of areas is still the more important
method, as on it depends the distribution of work and pressure,
while a considerable deviation from the best velocity will have
an unimportant influence on turbine efficiency. The first
experiments on reaction were by Mr. George Wilson in 1872,
but as his tests did not include the determination of the weight
discharged they arc less valuable.
Biichner's Experiments.  A number of experimenters have
determined the weight of steam discharged by nozzles and tubes
and at the same time measured the pressure in sideorifices at
one or more places. The most complete appear to be those of
Dr. Karl Bikhner * on the flow through tubes and nozzles.
Omitting the tests on tubes and on nozzles with a very small
18, p. 47.
iijHT, tin* no//lrs fr tt
owing *r*4)tt4tift" .tftd
h trstiU, will 1 tuotrti have the fo
VH Tt'.vtU* I\ UK WfHNtK. M.t.ltlMK.NSinNS IN
8 'I*
I V 1 *
o.ij
All thr rttu'u'tr* It4l ; iviffuirit.il ffiit fur whit h thr hmfj
!* givrii in thr itl*v* uMr *m fading ihr t'Mumiing ai rntraai
lifiii'i thr jJkiMtirf ,ii ilir fhr<nit 4tii !,ir in h*ivr had consi
fl'14r tnllurflir tfl ihr ti'.slf s!tisiiili  lllr ifrvHirr, ThtTt? W(
fntfti tfir t ihrrr 4tUltlitttitt '^wlr nirilurt rvrnly filHtribuU
frttrn rr.*!iifi" its ihr^r urifitt* 1!* htu*r njikr% intrrmiting co.
lillatit*fis t silii rrilifSg liir )*r)viV)4f if llsr lltliil in I hi" iljbe, I
thr arc m*! iiiitrfrtiii (ri>m iiir ihni arr brought out
thr in% f e*ligilii'* f Si<*rU4a ,i*I rr tn! iiulinirt) ill this d
i'Uvtion, Thr t*tli aiwl fr^wlt'* lf*i ^iii ts f ihr r*:% m I0
Slr*im ff fllr*tf !'*!%
ratiif Wfhu h r!lly *lr
cf irin : iltig, Thr rr.>
afcl f n rigli! way ii*r
!lrfl IfiifH a tfcttlrf llmUgh 1 86j
*l ^ir.itti 3tii *i frjiiititi wf i ptra
**fr 4 II ii.'*i*airI on tnr
Thr ^ir^nt (rm ilir nu/^tn was a
trfimmfrr riiiitwlrs ilir t*rrot c
hr <MfurfiHr ;i! lw firr rrttl, wh
ff*f In  4llfilrtif*t hi an of I
Bt)CHNER'S EXPERIMENTS
439
results. The discharge was also computed by GrashofPs
equation on page 432, and the ratio to the actual discharge is
that set down in the table ; the variation from unity is not greater
than the probable maximum error. The method of the compu
tation of velocities at throat and exit by the experimenter is not
very clear, but it was made to depend on the equation (268), using
the proper pressure and the discharge computed by GrashofFs
equation.
TKSTS ON FLOW OF STEAM.
Du. KAKI, BifcriNKR.
Numlxsr
and
designa
Prewmre IKIU
ids ulwolulc.
itUio of
hrtmt to
initial.
charac
pouncm
Ratio
of actual
in com
putecl
Velocity
it thrtmt
Velocity
at exit.
Ratio
>f actual
to com
putcd
tion.
Initial
Thnmt.
Kxll.
Hxirrnul
Hcctmil.
din
charge.
velocity.
I2E
l3
104.4
a 5. 3
n.fi
0573
00503
i8eo
3030
0.928
aaa
160.5
9 j . 4
ai.7
y'.6
0577
0.0449
jf {S
179
3030
0.930
3~aa
1473
83.0
20.7
*38
0.564
0.0411
0*
l820
a ggo
0.926
42 a
131 .3
75' '
18.5
0.572
0.0370
1790
aggo
O.cpg
Saa
117.1
6*7 . 6
16.8
13.8
0.577
0.0331
1780
296
0.925
332!)
180.2
ga. t
165
14. t
0.511
o . 0494
1940
3260
0.930
__.
1400
76.8
91.2
13.6
0.529
0.0394
1860
3060
0957
37 _ 3 a
131.5
70.4
105
13. 8
0S3S
0.0363
*&3 *&
1850
3020
0.950
3 83a
"57
62.0
17.4
138
0.536
o.oaig
d d
1850
3020
0.944
393!)
183.6
99.6
_
18.5
0.541
0,0501
,,.
1830
51
0.987
__.
103,0
68.6
38.1
IS 4
O.66o
0.0481
1550
2 1 go
0.932
43 5 b
89.3
S7
32.8
14.9
0.658
o.o4tg
ao w
58 o S
1 SS
2180
0.932
43 5 b
75.3
493
27.9
14.7
0.656
00343
&> S o
1560
2150
0.923
445 b
fil .0
37.6
33.3
145
0.643
0.0283
H
1560
2160
0.939
4S~Sb
4S4
23.0
16.9
145
o.6t8
o.oait
1630
3130
0.933
47Sc
102.5
65.4
__
15.0
0.637
0.0549
1630
2520
0.937
4851
8.8
SS 7
32.3
14. H
0.635
0.0410
* w
1630
M 53
0931
74.2
46.9
l8'5
14.6
o , 63^
0.0344
S 3 8
1620
2530
0.935
5~Se
50 a
371
14.9
14.4
Q.62J
0.0277
W 1.
1630
2490
0.933
The nozzles 30 and 3?? had tapers of 1 17.2 and i .4.9 which were
probably too great, so 4hat they may not have been filled with
rni
ti
ferrf,,* ' >
'I }
! > I
!,%>
^
t'M'iiS
strum; thi> might aacmni for tw small ratio of thr throat to t!
initial imsMirr; the m/./!r st* t whn h ha>i .1 taj*rr uf 1:13, al
.show* a small ratio ot' throat to initial n^.tjf',
Tlsr moot intrristiitjt fraiuri of ihr fr.i, i, ihr ratio tf t
vi'ltnity ill r*il, lotnjnitri:! ly ihr imilunl rviVrml UmlKtvtr, frc
llir iT'*Hiirr at Ilir **Sir tritiiT IHMr thr s:\if lnnt llir m/./U\ Tl
tlws ntl Ii*r4r ti <ri'li<l iti lip' lhrMt jtrrv,ttrt\
tuit lr?t'i mi llir m//Jr'*, j& am! .;/ ihr IIUMD v.ihtr tf this
iilul o.ij i \vltiilt Mrr<"M,jfi!'> ! a viSr y C';,i,,
Ratstw's Experiments l'h*.r ir.i'.* l^ivr airnwly b
rrftrrw} ! in tntir ts*n with tiriiiltMif'* furmuU. Ttu*y dl
llir strain %v,i' MHrH'>rt i> a ^truIU of i oil! Wit
ftirmril a jit lomlmwr; lli ;m<nml f .train
from lilt fiw i*f irtiif*cf,8!fr .iiwl tlw atiu*unt of t*h] watrr u
whit'h Iiilttf vt^ tlrtrritmiril In !l.w ing it through irj orifii
fllilttllff ff ft~*ifh i% t* l;lff*" t* itlt!r Ifffr, l! Ilial* I*' t'flOUgK
hay that lit', iliajtram^ ifp^v a urv i?fr.s! trgitiartty In his resul
M that wtwlrvrf rff*r llsrfr may ! sh t IK iftrltiitrd to I
mrthiMl. whuh lr^ *ivnil, tn lir i iisi% llir isiitwtilnty
tlflftcfl*4f,
* *^ritlttlf, 111 or*kr !" tliirfiiiior thr
. s 4 , t ...;. i * \f>
in %lri4ftt~Rt/ir u li ii> *rr tr.ri u* inj i**f', AH
f in VT 'i i in iii **! 3it A s'a Itinn tul***, ltivin
Ulr urilur. Uth mlwtt thr f,vli rrr trforming tl
iltirliwfi in at! itifrt !**r .at$l wlwfi ijw Itrtrpflg frrt'ly !i
thr iifi'tiiirfr, Itr aU* ti,rs :>! *riilHrt iwir through i
i i"j that if m**k*t pf.u I j* ally imtlil'Irrrnrt*
II%t'lifr S't ffrt or into thr < tsllililfiifig ttlJn* wf all
jZfit.t*,**} :*fl> 3''.
lit* 4* .,'.' In* ls(
*}*,*. ,,, it it
ROSKNHAIN'S EXPERIMENTS
441
For a wellrounded nozzle such as is used for an injector having
a taper of one to six, he found the following results:
Absolute Prtjwurf.
Initial. Throat.
Sj.o
135
105
75
45
61.5
Ratio,
o . 606
0.585
550
0.546
Calculated Veloc
ity at Throat.
1407
1448
1504
Stodola's Experiments. In his work on Steam Turbines,
Professor Stodola gives the results of tests made by himself on the
Jlow of steam through a nozzle, having the following proportions:
diameter at throat 0,494, diameter at exit 1.45, and length from
throat to exit 6.07, all in inches. The nozzle had the form of a
straight cone with a small rounding at the entrance; the taper was
i :6.37 Four side orifices and also a searchingtube were used to
measure the pressure at intervals along the nozzle; the searching
tube was a brass lube 0.2 of an inch external diameter closed at
the end and with a .small side orifice. This orifice was properly
bored at right angles; two other tubes with orifices inclined,
one 45 against the stream and one 45 down stream, gave results*
that were too large and two small by about equal amounts.
Stodola made calculations with three assumptions (i) with no
frictional action, (2) with ten percent for the value of y, and (3)
with twenty per cent; comparing curves obtained in this way for
the distribution of pressures with those formed by experiments,
he concludes that the value of y for this nozzle was fifteen per cent.
Rosenhaiu's Experiments. ~ The most recent and notable
experiments on flow of steam with measurement of reactions
were made at Cambridge by Mr. Walter Roscnhain.* Steam
was brought from a boiler through a vertical piece of cycle
tubing to a chamber which carried the orifices and nozzles at its
side; the reaction wan counteracted by a wire that was attached
to the chamber passed over an antifriction pulley to a scale
pan, to which the proper weight could be added. Afterwards
he determined the discharge by collecting and weighing steam
* Proc. hat. Civ, JKng., vol. ex), p. jtjg,
Tl su.im irrvurr wa, * ontrolled
U'' liui ihn. w.i* , t iur numtUR
under similar ,unliii"n
a ihrottlfvaUr. It  I't
A
Ihc .IMHI
PRESSURE IN THE THROAT
443
a direct calculation cannot be made, but a curve can readily be
determined from which the pressure can be interpolated. The
velocities corresponding to these pressures have been taken from
Rosenhain's curves and the velocities were calculated also by the
adiabatic method. Since the diagrams in the Proceedings are to
a small scale the deduction of pressures from them cannot be very
satisfactory, but the results are probably not far wrong. The
table on page 442 gives the coefficient of friction obtained by
this method.
Lewicki's Experiments. These experiments were made by
allowing the jet of steam to impinge on a plate at right angles
to the stream, and measuring the force required to hold the plate
in place; from this impulse the velocity may be determined.
It was found necessary to determine by trial the distance at
which the greatest effort was produced. One of his nozzles had
for the least diameter 0.237 and for the greatest diameter 0.395
of an inch or a ratio of 1.28, which is proper for a pressure of 80
pounds per square inch absolute. His experiments gave the
following results as presented by Biichner:
Steam pressure 77 99 108
Ratio of computed and ) . 96 0.96 0.955
expt. velocities ) y * yoj
Coefficient of friction . . . . 0.08 0.08 0.09
These experiments like those for reaction are liable to be vitiated
by expansion and acceleration of the steam beyond the orifice.
Pressure in the Throat. Some of the tests by Biichner show
rather a low pressure in the throat of the nozzle, but in general
tests on the flow of steam show a pressure in the throat about
equal to 0.58 of the initial pressure provided that the back pres
sure has less than ratio 3/5 to the initial pressure; this corresponds
with Fliegner's results and should be expected from his com
parison with molecular velocity on page 430. The following
table gives results of tests made by Mr. W. H. Kunhardt * in
the laboratories of the Massachusetts Institute of Technology:
The excess of the throat pressure above 0.58 of .the initial
* Transactions Am. Soc. Mech. Engs., vol. xi, p. 187.
444
,,,,.,.,...;' fur flu* IrK fififttltriTiS t U i i. l IK* aUrihutrri to the
I'Xfrjwivr Srfiittlt of ihr iuU. Luiifirr ml** ir>tn hy Hurhner,
*howtfl ihr jHtnir rlln I in ,n \4gr rain. I ilrgrrr.
Ha>W OF s1T..\M TtlltMli.ll ^IIMKI 1 rtlilA Wll'H Rr HANDED
j.s<a*
* Iwgf,
J > 1 3 *
i 5 li !
* " l! 'H i > w
*
V.*
14 ., n )
I , t* * <
I fat ">'*
8s I *, , t ! * ''"'
1 * i . * *
;**' *'
i ii. . .
$ j ' i . *
s , * . *
t '
* ''t%
is* f" 1
*
sf
5
1
4 *
**
*
? M
5
% ,
*l
I
r
w^
44
5
*
6
*
S
4
i*
a
1
a .
i
4n
S8f*
*
s i *
5fc
.' H ; *.!
WS ; l*,
in i *J
tutMivrr
150 I*V
Till* tiii'tittft! of *ft i
irnt lo J al
ii4 fft? !it*>
qf {tttumlH utrsululr
thr t.iitrltlalif uill
, Kntutrnl Ihr
"f >lr4m rr htr
tr urn ir
rii^sufl 8 * tf ft
*i ^ir^f
If'tt hr* til
ftfrifr may in*
> lll
DESIGN OF A NOZZLE
445
The quantities just obtained are the amounts of heat that
would be available for producing velocity if the action were
adiabatic. In order to find the probable velocity allowing for
friction, they should be multiplied by i y, where y the coeffi
cient for friction may be taken as 0.15 for the determination of
the exit velocity V v As for the throat velocity, there are two
considerations, the frictional effect is small because the throat is
near the entrance, and all experiments indicate that orifices and
nozzles which are not unduly long deliver the full amount of
steam that the adiabatic theory indicates; therefore we may
make the calculation for that part of the nozzle by the adiabatic
method. The available heats for producing velocity may there
fore be taken as
434 and (i 0.15) 288,5 245,
and the velocities are therefore (see page 436)
K s  ^644 X 778 X 434 1480.
K 8  V644 X 778 X 245  3500.
The quality of steam in the throat is
^ 3  # a r, + r 3  855.1 + 885.9  0.967.
To find the quality of steam at the exit we may consider that
if x 9 f is the actual quality allowing for the effect of friction we
have
+ 3377  245  94.3) + *Q26  0.833.
Though not necessary for the solution of the problem it is
interesting to notice that adiabatic expansion to the exit pressure
would give for
x a x n r a + r s 810.8 4 1026 0.790.
Now 500 pounds of steam an hour gives
500 ~h 60  0.139
44
144
The iJiamitm art,
M.l'Il'S
of a pound JHT stronci; r0nsrwntly ihr anas at the throat am
the rxit will IK by niwitt>ii i jfuS i KI' 4.U. in Mjimri inches
0,0597
3500 0,827
If ihr tiifMr is liikrn i U *' in nn, thr tntttt <tl jmrt witlha\
a Irngth if
tuts.PJt* c.jHo  ;.i rn;
ant! alUiwinn fif ih r*m!in *ii ttw~ rnirituf ami for a faircun
llw lhrwi t* tin i**nr, il luul lrnth ntny be eigl
u rupam tiriim n
ttnly, wwultl havr thr inmjmUli*
uf ihr atmcphe:
a,* follows;
175,1
ff friin ,o ilir
ihr vrlmily *! r%il will lit
Taking ihr tw
l l*r
The tittiiy of ihr ioiw ihr rt)ii<ittun
tit, it *
Thr *il Stir rsyf will m*w Utnmr
tij.ii til '*" i iu uj.ffltl * lft.f4 * txstftt " ** O.lOo
* ^1^^*' * *f f f ' ' * w ,^ * '
tntS ihr t ! rr*f**mliK tlUwuirr i* tt.4*** ' A 1 * ****' n **"
thr 3 onr in irn, ihr Itn^ih 4 ihr onit al fri f the nox
anil iu total am! intri ny ! 24 inch
CHAPTER XVIII.
INJECTORS.
AN injector is an instrument by means of which a jet of steam
acting on a stream of water with which it mingles, and by which
it is condensed, can impart to the resultant jet of water a sufficient
velocity to overcome a pressure that may be equal to or greater
than the initial pressure of the steam. Thus, steam from a
boiler may force feedwater into the same boiler, or into a boiler
having a higher pressure. The mechanical energy of the jet of
water is derived from the heat energy yielded by the condensation
of the steamjet. There is no reason why an injector cannot be
made to work with any volatile liquid and its vapor, if occasion
may arise for doing so; but in practice it is used only for forcing
water. An essential feature in the action of an injector is the
condensation of the steam by the water forced; other instruments
using jets without condensation, like the waterejector in which
a small stream at high velocity forces a large stream with a low
velocity, differ essentially from the steaminjector.
Method of Working. A very simple form of injector is shown
by Fig. 91, consisting of three essential parts; a, the steamnozzle,
b, the combiningtube, and c, the deliverytube. Steam is supplied
to the injector through a pipe connected at d; water is supplied
through a pipe at/, and the injector forces water out through the
pipe at e. The steampipe must have on it a valve for starting
and regulating the injector, and the deliverypipe leading to the
boiler must have on it a checkvalve to prevent water from the
boiler from flowing back through the injector when it is not
working. The watersupply pipe commonly has a valve for
regulating the flow of water into the injector.
This injector, known as a nonlifting injector, has the water
reservoir set high enough so that water will flow into the injector
447
4
Ki lks
through ihr Jnilurmv t* ^r.tviiy, A /I///MJC injrrtor hm a a
dt'virr for making a uutiuw l ilr.iw tvairr frmn a reserve
inlow thr injnlur, wlitrli will lr tU" rihnl l.ilrr.
Tu start fltr tiijni**!' '.StMttit li\ Fti;, ji, tin ^iramvajvt' is fir
ojK'nni *y r *tilly it* bUw mil 4itv \vairr lli.il itu\ haw gather!
lilwivr llir V.tlvr, tttfili ihr i*vrrJ!s%v, aiitT $ <* rsM'ntiiil to hai
dry <sUMim fur Htarhu^, 11i* ?*lratn t.ilvr H t!u*n rltm'd, an
ttir WiiUTvsiivr 8 s * t*riti wti\ .V* 'tnfi an wal*r iitt*ari at tl
owrllow liiiwrrfi ilir tumUftuiglubc iifitl I he (vHvvry*tube tt
H Witfr, 4l tlir jrl rt! ilraill
Mlr ami i* iwinirftit'ti by ihr a
$1 ft vrlmJly, s* ii
llir irtil*iftiitiiiiil*r ii
IfUti llir imiirf, Wllrll ihr ittjr* tf 11 'tfljff  lai:ifH
l IK furtttnl at tiir 'fftiiff' liflWrrfi llir fniiiiitig
tllfe, ihr v.ilvr it! llir vrriUw * isn
winilti ihr Wiiirr Jisiti nil
lltt* arlir tf ihr injriur,
Thtory of it llir IWM fumlarstrnMt (
thf lltrtiry wf llir injnixif arr iriirt from llir of tl
f
THEORY OF THE INJECTOR
449
The heat energy in one pound of steam at the absolute pressure
p 1 in the steampipe is
i ,
where r l and q l are the heat of vaporization and heat of the liquid
corresponding to the pressure p^ is the mechanical equivalent
A.
of heat (778 footpounds), and x^ is the quality of the steam; if
there is two per cent of moisture in the steam, then x l is 0.98.
Suppose that the water entering the injector has the tempera
ture t a , and that its velocity where it mingles with the steam is V w ';
then its heat energy per pound is
and its kinetic energy is
where q a is the heat of the liquid at t v and g is the acceleration
due to gravity (32.2 feet).
If the water forced by the injector has the temperature t 4 , and
if the velocity of the water in the smallest section of the delivery
tube is V w , then the heat energy per pound is
and the kinetic energy is
V
'
Let each pound of steam draw into the injector y pounds of
water; then, since the steam is condensed and forced through
the deliverytube with the water, there will be i \ y pounds
delivered for each pound of steam. Equating the sum of the
heat and kinetic energies of the entering steam and water to the
sum of the energies in the water forced from the injector, we
have
y ~
(2
450
IStH'luKs
Tin trims (irfx'iuitng on iht uiui iiir^ IV ami r w are Rev
Sargr ami tan tomtnonly U fitgirt ftf,
Tt KII ,iii ilra of ihr inllwiur of ihr fortiur, wr may consid
(hat th' *rtN^uri* foiling w.iir ini a nun tilling injector is 8'
doin, f *'viT, itnaur ttt.itt ihr ir?Mirr if ihr almt>sht*re, a:
ihr i'rrrr*MmSing jjfr^iifr for a lifting injritor is always le
Now, ihr jirtNMin tl ihr tmoHphrrc IH t*wivt!rnt to a head
If  144 * U; ; f *'4  .U trii.
A lilcriil cMimair of v nhr (Ktumin of waur JHT KJ>und
hitam) is lifiiTit, *riirrftrr,
IV 5
In wrcItT ihfli n injnior tlwll ilrlivrr w.iirr agiiinii thestea
jtfTwtifr ill A Iilrr it"* vHo* llv IWM^I i*r gfr.ilrf thilfl Would
** 8 iI rttt't lv ii tirjitl tijiiiuilrtil In ihr boil
l*itkili Ihr ltlrf .fr'i"*itrr at Jo utimU by
^iiigr, ur ,*fn *fniiii'< atviolulf, llir rUtvalrrI liratl will be
14 , )t*'\ : *. tt
Again liflrrn fr v, Ihr valur ff ihr Irrm tlrf' fitting on
I
t i %, i f i t ..
thr s.ilii tti an llljnlnf i* nrdfly dry
that flir Irrm ilrjirnflmK n ih*i U4ntii> will h*ivt* the vilu
ll b, thrfrfrirr, rifltlrnl ittiif ihr Irflli tfrmttnH R V,
in inDurncr f lr%% one jrr ml ami thai lit*' trrm ciepem
un IV
THEORY OF THE INJECTOR
451
For practical purposes we may calculate the weight of water
delivered per pound of steam by the equation
y =
(270)
This equation may be applied to any injector including double
injectors with two steamnozzles.
The discussion just given shows that of the heat supplied to
an injector only a very small part, usually less than one per cent,
is changed into work. When used for feeding a boiler, or for
similar purposes, this is of no consequence, because the heat
not changed into work is returned to the boiler and there is no
loss.
For example, if dry steam is supplied to the injector at 120
pounds by the gauge or 134,7 pounds absolute, if the supply
temperature of the water is 65 F,, and if the deliverytemperature
is 165 F., then the water pumped per pound of steam is
867.?; f p
i :.;\ ..<...*!.. ..... .. V
ft
10.5 pounds.
From the conservation of energy we have been able to devise
an equation for the weight of water delivered per pound of
steam; from the conservation of momenta we can find the relation
of the velocities.
The momentum of one pound of stearn issuing from the steam
nozzle with the velocity V t is K, + g', the momentum of y
pounds of water entering the combiningtube with the velocity
Vu is yVu * K'> and t t! momentum of i + y pounds of water
at the smallest section of the deliverytube is (i + y} V w * g.
Equating the sum of the momenta of water and steam before
mingling to the momentum of the combined water and steam.
in the deli very tube,
V, + yVJ  (i + y) V w (270)
This equation can be used to calculate any one of the velocities
provided the other two can be determined independently. Unfor
UtnnUly imrr t<> *.mr m.rilamt> aUuil alt il ihr velociti
thai ih j!*rf "i,'r% f tip iui?urs ami i sin form*, and
lions f tii" M\rtai ittrinlrtTs M us iujrt ft.n luu tnTi
tii.iinh l> r%ff iisstffit, Thr JH.I \joMUit t*f this matter
iivtn ly Mr. Suit kl.uu! ki*rH,* \vhi hui nuijr nmny fxjwr
iisinis for William Srl!r & t"*. Ilir r.it Ikal iari tf whi
ftilltiWH i% liiFgdv ijrawn fr<m hi, wurk.
Velocity of titt Sttawffl, hMaii. i;r*ii n$ir%
vvlwrt' r, ami y
ilv t4 i*ji .1! slw
ami il hrat of tl
r * r alii) f } and
tf llir lulw f*f whis
nf tltr *4rattt *il liir
thr tiialis at tlw
?iS,ifril, v t } the ijtlili
<; jS i* unity I ami * 2
.!* iilir hy iilcf oft
it* ;iW4t!!r rfjjratufr''> t irr"t)K:nrling
jtfi f 
ami uihrr* h*ivr i throat Atnl . slmfgmK ffiiti, tl will
ftUimi ill Jill . a '*"* ill* Itfjf8f.f itt)!' itjjrn
t*T\(mi ill*" 'lr,ii lss s ,*^Sr r Ifs., ijl.tfi tl;ll
llir ll*, il!s * ufricvjurfttiv thr f'"!'ii3rr
f llir *ilrit fil fit ^/lr illl ah<* Stir %rlisl a! that liiil* t
iifilv tii iJji" initial j*rr'vsutr. \',> r' ir*li*i in llir rtt*rd
iiiilirfj ittr *ff"vifr aS ^rjunjij, ;il .ttii *ifl f 4fi rxfici
/,ilr tU*}*t*mt n ilii' r,t!i,. *4 !iw .SIT.S, ,,! ilt.ii fail tu ihc.thr
1 1 Itflfl *ifr I iin*ii,"iiirfilly iiii**t **sfiff4, AIs4, <i?> W'iis rrajl
Hrfr /', iliul 7'
thr irr!rr
i$*llS *ii llif *w5f
i
VELOCITY OF THE STEAMJET
453
sized by Roscnhain's experiments, the steam will expand and
gain velocity beyond the nozzle, if it escapes at a pressure higher
than the backpressure. For an injector this last action is
influenced by the fact that the jet from the steamnozzle mingles
with water and is rapidly condensed. Some injector makers
use larger tapers than those recommended in the preceding
chapter for expanding nozzles. The throat pressure may be
assumed to be about 0.6 of the initial pressure; with the informa
tion in hand it is probably not worth while to try to make any
allowance for friction.
The calculation of the area at the throat of a steam nozzle by
the adiabatic method will be found fairly satisfactory; the calcu
lation of the final velocity of the steam will probably not be
satisfactory, as complete expansion in the nozzle seldom takes
place, but it is easy to show that the velocity is sufficient to
account for the action of the instrument.
For example, the velocity in the throat of a nozzle under the
pressure of 120 pounds by the gauge or 134.7 pounds absolute is
{2 X 3 2 2 X 778 (867.5  0.967X894.6
 1430 feet per second,
having for x z
7' / f \ T
# 9 . ~a./o. + <9 t ~ # 2 J = ~ (1.0719 + 0.5032 0.4546)
 0.967,
provided that p 2  0.6^, 80.8 pounds absolute.
If, however, the pressure at the exit of an expanded nozzle is
14.7 pounds absolute, then
(1.0719 + 0.5032 0.3125) 0.877,
and
J439
bX 32.2X778 (867.50.8775X966.3+321.1180.3)}*
2830 feet per second,
454
INItttTUKS
whirli U nearly fwirr ttu! j.i c.tlrui.itn) fur ihr \TK ity at the
jimultr.Hl SIT lit n uf ttu* *4r,ifti .'/ tr. Sin* r thrrr is usually
vacuum Ir)inl thr ?lr;un m*v.!r, ihr ttruil .fr.tm velocity fe
Ukrh to tr otnnitlrralijy Urgrr, luil ffni. Mi$tirt iriucity will
Millar ft n r*j4,iii* ihr t)yrunu< * *l ihr ..
Velocity of Entering Water. Thr \rlnt iiy f tht* water in
ihr t'tintliililrill Illfw whrrr tl titin^Ir^ wilh ihr 'tr;m Urtnd8on
(>ii ihr lift nr hiiitl frum ihr fr>*rm*tf' l< ihr injtrtor, (6) the
lirrsjittrr i**f Vsifiiwini in i fir i Nitifsiinitt! till***, mn\ irl on th*
i ?  w ** feidiv
rr>tHUittrr whit It thr tt.ilcr i*t*rrinti  fr*m frittiun uml m
In ihr jir Viilvr 1 *, ;tttt{ nrva^r' f llir injn tur. Thr first
lhr*r tun In" nuMsurrt! ttirrt fly fsr any ^hrti iHr; fr example
whrrr a litl i nunir ift .in ittjriinr. Iti *{rtrrinininu the pro
s
jrli*n> tf an injrttur ii i> iifr i ir'uitr ihai iltrrr in neither
lift mr hrttd fr *i mnH^iiu' injr*ir, inl ihai ihr lift fora
lifting in : lr s<* lutgr r i>tn tr nJl.unrl with trrUil
$railiir Tlir lifi l*r 4ii injntor i> utttitHy fin
Thr vat lit ihr Milttlniiltli* Ilr fltrti 4liw*lil1t to or 24
iru hi'H if mm tiry, *rii"t*t*fiilifi.* l* *'$ *r ; li f water; that
in, ihr ilr*Ui?i' ftrrvmrr nuy l* i r . junih r jtiart' Inch.
Thr viti uttnt iilirf ihr sirtni siful %%a!rf iirr tfiftthintt) appears
tt* lir litniii'ff liv ihr irmiwf iii tur tl ihr !rf; thtH, if the tem*
*>. Bui ihr trmjrrjiiurr > tkr In iSw fklivtry
ihr t .tfttSrwii ^icititt ir rit fitito,*} and we
moving with *i mmlrralr vrUftily,
"tlir frst%i4Hir *if ffii lifl ill ihr pi}**, .jilvr^ afttl
f iiirrl?r^ lw nrvrr hrr tjclrrminr*!; titnr llir \rtt4 ity IS high
If Wr a^itjlllr llir *rrdlrst 141 SIM III 1 u*lfr=iii:f f jy feet 01
, tlir ftiii^iftiiiffi VrUw tly 4 ihr w.4lrf mlrfifig the t'ttmbining
tir Will fi rprrt
\ 4;ll V"^ * \ji.j * j  4^ fret,
If, on ihr rtitiir^iry. iltr rilrsiivr hr4l rdi jug vcltjciiy li as
fcrl, Ihr
SIZES OF THE ORIFICES
455
V 2 X 32.2 X 5 = 18 feet.
It cannot be far from the truth to assume that the velocity of
the water entering the combiningtube is between 20 and 40
feet per second.
Velocity in the Deliverytube. The velocity of the water in
the smallest section of the deliverytube may be estimated in two
ways; in the first place it must be greater than the velocity of
cold water flowing out under the pressure in the boiler, and in the
second place it may be calculated by aid of equation (271),
provided that the velocities of the entering steam and water are
determined or assumed.
For example, let it be assumed that the pressure of the steam
in the boiler is 120 pounds by the gauge, and that, as calculated
on page 451, each pound of steam delivers 10.5 pounds of water
from the reservoir to the boiler. As there is a good vacuum in
the injector we may assume that the pressure to be overcome is
132 pounds per square inch, corresponding to a head of
132 X 144
 a 
62.4
, ,
= 305 feet.
Now the velocity of water flowing under the head of 305 feet is
V2gh Va X 32.2 X 305 = 140 feet per second.
The velocity of steam flowing from a pressure of 120 pounds
by the gauge through a divergingtube with the pressure equal
to that of the atmosphere at the exit has been calculated to be
2830 feet per second. Assuming the velocity of the water enter
ing the combiningtube to be 20 feet, then by equation (271)
we have in this case
v _ Y yV2_ , 2830 + 10.5 X 20 _ ^
i + y i + 10.5
this velocity is sufficient to overcome a pressure of about 470
pounds per square inch if no allowance is made for friction or
losses.
Sizes of the Orifices. From direct experiments on injectors as
vrell as from the discussion in the previous chapter, it appears
that fhr quantity of siram Ulivrr! l*y ihr *it\tmmu*le can
caU'uliiU'fl in *S1 f.r.r*, lv ihr tmthI f*r the tbw of stea
through an rihir, a vanning ihr jrrv>iWr in tin* orifirr to be
of llir ;itMUllf I'fCHHurr 4lvr lllr nfifur,
N*ow cat h }M*tmti f !t'4ftt l*rirH y n*iiitt'* of water from
rcHtrvoir t< ihr ImiSrr ; Mn^ruily if tr jtirtiS^ <irr ilrawn Ir
ihr rrstTvoir *r nnumt ih injri l*r wilt HH 11 t y f'ttniRds
^Iriiiw i*r srtttfitl,
llir sftrt ilk vnitimr >f ihr n%?Mrr ! ,t!tr 4111! slrail in
wlirrr .v, i* ttir tii4ii
t/4tttim, ,iml <' i tisr
of liist
.4 tin
iliir to vif
r. The volu
unit tltr ami *f
fi
whrrr T i lisr %rl** sH
In i
llir
H llir iPfriftif
*f
r inisirsi
t M,J 
' anti I", 11
to i
frrl. st% fnUfid
fmm 6*
! tlrhvrf t JtJ 18 tlll.r t fl
. IX
SIZES OF THE ORIFICES
457
In trying to determine the size of the orifice in the delivery
tube we meet with two serious difficulties; we do not know the
velocity of the stream in the smallest section of the delivery
tube, and we do not know the condition of the fluid at that place.
It has been assumed that the steam is entirely condensed by
the water in the combining tube before reaching the delivery
tube, but there may be small bubbles of unconclensed steam still
mingled with the water, so that the probable density of the
heterogeneous mixture may be less than that of water. Since
the pressure at the entrance to the deliverytube is small, the
specific volume of the steam is very large, and a fraction of a
per cent of steam is enough to reduce the density of the steam
to one half. Even if the steam is entirely condensed, the air
carried by the water from the reservoir is enough to sensibly
reduce the density tit the low pressure (or vacuum) found at the
entrance to the deliverytube.
If Kjp is the probable velocity of the jet at the smallest section
of the deliverytube, and if d is the density of the fluid, then the
area of the orifice in square feet is
w
(274)
for each pound of steam mingles with and is condensed by y
pounds of water and passes with that water through the delivery
tube; w t as before, hi the number of pounds of water drawn from
the reservoir per second.
For example, let it be assumed that the actual velocity in the
deliverylube to overcome a boiler pressure of 120 pounds by the
gauge Is 150 feet per second, and that the density of the jet is
about 0.9 that of water; then with the value of w 2.78 and y
10.5, we have
, ^^^^2^^* ^___ ra 0.000361 sq. ft.
150 X 0.9 X 624 X 10.5 J
The corresponding diameter is 0,257 of an inch, or 6.5 milli
metres. If this calculation were made with the velocity 266
(computed for expansion to atmospheric pressure) and with
458
INJECTORS
clear water the diameter would be only 0.183 of an inch; this i
to be considered rather as a theoretic minimum than as a prac
tical dimension.
Steamnozzle. The entrance to the steamnozzle should b
well rounded to avoid eddies or reduction of pressure as th
steam approaches; in some injectors, as the Sellers' injector
Fig. 92, the valve controlling the steam supply is placed nea
the entrance to the nozzle, but the bevelled valveseat will no
interfere with the flow when the valve is open.
It has already been pointed out that the steamnozzle ma
advantageously be made to expand or flare from the smalles
section to the exit. The length from that section to the end ma
be between two and three times the diameter at that section.
Consider the case of a steamnozzle supplied with steam a
120 pounds boilerpressure: it has been found that the velocit
at the smallest section, on the assumption that the pressure i
then 80.8 pounds, is 1430 feet per second, and that the specifi
volume is 5.20 cubic feet. If the pressure in the nozzle i
reduced to 14.7 pounds, at the exit, the velocity becomes 283
feet per second, the quality being x 2 = 0.8775. The specifi
volume is consequently
v z = x 2 u 2 + o = 0.877 (26.66 0.016) f 0.016 = 234 cu. ft.
The areas will be directly as the specific volumes and inversel
as the velocities, so that for this case we shall have the ratio c
the areas
5.20: 23.4 ;
2830 : 1430
= 1:2.27;
and the ratio of the diameters will be
Vi V2.27 == i: 1.5.
Combiningtube. There is great diversity with differer
injectors in the form and proportions of the combiningtub(
It is always made in the form of a hollow converging con<
straight or curved. The overflow is commonly connected to
space between the combiningtube and the deliverytube; it is
Sellers' injector, Fig. 92. in the latter case the combining and
delivery tubes may form one continuous piece, as is seen in the
double injector shown by Fig. 93.
The Deliverytube. Thin tube should be gradually enlarged
from its smallest diameter to the exit in order that the water in it
may gradually lose velocity and be less affected by the sudden
change of velocity where this lube connects to the pipe leading
to the boiler.
It is the custom to rate injectors by the size of the delivery
tube; thus a No. (> injector may have a diameter of 6 mm. at
the smallest section of the delivery tube.
Mr. Kneass found that a deliverylube cut off short at the
smallest sect itm would deliver water against 35 pounds pressure
only, without overflowing; the steam pressure being 65 pounds.
A cylindrical tube four times as long as the internal diameter,
under the same conditions would deliver only against 24 pounds.
A tube with a rapid flare delivered against 62 pounds, and a
gradually enlarged tube delivered against 93 pounds.
If the delivery tube is assumed to be filled with water without
any admixture of steam or air, then the relative velocities at
different sections may be assumed to be inversely proportional
to the corresponding areas. This gives a method of tracing the
change of velocity of the water in the tube from its smallest
diameter to the exit.
A sudden change in the velocity is very undesirable, as at the
point where the change occura the tube is worn and roughened,
especially if there are solid impurities in the water. It has been
proposed to make the form of the tube such that the change of
velocity shall be uniform until the pressure has fallen to that in
the delivery pipe; but this idea is found to be impracticable, as
it leads to very long tubes with a very wide flare at the end.
Efficiency of the Injector.  The injector is used for feeding
boilers, and for little else*. Since the heat drawn from the boiler
is returned to the bailer again, save the very small part which
is changed into mechanical energy, it appears as though the
effiuwy vva frdVti, am! ilt.a injrt i^r t a*. $**tit as a not
provided that if \\uik wiih KTUMU , VW may alnu*t rotisi
tttr ifijrtfttf ti* ait a*. i iVr.i tt.ifff hra!r, trralin^ lltr pump
in of fffti W.ilfl" !' jilt il"fitiil. Il ha* ah'cath Srt'rfl ifi*t
till*' I'* If'^s
f llir
ifir
r *;f
ill llir
1 iflC
lift*
llf.
placed higher than the reservoir a special device is provided for
lifting the water to start the injector. Thus in the Sellers'
injector, Fig. 92, there is a long tube which protrudes well into
the combiningtube when the valves w and oc are both closed.
When the rod B is drawn back a little by aid of the lever H the
valve w is opened, admitting steam through a side orifice to .the
tube mentioned. Steam from this tube drives out the air in
the injector through the overflow, and water flows up into the
vacuum thus formed, and is itself forced out at the overflow.
The startinglever H is then drawn as far back as it will go,
opening the valve x and supplying steam to the steamnozzle.
This steam mingles with and is condensed by the water and
imparts to the water sufficient velocity to overcome the boiler
pressure. Just as the lever PI reaches its extreme position it
closes the overflow valve K through the rod L and the crank at R.
Since liftinginjectors may be supplied with water under a
head, and since a nonlifting injector when started will lift
water from a reservoir below it, or may even start with a small
lift, the distinction between them is not fundamental.
Double Injectors. The double injector illustrated by Fig. 93,
which represents the Korting injector, consists of two complete
injectors, one of which draws water from the reservoir and
delivers it to the second, which in turn delivers the water to the
boiler. To start this injector the handle A is drawn back to
the position B and opens the valve .supplying steam to the
lifting injector. The proper sequence in opening the valves
is secured by the simple device of using a loose lever for joining
both to the valvespindle; for under steampressure the smaller
will open first, and when it is open the larger will move. The
steamnozzle of the lifter has a good deal of flare, which tends
to form a good vacuum. The lifter first delivers water out at
the overflow with the starting lever at B; then that lever is pulled
as far as it will go, opening the valve for the second injector or
forcer, and closing both overflow valves..
In]ctoni.  In tin ilisiusMons f Injector
thus far givtri it lu* Um *vwwil th.il thry w*rk at full cape
jtv but a 1 * an injrviur ttui4 lr iWr t lrwK the waterlew
in a tKiiliT tt jtrompily tt* jr'Hr hri^ht, it will lave muc
mrt* tluin the fiijwiiy wrctlni fur IrnSiii^ thr IniuYr stradib
Anv injittcir nwy t* *U t* *'rk *it t rriltuwl tajmdty b
mtttftiif! tlir ujniiiK * ? t ^* rtiMtttviilw, tml the Em
of it* i* ** ft ttf, Thr limit may tic rfttrmlrti mi
what hy ih *atrr iw4j ^v ntui w limit
tttr Wiilrf fttlly,
Thr irigitMl liiffiifti ifiilt*f mViitU
ittr t
iifwl ii! h*il ii U
iv *hii h fhr rllr.
Ulitl. Tlmn ln*lh m'iilrr
illiiti !hr
am! lltr ii
**n4 *vr fi lulu tht? Mtt
*roi of l!l: '^rafli jrl U? it
p l*rr
llmt the tr?u
iutrf whu h Ihry Wrrr
*U!r! * *'k ihrutigh^t
^. liir tihjrction
Ut l.y atwl in
SELFADJUSTING INJECTORS 463
In the Sellers' injector, Fig. 92, the regulation of the steam
supply by a long cone thrust through the steamnozzle is
retained, but the supply of water is regulated by a movable
combiningtube, which is guided at each end and is free to move
forwards and backwards. At the rear the combiningtube is
affected by the pressure of the entering water, and in front it is
subjected to the pressure in the closed space O, which is in
communication with the overflow space between the combining
tube and the deliverytube, in this injector the space is only for
producing the regulation of the watersupply by the motion of
the combiningtube, as the actual overflow is beyond the
deli very tube at K. When the injector is running at any regular
rate the pressures on the front and the rear of the combiningtube
are nearly equal, and it remains at rest. When the starting
lever is drawn out or the steam pressure increases, the inflowing
steam is not entirely condensed in the combiningtube as it is
during efficient action; lateral contraction of the jet therefore
occurs when crossing the overflow chamber, causing a reduction
of pressure in O, which causes the tube to move toward D and
increase the supply of water. When the startinglever is pushed
inward, reducing the flow of steam, the impulsive effort is
insufficient to force a full supply of water through the delivery
tube, an'd there is an overflow into the chamber O which pushes
the combiningtube backwards and reduces the inflow of water.
The injector is always started at full capacity by pulling the
steam valve wide open, as already described; after it is started
the steamsupply is regulated at will by the engineer or boiler
attendant, and the water is automatically adjusted by the movable
combiningtube, and the injector will require attention only
when a change of the rate of feeding the boiler is required on
account of either a change in the draught of steam from the
boiler, or a change of steampressure, for the capacity of the
injector increases with a rise of pressure.
A double injector, such as that represented by Fig. 93, is to a
certain extent selfadjusting, since an increase of steampressure
causes at once an increase in the amount of water drawn in by
the lifter ami an inrrea*e in I he ilow f *tram thrtuigh the steam
mwv.le of the fortrr. Stu h injettoi^ havr 4 \\iiU range f action
ami i an le toiiirolleil l\ regulating ihr i.ilvr un the steam
pipe.
Reitirtiog lajtcton* li ihr at lion of any of ilu* injector
thus far <ir^.Tibrl ? inierruie*l for any rea.ow, ii is neiessary tc
^Snii uii Meant and start the
injrrtor anr\v; .Mtmetimt*H tht
injrt'tor ha Iwome hinted
y t
urrt'umi thii
sliilii uliy \arioii 1 * ftirros o
re .i.it HUH' 'ttj 1 "* il *f' <i havr Inti
l\i.tI, Mti h at t hr Sellers
I lit "i i. TiiJ^ ij'tr ha
l^'ssf !*.<! ti*//Sr' in linr, th
vwlv
itir ilrlilrfy llllr lil'th
'brrr is al.M a slit]
ifi<l an ovfrflttf
wi*l* rt*' *>wI iiwkrs n varuut
y ul* wmlrr utt tonclitionH; til
i lulir ml *MI
in llw m
"tlir %irmmt/./1v HJ
whtt'li druWH sirr from ihr n
water n5iM? thnniitU iti f * ilr
until llr r*fwrn%*ili if ^lr
tr!liil varttum llwl lr*wt tij
tu! ami HII^ tiff ihr f4ir u ihr M%'rri!*w; ihr tnjtrtorthe
ftrrn Wrtirr Ui ihr Uiihr. If ihr inj'ir ftlr fr any raw
tin litishinK fitU ami ihr in)ir uk ilir ^UirtinK Kiti<tn
will Mart a 1 * * 4* MJipIir"! wilh Wrtirr rtSlfl ^Iriim.
Injvctar. Tlw nu*i r mi !yj f Seller** injccn
tnventeti ly Mr. Kneuv* ,iil rrjrrwirtl ly Fi. u? b l!h 1
titriinii*iti! **rif ifliHiiii*. li i ! % a liiiIr iiiin if with all the je
In im* line; i, A. ami urr ihr *ir4ii m*vU, ilu r*imlining'iub
and the tlvliveryiuU f ilu ftiftrr. iltr Win" i> *rjtMtl of ii
INJECTORS
465
SU
annular >tr;tm no<v.h /, .nul ihr annular tlrliviT
rounding ilu iio^lr i. Thr proportion*, art MU h that the lifti
ran always prtHlwr a in lion in ihr fm{ pipr r\rn when the:
is a UiM'hargr fr*ni thr main *>lram mwlr, ami it is this fa,
that rM;tMi.hrs tSir fr?4 4 tiling fi'.iiitrr, Whrn tin* fraiwati
riMs t Slir !tli*r>' it mrrl* ihr *lrain from tttr Uflrrnoswh? ar
is fnrwl in u thin sluri am! iih liigli vrhn ity tntti ilu rumbimn
tnl i" tf thr fMfc'rr, wlur* ii mi"* in coniat t with thr ma
sinunjft, ami itittinlifsi? wiih ant tmln^in^ if, rm'ivts
liigh VrltHily which rnaSlr J! Is* \w* thr ovrrilow urilitt's ai
prtH'fftl litrutigh thr iirlhrf^, Inlw lo ihr l*tirr,
la'kr any tlouliU* njir, ihr lili*i' ami lrrr hiixv ;t co
hkirntblr f^ltgf tf aiii*n lhj^h whith sltr wulrr i* itiljusli
to llir '4rif MtJ}K i: ( t flsri* s, ,i itstthrt a<l j ; 4iiirfil in tl
injcttor, for whrn .1 K ***! ^uuj r, r'.ial!i*hrii in ihr s>a
HttrrttumlinK itu* *omtininK luUr. %%,iir tan rtiur through t
tlitrk vrthr /, am! i!winj; through ilu Mfilr*. in ihr r'cirobi
Inu tttlr mitt,*li^ wiiti Ilu fri in ti, ami i frriS with that (
intt lltr Imtlrf,
1'ltr \tram t.tltr ** ^ralx'il on tli* iml  t lu liflrr n
ami It ha^ 4 4i>!rtttlifi! 4iii? whuh rn!rt iSir fortiTno%2
Wlirli llw valvr i*. rtiri l ^tafl tlw injrt lor. *.lriitti k SU
plirtl lir^l to ihr niiirirr, *iml iot iiflrr, hy withdrawing I
4tig, to ihr fifitf. !l liw 'iram i\ tlr> ihr
may ! fiti%*ril l*ark r*itiilv if ilwrr ii uiirit"*ni
tin tttnsm it% thr '*i4fiifi 7houll lr niovrtl a lit
way to lsr*4 ifi I hi' niivr f thr liflrr, ami llint II 1% tlra'
. fiir latk a.', s! will if .a.'s %in a% Wislrt ;ifff% at itir ov>
How. Thr Wiilir 'asi4% ina% t rrgubilr*! by ihr vulw
wiiwli liin l rolalri! a *fl *f it Itifii, Thr ffiililfiittffi cldivt
of ihr injrt lor >> Muliutu*! o> tlii* llii* vatvr ill! mil
j*tir ii ihr \rr!l*.w, a ml shrn ojirntng It t*noy
lltr r. ,i' of tlraffi,
Whrn ^ii4f wiih 4<l %%i!rr !hrs injrilor wa^tt'i* v<
lilllt 8 in Hiariinjr If Uu* 4njr*?r i> hoi or i' lillr*} with i
Uflrl, ii will w,n*r hil w^ilrr till I hi iBJ
EXHAUST STEAM INJECTORS
467
cooled by the water from the feedsupply, and will then work
as usual. If air leaks into the suctionpipe or if there is any
other interference with the normal action, the injector wastes
water or steam till normal conditions are restored, when it
starts automatically.
Exhaust Steam Injectors. Injectors supplied with ex
hauststeam from a noncondensing engine can be used to
feed boilers up to a pressure of about 80 pounds. Above
this pressure a supplemental jet of steam from the boiler must
.be used. Such an injector, as made by Schaffer and Buden
berg, is represented by Fig. 96; when
used with low boilerpressure this in
jector has a solid cone or spindle in
stead of the livesteam nozzle. To
provide a very free overflow the com {*
biningtube is divided, and one side is
hung on a hinge and can open to give
free exit to the overflow when the
injector is started. When the injector
is working it closes down into place.
The calculation for an exhauststeam
injector shows that enough velocity
may be imparted to the water in the
deliverytube to overcome a moderate
boilerpressure.
For example, an injector supplied with steam at atmospheric
pressure, and raising the feedwater from 65 F. to 145 F.,
"will draw from the reservoir
FIG. 96.
966.3
180.3 113.0
3. J = I2 .9
io  33i
pounds of water per pound of steam. In this case as the~ steam
nozzle is tonverging we will use for computing the velocity the
pressure
0.6 X 14.7 = 8.8 pounds.
This will givr
f
954,6,
! " * ' I t *"* *' ^* "'ijj *4/"
ihr wltH'iiv 4 ihr water riitrfing ihr rnmbining
Itiiir will givr for ihr \rtti!y<f lltr r! in ihr ttt$Itt ing tube
\\ " ?l "' *"' I i' frrl,
I t j,tj
llib vrlw'ily i** rtjuivalrni in iSi.il ^trtfliiirtl ly \\ t*!tllr rrssur(
til
!*'...' f4 '^ l(5
f4. 4 * >44
imitndft atM*iiilr of a piti*r *ii'%, 4 *iirr nf n. i*uiiib, Kf> allow
itiirr in* tfwitlr ftir rrthulin *l ilcft^ity by bubble* cif %lt*ain ii
ihv \ siiwltiniii* tut* it lf forit*uu*" if I'lj^'** ami valvi*s. 1
M *
'A ,U
%lii:h tin injector tun fil*r .nlvafiiAifr i*l rtiar}.Ifi cilhc
in thr %lriiffi m*w.lr t*r tiryom), llir vrUn iiy may I* gflrr lha:
rilfltMitri ami *i !rl!*r 4tliw rlHiir.
IJalr ihr ii"l Hlrrt til i"' ff; uil il* us* (or fcIin
WATKREJECTOR
469
the boiler with an exhaust steam injector will result in fouling
the boiler.
Waterejector. Fig. 07 represents a device called a water
ejector, in which a small stream of water in the, pipe M flowing
from the reservoir R raises water from the reservoir R" to the
reservoir K r .
Let one pound of water from the reservoir R draw y pounds
from R" t and deliver i f y pounds to R', Let the velocity of
the water issuing from A be vj that of the water entering from
R" be Vj at A^; and that of the water in the pipe O be v r The
equality of momenta gives
v 4 yv t * (i \y)v l (275)
Let A* be the excess of pressure at M above that at N expressed
in feet of water; then
(// + *);
v
Substituting In equation (375),
"i \ yVx *
Vll
It is evident from inspection of the equation (276) that y
may be increased by Increasing x; for example, by placing the
injector above the level of the reservoir HO that there may be a
vacuum in front of the orifice A,
_,
If the weight G of water is to be lifted per second, then
pouncls IKT second must jmwt the orifice A, G pounds the apace
at JV, and ft 4 ) G pounds through the section at 0; which,
with the Hevcral velocitiw* v, v v and v,, give the data for the
calculation of the required areas,
PROBLEM. Required th calculation for a waterejector
47
IN M'',r TURK
to r;ti**t' i ,?ocj gallon'. *>f vv.ttrr in hour, //  tfi ft,, /; .,, ta
.v  .ifi.^
\ .1' N I ...... *; N //  ........ x !*  !; N /I * .f  \ '*,
The vri ilir> an*
f.
I <.'# S, J4 rr rr
if*  ,tJ,t< frri *rr
4  !f.*K Irr! r ^
n^j iils fnt jr 'irt
itfr frrl;
frrt,
The ili4iinirr"s Mtrrr^)*tintifl^ I** Stir vritw . i am) r i
t ti.iS *( ft ill* It;
tl s t.i,0 *f silt int. It,
Thr afrit *i ? i f iiftiniliif (tm, having tltr ^nM 0,4 of u
inrti,
Ejtctor.  Whrn flu* rj itir t% isrl fur fiii
thrri i** n* iitititfiliigr in hratrnK tlir m'airr, is I* a very
. Tltr rfifilrRry sb ftlrh $lti*ftiV
I tor ifl'ifflifirtrfit 3 in Fig, 981 :
" """"'"' "'"" I tort t tlir tlriiin ttti^Si' 1 *! ttii! dtllf
_ ,_.., ......... .a sUfiim f wiiirr il i hi
vrii iiv, tftoit to, it"* in I hi*
xjfititt, (irtiVrft i l.i
4 lrv \iMi!\, Ki to i'islsli*
IftiantJly l tile r%rw **f liir %rlity, wi ll;il >i Cftli
uf t*r Itflnl 4 4 mat! torii
EJECTORCONDENSERS
471
Ejectors are commonly fitted in steamships as auxiliary pumps
in case of leakage, a service for which, they are well fitted, since
they are compact, cheap, and powerful, and are used only in
emergency, when economy is of small consequence.
Ejectorcondensers. When there is a good supply of cold
condensing water, an exhauststeam ejector, using all the
steam from the engine, may be arranged to take the place of
the airpump of a jetcondensing engine. The energy of the
exhauststeam flowing from the cylinder of the engine to the
combiningtube, where the absolute pressure is less and where
the steam is condensed, is sufficient to eject the water and the air
mingled with it against the pressure of the atmosphere, and thus
to maintain the vacuum.
For example, if the absolute pressure in the exhaustpipe is 2
pounds, and if the temperatures of the injection and the delivery
are 50 F. and 97 F., then the water supplied per pound of
steam will be about 20 pounds. If the pressure at the exit of
the steamnozzle can be taken as one pound absolute, the velocity
of the steamjet will be 1460 feet per second. If the water is
assumed to enter with a velocity of 20 feet, the velocity of the
waterjet in the combiningtube will be 88 feet, which can over
come a pressure of 50 pounds per square inch.
CHAPTKR XIX,
Till: rrcrnl rnpul UvrUimrW of Htrutn turhim* may b
ttttrtbutit) Uirgrly to llir j*rffrt ting *tf flirt bin It ill rnmtructbn
making it *iiti4r to t'ort'ttrtut Lif>*r liinrry with lltr
rriiirrt for itir high sjrrti<* ami thw adjustment:* whk'h
motor* tlrmuimi.
An itcirfsjitait tfr4tiitcitf of ^u.itn itirbmr*. iru hiding details a
cki*IfP rcifl.l flit licit!, iifiil fH4tiJt?rfijfiil, tvotiltl rrcIf'r u m'fmilt
tralisr^ but tiirrr if* AH jilvsinl;i^ % in tliht ts'vslnn lirrr itir ttM*nm
irtililritts iftii In ih*' ifnf**rf4i!fi 4 tirai into kineti
rorfigy, **tl tlir iipplit a lion of ihh rm*fj?v to tlir moving jrt
ttf itir iiifliiiif. For thin riir it r* nnf'mti i givr altentb;
In thr us lifi of jri* f ihiiih o i,4iir\ 4fnl ! llir friirlbn of jet
i.HHljifig jffoftt ilii%ilft ofilt'*"' 'li"i 1 S 4 ilia! tillirrwiif Woul
Ijtt*<if ftft"ttii l* thi* tfriiti;r,
Tlir fnlm*i4l iiir% of ilw ilintri' f iiirliliir* are th
wl'trtlirf lliry arr tlfivcfi by walrr <*r ly %tritffr, but the Ui
of ttfl dbiitk fliliii likr *Iifii iftnlr4tl of a whic
ha.** ifailii*ilii t rt*fiiifil tlrntily, Itmh to In th
lfiiiitiifi i*f I how ififirir', Or friilitrr
rvttlrftf from i!irst'ir%'4iifil lti* Howf ilifitlb to tliiifJtpr XVII
namely, lh*t rturnlin^Iy Ii?li n^milk% ifr ItiiWr to l>e dttve
irfl, TIlUH, if *i'igr 444 si Wir* foum! tlttlf S 4rafli jfroi
tt. fifrisitwr uf t % ii*iiftiH *'f i iMiifr iitcti ittlti ft VftCUUl
til ^6 iittlni of turf* lify *3 <tiintl4 iil*'itsi" i through a propf
!ftll/,/,lr, tri:rli*rij i lrnil\ 4 n.*j frrl Jurf tri : ttfltlt with S
alltwrifi of M.I^ for fruiion. Thb fitwg*" of prrH^urt' com
tw a hvttr^ulu hrul *<
IMPULSE 473
and such a head will give a velocity of
V Vs x 32.2 X 376 = 156 feet per second,
But so great a hydraulic head or fall of water is seldom, if ever,
applied to a single turbine, and would be considered inconvenient.
One hundred feet is a large hydraulic head, yielding a velocity
of 80 feet per second, and twentyfive feet yielding a velocity of
40 feet per second is considered a very effective head.
If heads of 300 feet and upward were frequent, it is likely
that compound turbines would be developed to use them; except
for relatively small powers, steamturbines are always compound,
that is, the steam Hows through a succession of turbines which
may therefore run at more manageable speeds.
The great velocities that are developed in steam turbines,
even when compounded, recjuire careful reduction of clearances,
and although they are restricted to small fractions of an inch
the question of leakage is very important. Another feature in
which steam turbines differ from hydraulic turbines is that
steam is an elastic fluid which tends to fill any space to which it
is admitted. The influence of thin feature will appear in the
distinction between impulse and reaction turbines.
Impulse. If a well formed stream of water at moderate
velocity flows from a conical nojwsle, on a flat plate it spreads
over it smoothly in all directions and exerts a
steady force on it. If the velocity of the stream
is V t feet per second! and if w pounds of water are <
discharged per second, the force will be very
** r J Fro.
nearly equal to
Here we have the velocity in the direction of the jet changed
from F, feet per second to aero; that is, there is a retardation, or
negative acceleration, of V l feet per second; consequently the*
force is measured by the product of mass and the acceleration,
g being the acceleration due to gravity, A force exerted by a
jet or stream of fluid on a plate or vane is called an impulse. It
STKAM I't'KlitSKS
/* f < ;
A 1
I/*
li'J
U im(>ortant io keep flrarly in mind that we are dealing wil
vrlinily* flutnge f vttmtiy ' ,tr ehraiinn, uml forcv, and thi
the ftn v e i measured iii the ii^iiiil w.ij. The use of a specl
name fr the funr whi It in devehipfd in thin way is unfurtuna
but il is IMI Well rsttltisitri It* IK negtet led.
If ihr jilair or v*iftr inMi*;td *f rmuiirtinK at rest, moves wl?
the veltH'tty uf V feel *r iei'und the change in veliKiiy or negati 1
at'cclf ration will IK* \\  I* f*ei per setumt, and the force <
inipubc will IH*
r
n.
Tltb furcr in one %rr*fti will m**i.e the dittamr i* feet and w
tin ihr work
'* .ft* fli /
1 I I 1 , , , (37.
* * * ' 1 7
footjxnmth.
Since the vane would "** move heymd the of the ji
it would he neie^wiry, in *fder to *Iii4tii Mntinuoitii action on
mtitor, it* provide 4 . teuton f v;itte't, whi Ii nti^ht IK* mount
(in lip* rim of 4 wheel. Therr wiutd !*, in ttftijiirfiti*, wai
cf energy due ii the inntiitn of the viinet in a rinlt* and
Hptatterifim and tther im*rrfe t 4ti*n.
tl ilir vrlix'ily of ilir r f water i it would fill! Ilispre
fairly %w ihr plair in Fig, .. when ii t* at ri !! *i it ml a cru
f the. ?hMW ^ very trir enVient
lw% r.<ttmtttKty vrliictU fpt
it ntwwjr, an*! the jet i* ra.itly lrken, " llwl liilwrst* Iflf
*n waller, Is t
fur foll'twin}! Ii Irtiii l
III I lie 'ilt^Wl !*wn l lltr li k ftfrviiirc', tlf
will cunt in tic l**'v*i!ii ilir j/,lr further irtrlcrtllon off
under iinfavaru)*!* Mn.!t! *'!,
tt U In hwW Ihr I**! irftt y f ilir *ifnile ICtl
of a jrl *R a % J aiir Ii %r have dit* Ht.wt, will Iw Mtilaindl
ihr vclm'ity I* of ilir %,ir li.ilf the vrlmhy t f , of the j
IMPULSE
475
For if we differentiate the expression (276) with regard to V
and equate the differential coefficient to zero we shall have
and this value carried into expression (276) gives for the work
on the vane
LJy a ;
4 $
but the kinetic energy of the jet is
i w
so that the efficiency is 0.5.
If the flat plate in Fig. 99 be replaced by a semicylindrical
vane as in Fig. geja, the direction of the stream will be reversed,
and the impulse will be twice as great. If the
vane as before has the velocity V the relative
velocity of the jet with regard to the vane will
be
t
and neglecting friction this velocity may be attributed to the
water where it leaves the vane. This relative velocity at exit
will be toward the rear, so that the absolute velocity will be
j/ _ fy _ y) s aV V .
The change of velocity or negative acceleration will be
V t  ( 2 V  V,)  a (V l  V),
and the impulse is consequently
PW /T/ T/\
s* .2 (V j V ).
o
The work of the impulse becomes
 .2 (V,  V) V  2 ~ (V,V  V 2 ) . . (277)
o o
The maximum occurs when .
Jl (V v  V 2 )  V,  2 V  o or V  i V..
i * VI i/ 1 **
a7
476 STEAMTURBINES
But this value introduced in equation (277) now gives
which is equal to the kinetic energy of the jet, and consequently
the efficiency without allowing for losses appears to be unity.
Certain waterwheels which work on essentially this principle
give an efficiency of 0.85 to 0.90. The method in its simplest
form is not well adapted to steam turbines, but this discussion
leads naturally to the treatment of all impulse turbines now
made.
Reaction. If a stream of water flows through a conical
nozzle into the air with a velocity V l as in Fig. 100, a force
(278)
FIG. too.
will be exerted tending to move the vessel
from which the flow takes place, in the
contrary direction. Here again w is the
weight discharged per second, and g is the
acceleration due to gravity. The force R
is called the reaction, a name that is so
commonly used that it must be accepted,
Since the fluid in the chamber is at rest, the velocity F t is thai
imparted by the pressure in one second, and is therefore an
acceleration, and the force is therefore measured by the producl
of the mass and the acceleration. However elementary this maj
appear, it should be carefully borne in mind, to avoid future
confusion. x
If steam is discharged from a proper expanding nozzle, whici
reduces the pressure to that of the atmosphere, its reaction wil
be very nearly represented by equation (278), but if the expansior
is incomplete in the nozzle it will continue beyond, and the
added acceleration will affect the reaction. On the other hand,
if the expansion is excessive there will be sound waves in th(
nozzle and other disturbances.
1
GENERAL CASE OF IMPULSE
477
The velocity of the jet depends on the pressure in the chamber,
and if it can be maintained, the velocity will be the same rela
tively to the chamber when the latter is supposed to move. The
work will in such case be equal to the product of the reaction,
computed by equation (278), and the velocity of the chamber.
There is no simple way of supplying fluid to a chamber which
moves in a straight line, and a reaction wheel supplied with
fluid at the centre and discharging through nozzles at the cir
cumference is affected by centrifugal force. Consequently,
as there is now no example of a pure reaction steam turbine, it
is not profitable to go further in this matter. It is, however,
important to remember that velocity, or increase of velocity, is
due to pressure in the chamber or space under consideration,
and is relative to that chamber or space.
General Case of Impulse. In Fig. 101 let ac represent the
velocity V l of a jet of fluid, and let V represent the velocity of a
curved vane ce. Then the
velocity of the jet, relative
to the vane is V^ equal
to be. This has been drawn
in the figure coincident
with the tangent at the end
of the vane, and in general
this arrangement is desir
able because it avoids
splattering.
If it be supposed that
the vane is bounded at
the sides so that the steam
cannot spread laterally and
if friction can be neglected, the relative velocity F 8 may be
.assumed to equal F 2 . Its direction is along the tangent at
the end e of the vane. The absolute velocity 7 4 can be found
by drawing the parallelogram efgh with ef equal to F, the
velocity of the vane.
The absolute entrance velocity V i can be resolved into the
Fio. ior.
4/8
STEAM TrtltsiNfr'.X
two cmfKJiirf* tit and i at right anglrs to ant) along the direc
lion of motion of the vane. The former nay t*r called the
velocity of How, I*/, ant! the latter the veliHtty t$f whirl, F,,.
In likr manner the aimolute exit velocity may br resolved into
the comonents rl and %% which may In rullril the rsil velocity
of whirl IV, ami the ctit vcUntty of flow, P/.
Tlu kinetic rnrrgy curr^H>mling ft* ittr abuilutr rxil wltxity
F 4 w the lost or rejected riirrgy tf liir cumbinatiun of jrt and
vane, ant! for gotnl ertutrmy ?htuUI l" itMiir smii}), The rxit
veltKity of whirl in genera) nrrvts mt HMM mrxsc and should
IK* wiidt* /ero tti o)latn lilt* tn^t rcMitf*.
The r!wtgr in the vrlmiiy til whir) U the retardation or nrgi
ttve acfrlenttion determine* ihr driving frrr <r tmiuUe;
and the change in the velocity tf mw in tike manner firtitlisra
an Iro>ubr it to ihr motion of the vanr, whtrh in
a turbine w frit OH a on the *tmft.
Let tht* angle aed the jet with tin lint* of motion
of the vanr lie rere*entt*l by *t let l and 7 represent Iht
anglts bed ant! Ink wlikh the at the entrance exit ol
the %"ne make with the Hoe,
The driving tmtuUe w in to
'F.
and the thrust i* to
U9
7* ..... 4 I f f,:
** " I * / ~ * /
which be
?*  ^ (I* sin tt I" 4n 7i ,
S '
If is mi velwity f whirl al the rxil the
i **' t*
I* I , tti** r ,.>..
I*
delivered to the vanr  r srttintl Is
it* *^*i*
If ~ ; I 1 I , *%, ......
GENERAL CASE OF IMPULSE
479
and since the kinetic energy of the jet is wVf 4 zg the effi
ciency is
V
 cos a (284)
e 2
To find the relations of the angles a, /?, and 7, we have from
inspection of Fig. 102 in which el is equal to ef,
V l sin a = F 2 sin /? ...... (285)
V = F 2 cos 7 ....... (286)
V = Fj cos a F 2 cos /?;
from which
cos a
sn a
cos =
sn a cos 7
and
 1 sin p  sin //
.'. sin p cos a cos p sin a = sin a cos 7
sin (P a) = sin a cos 7 (287)
The equations given above may
be applied to the computation
of forces, work, and efficiency
when w pounds of fluid are dis
charged from one or several noz fl_
zles and act on one or a number
of vanes ; that is, they are directly
applicable to any simple impulse
turbine.
Example. Let V v the velocity
of discharge, be 3500 feet per
second as computed for a nozzle
on page 444, and let a = 7 = 30. By equation (287)
sin (P a) = sin a cos 7 = 0.5 X 0.866 = 0.433.
.'. p  a = 25 40'; p = 55 40'
= 2020
,. r , sn a
y y 
2 J sin p 0.866
V = F 2 cos 7 = 2020 X 0.866 = 1750
e = 2 X 1750 X 0.866 s 3500 = 0.866.
4^o
Ho Axiiti Thrust.
llir butltlrrt of itttfniUr >tc;im lurl
ultriimtr nun Is im(iort;uu
uvtmlmj* ;t\u! thrust, whirl:
In ilow In i,ikii the rntt
iin*l cvit 4iiffSr of ihr \
ru.tl f jrnvin that fri
tfut uthtT f"r"j:4iif!t"r*t 04
i Iril. Thi** is
v
in llii% i =.'"
t l I", .in 7 kl t
w I 1 *V I'* fii.iftr lMIH.ll III ,1 iifti
^ f * 8 <
> rtful t I',, *iiwl iihu this
* 8 .ill *t i' fri,8 r*l
f t Ir iSir 's.iitjr i mu
*/^ ,, Ij
fte te*.
til r sin '
itnl i'iifisr*rntl,' ilirrr b titi anbl tvUr*I>ttm.
Ttsr *Ir Laviit ttirlifir hit.% fly ltr '! of fisi/^li"* wtiii h rjc
llir litiim at Hit* r Iw i hi* lw : k prr^Hiirr. am) ifi'M*tiirfill](
vcUnily if thr ^afirt* i:* vrry ami fvrfi w.lh 'iliwli tt"
II i' iliOUult Ui intlitftrr llinti l$'*fat turiU Tim tltfttrtil
ftirl by I hi* u f i,f t ilriiliir %lt*ifl, aft! ,'ii%r*rtllH" ii%i*il t'
I Hkrty l* t* irinlilr"*nii*r; m A ntiiliet of fail ttu turhiru*
llutt llir iuUl fi*fi'r lif llirrr i'i ny) IK* a
Thr im)Jttrtitnrt f iivi.lii! ;i*ul thrust in*tlirr IVJK^ nf iia;
i.^% tftH^ti fill! it 1 1 1 K*tl f H lit.'' *1<1 f'C"i, itftll ill
may In an a(ivanuttr t lr r*niiii' in mu'ifi'
If 7 is mit* )r rijsi.il ! /I in ntiil$Hft fjS;' I wr Sw%r
and fruit! trtHj
in*i:$if f whir! wr
,', tut fi  ml * , , , . , 
f Fi. t<j it t% rvi*Jrnt thai T $% kill n
DESIGN OF A SIMPLE IMPULSETURBINE 4 8r
If this value is carried into equations (283) and (284) the
work and efficiency become
w
W^} j K t 3 cos 2 ( 29 o)
and
This freedom from axial thrust appears to be purchased
dearly unless the accompanying reduction of velocity of the
wheel is to be considered also of importance.
Example, If as in the preceding case the velocity of discharge
is 3500 feet per second, and if a. is 30, we have now the following
results,
cot/9 ^ \ cot a  j X 1.732 " 0.866 /. /?  49 10'
V  Fj cos (v  X 3500 X 0.866 = 1515
e =* cos 3 30 0.75.
Effect of Friction. The direct effect of friction is to reduce
the exit velocity from the vane; resistance clue to striking the
edges of the vanes, splattering, and other irregularities, will
reduce the velocity both at entering and leaving. The effect of
friction and other resistances is twofold; the effect is to reduce
the efficiency of the wheel by changing kinetic energy into heat,
and to reduce the velocity at which the best efficiency will be
obtained. There does not appear to be sufficient data to permit
of a quantitative treatment of this subject. Small reductions
from the speed of maximum efficiency will have but small effect.
The question as to what change shall be made in the exit
angle (if any) on account of friction will depend on the relative
importance attached to avoiding velocity of whirl and axial
thrust. If the latter is considered to be the more important,
then y should be made somewhat larger so that the exit velocity
of flow may be equal to the entrance velocity of flow. But if it
is desired to make the exit velocity of whirl zero, then 7 should be
somewhat decreased,
Design of a Simple Impulse Turbine. The following compu
tation may be taken to illustrate the method of applying the
482 STEAMTURBINES
foregoing discussion to a simple impulse turbine of the de Laval
type.
Assume the steampressure on the nozzles to be 150 pounds
gauge and that there is a vacuum of 26 inches of mercury; required
the principal dimension of a turbine to deliver 150 brake horse
power.
The computation on page 444 for a steamnozzle under these
conditions gave for the velocity of the jet, allowing 0.15 for
friction, F, = 3500 feet per second. The throat pressure was
taken to be 96 pounds absolute, giving a velocity at the throat
of 1480 feet per second. The dryness factor was 0.965 at the
throat; at the exit this factor was 0.833 for 0.15 friction and for
adiabatic expansion was 0.790.
The thermal efficiency for adiabatic expansion with no allow
ance for friction or losses whatsoever, as for an ideal noncon
ducting engine, is given by equation (144) page 136 as
xr, 810.8 _ ,
e = !  a_a  i    = 0.262;
r i + ffi ~ ? 8 5 6  + 3376  94.3
the corresponding heat consumption is
42.42 f 0.262 = 162,
by the method on page 144.
Let the angle of the nozzle be taken as 30 as on page 481,
then the angle ft becomes 49 10', the efficiency is 0.75 and the
velocity of the vanes must be 1515 feet per second.
Suppose that ten per cent be allowed for friction and resistance
in the vanes, and that the friction of the bearings and gears is
ten per cent; then, remembering that 0.15 was allowed for the
friction in the nozzle, and that the efficiency deduced from the
velocities is 0.75, the combined efficiency of the turbine should
be
0.262 X 0.75 X 0.85 X 0.9 X 0.9 = 0.135;
which corresponds to
42.42 f 0.135 = 3*4 B.T.U.
per horsepower per minute.
DESIGN OF A SIMPLE IMPULSE TURBINE 483
Now it costs to male one pound of steam at 150 pounds by
the gauge or 165 pounds absolute, from feed water at 126 F
(2 pounds absolute)
r i + ^ ~ & = 856.0 + 337.6  94.3 = 1099 B.T.U.,
consequently 314 B.T.U. per horsepower per minute correspond
to
1314 X 60 f 1099 = r 72
pounds of steam per horsepower per hour.
The total steam per hour for 150 horsepower appears to be
150 X 17.2 = 2580.
If the nozzle designed on page 444 be taken it appears that
five would not be sufficient, as
each would deliver only 500
pounds of steam per hour. But
if allowance be made for a mod 
erate overload, six could be
supplied.
Not uncommonly turbines of
this type are run under speed as
a matter of convenience. Sup
pose, for example, the speed of
the vanes is only 0.3 of the
velocity of whirl, instead of
0.5; that is, in this case take
V = 1050.
This case is represented by Fig. 104, from which it is evident
that v
Vf = V/ = ai = 7, sin 30 = 3500 X 0.5 = 1750
V u V l cos 30 = 3500 X 0.866=3030
tan /? = ai = id = 17504 (3030 1050) = 0.884
P  4i 3'
The two triangles aid and elh are equal, and
le = id = 3030' 1050 = 1980;
FIG. 104.
484 STEAMTURBINES
consequently the exit velocity of whirl is
W/ = ek = 1050  1980 = 930.
Consequently the work delivered to the vane is
IV IV
PV = [3030  ( 930)] 1050= 39 6 X I0 5
S S
, w
416000
g
But the kinetic energy is wV* * 2g, so that the efficiei
416000 X 2 T 3500 = 0.68.
The combined efficiency of the turbine therefore becomes
0.262 X 0.68 X 0.85 X 0.9 X 0.9 = 0.123
instead of 0.135; and the heat consumption becomes
42.42 f 0.123 = 345 B.T.U.
per horsepower per minute ; and the steam consumption inci
to
345 X 60 f 1099 = 18.8
pounds per horsepower per hour. The total steam per
appears now to be about
18.7 X 150 = 2800,
so that six nozzles like that computed on page 444 would
only a margin for governing.
If the turbine be given twelve thousand revolutions per m
the diameter at the middle of the length of the vanes will fo
D = 1050 X 12 X 60 r (3.14 X 12000) = 20 inches,
The computation on page 444 gave for the exit diamet
the nozzle 1.026 inches, and as the angle of inclination ti
plane of the wheel is 30, the width of the jet at that
would be twice the exit diameter or somewhat more, due t
natural spreading of the jet. The radial length of the ^
may be made somewhat greater than an inch, perhaps irV in
The circumferential space occupied by the six jets will be i
TESTS ON A OK LAVAL TURBINE
485
!..! inches out of 62.8 inches (the perimeter), or somewhat less
than tmelifih. The section of the nozzle is shown by
Flu.
Fig, 105, and the form of the vanes may be like Fig. 106.
In this case thr thickness of a vane is made half the space
from om vane to the next, ttr onethird the
pilch from vane to vane. The normal width
of the passage is made constant, the fare of one
vane and the buck of the next vane being struck
from I he same centre. The form and spacing
of vanes can be determined by experience only
and apiH'urs to depend largely on the judgment
of the designer. In deciding on the axial width
of the vanes it must IK' borne in mind that
increasing that width increases the length and therefore the
friction of the {mssage; but that on the other hand, decreasing
the width increases the curvature of the pannage which may be
equally unfavorable. Sharply curved passaged also tend to
proc luce centrifugal action, by which is meant now a tendency to
crowd the fluid toward the concave side which tends to raise
the pressure there, and dt'tTettses it at the convex aide. Mr.
Alexander Jude,* for it particular with a at earn velocity of
feet **r neconcl, computes a change of preuaure from 100 to
107, t fMtttnds on the concave side and a fall to 93,4 on the convex
uicle. Kven if this case should appear to be extreme there is no
question that sharp curves art to be avoided in designing the
steam jutssages.
on de Lftvtl Turbine* The following arc results of
tints on a tie Laval jurhine made by Mcssra. J, A. McKenna
* Tkftvy / A* A>a Twrbttu, p, 40.
ami J. W. Regan * and !>
Snall.t
\V. \V. Amm<*n ami II, A,
VAI MMttt. i< hri
) 1 i% i *1 3 >i
Slrasti jrf If *!.", t<
9 f *v*'f
it?,!* *if Wait* lt?!
r*r.,..rf
jirf wiwrtr
lii ?!" !,' 1";
VrS* ity *4 t'^ws
i >' I s ",
Vrl<* III* *f *"i
Mi, 4rs 6 .J rlr. Ifi,,
! .* i ! ' i i .;*
. . < s > s . . t
1
f4,
14 .4
I* 4
** i
i >* 4
*";
ii*" i;?"
'Tlfrfr nfr I lift
irm ltit%'r 5, t : i if
IIP a iiii'rT?itrn of movtfi}* '*! : i!$^fi ; ,;tfi
may flw thruugh * ir r%*t *
in it >nr iiti*Ir *i
mt^thmU l* Piilr llir lr>tm
of rhamt>rn in f ii *IB
% ; anr, Thr fir*!
tint an i% l*f iltr I*.,
of ih Citriw Thr H
titrlitnr, Iw* f
Tin* third U In llir f*ijfii% wtiitfi !IAI
two to sspvrn iiinitili*r In *! air lf*i iw. t *nif
til f'evwlwtff taR*%,
Till* !*ar*ll tllfliillr, i% ^ft fr:jifw ttrhrr!, toi
a vrry numltrr ! MH f *n*^ ,r., t$fif to
ctttf hundred iind liffy.
III fcttiit'r llir
to
i in tti
f ihr vaflr^ llir J*rf
l I*.
VELOCITY COMPOUNDING
487
Velocity Compounding. In Fig. 107, let V t represent the
velocity of a jet of steam that is expanded in a proper nozzle
down to the backpressure.
Suppose it acts on an equal
angled (/? = 7) vane which has
the velocity V. The relative
velocity at entrance to that
vane is F 2 and this velocity
reversed and drawn at F a may
represent the exit velocity,
neglecting friction. F 4 is the
absolute velocity at exit from
the vane, which may be re
versed by an equalangled
.stationary guide, and then
becomes the absolute velocity
F/ acting on the next vane.
The diagram of velocities for
'the second moving vane is
composed of the lines lettered
F '
K i '
F '
Y 2 '
F/ and
the
last of these is reversed by a
.stationary guide, and the
velocities of the third vane are
F/', F 2 ", F 8 " and F 4 ". The
diagram is constructed by
dividing the velocity of whirl
V w V l cos a
into six equal parts, and the final exit velocity F/' is vertical,
indicating that there is no velocity of whirl at that place.
It is immediately evident, since the velocity of flow is unaltered
in Fig. 107, and since there is no exit velocity of whirl that the
efficiency neglecting friction is the same as for Fig. 103, namely
e = cos 2 a
.as given by equation (291) page 481.
S'tT.\M Tt"li;
, 5nlrfr"",ifif !"* itrtcf tliiilr llir tttlk lrnr tin rar ;
It Is
vanr; tin MUM *I tlii wrk !" itfw lr.i
In Fig. 107 thr vrlii isy *4 whir! at n'U,ttur
1 t U'8
and the vrlinily l lfl l *'*it
fitl llic wutk li*!ir *n ih *,ir t.
r I* Was iliiillr
attil
ft ' .
SC tlliil Ihr r,
Thr tfi%tftitii%r
the til Ihr t*n
A in%'r*ili!4i$*fi
ftmr v4Ht"*i in
Thr iitfiifr in
jf vunrn
A ^fir. i% r4*i ; ,iifirj l%
an , r.
s
ihr lriritiu<
tion
VKMU'ITY COMPOUNDING ^o
409
ll is considered that this type of turbine cannot be made to
give good rtlit iency in praetiee on account of large losses in passing
through a succession of vanes and guides, especially as the steam
in the earlier stages has high velocities. The turbine, however,
has rertain advantages when used as a backing device for a
marineturbine, in that it may In* very compact, and can be placed
in the low pre**tire or exhaust chamber, HO that it will experience
but little resistance when running idle during the normal forward
motion of the ship,
In dntling with thin problem it is convenient to transfer the
construction to the eombined diagram at />/, Fig. 107; diagrams
for guides like thai! made up of the velocities V v 7 4 and V l being
inverted for that fnsrjmsr, It h clear that the absolute velocities
at exit from the no/le and the guides are represented by V it V l f
tint! l'," while the relative veiodties are V v V,' and V," which
with no axial thrust are equal to V v F/ and F/', The absolute
velwity al entrance to a given guide in taken an equal to the abso
lute velcK.it y ml exit from the preceding vane, thus F/ m equal
to V,, etc. Thr I^t absolute velocity V" is equal to ai the
constant vclwily of flow.
Thr ft, n t , ^j, it, and /f, art* properly indicated as may
be ern by rcmiiiring the original with the combined diagram.
If the is Mt't'tirotfly drawn to a large scale, the velocities
anil rifi In* mraMurtti from it, or they may readily be
alrutittrtl trigc*oomrtru*ttlly. Thus
tun
nn
i
I ros
,
etc.,
; F/ F, lift cosec t , etc.
The til thr vant and guides must be increased
invenely iiroMirttonitl i the vdodtit**, using relative velocities
for the vanrt4 and ni*Holute veltxrititni for the guides.
There appear* to b no rtmm why the guides should be
thrunt provided they can be properly sup
,'>t"t>.\M I'l
tir li 4i4fj*lv *
MlrtltR .* miiu'4trl. t
ami tttti"* llir f> i*
til ttiltfw frflWitt** i:nfl'iiiitl
F*lltwtng tlir ir14csii *
frui'ti Mt srttint:i l% llir
s:t in
limit vt'Uittiy t*f
THt* rfll Vi*IilV l
f sf*
l*tM*t!y tlf 1%
I*,
lli
lite
**iic's I*  ?
,iir ilfitwil in
tJ :;fii:f, I*,
'4.lf , 1"^  C
i" 4 $> 1,1 i<i off
1
r ^lltsr Imr AH
r, Irffrfrit I*/
" mil.
f fif I^",
tin
lt,4Vt*
Thi
lltiri
K T UK FRICTION ^
and a* ihr intrinsic rnrrgy tif thr jet is
I
A'
thr Hiiiirmy tf ihU itrrungcment without losses and friction
a{*H'af<* tu IK
%7,'CJ !< fit 35  0,92.
of Friction.   Thr dl:t of friction is to change some
of ihr kimiir mrrgy into hrat, thereby reducing the velocity and
ill thr Hiinir linn drying ihr strum and increasing the specific
vohmir M thai ihr Irngth of the ^uitlfH and vanes must be
imrrasnl at a Mtimwhal lar^rr ratio than would otherwise be
rrquirnl,
A tiiriiitHl of allowing fur frirlion is to redraw the diagram of
Fig, 107, shortming thr linrs that repnnent the velocities to
In unirr to firing out ihr mrtiuxi cirarly an excessive value
will lw. ii*' 4 igintl ft* ihr t tittlii/irru fur friction, namely, y 0,19,
wt i ha i ill* rtiirtiini lor vrltHiiy may have for its typical form
^ ~ x J^A it >')  o.c; Vigh.
Again ihr iurfliiirni will \n uHHumttl to IK,* constant for sake of
%i fit ft idly, iiitrr r.*iri tally a* but link* is known with regard to
il.H rrftl vahtr.
Tltr tliafcram htiwn
by Fig. i o*j wan tlrawn
liy trial wilh I*, 
ami with ' 40*". It
mluir 1* I* frrt  v
jrr *tTntl In.tratS if
5?, frrt, wiiktt wtnilt)
br irtiHr without frit
lion, titf*i Salirr quantity
hrintf i*flr**jitli *I ihr
initiil vrh.H'ily of whirl,
3030.
Starting With l\ ihr Vrlm'llV f ihr
is tlfitwu i* Ir!rfffttt!r ittr tnil9.il tr
of Vitnr*. The riil vtl* ilv l* f I* stuilr
It txii t% f'rfll llir gttf*ir,, 'Hi!' i
rftil'alirr ! llir JjHuJr^ IrfSl Ihr r%j! H
t t'*/  .** l*. Tw rrj'li!iiv>
liljlg^ro Thr vrliH lllri of rnfiif! J,1
Viiftrs it. 1 * itira.Hlifril nl! lisr iSsilt*^ tt *
jrl, llu ifllti}r l' ( I', J*
tr!<*t!v i'.r fbr !tf%i w .j
jiul !<* ;.) 1" 5 , ami tht
sifll l!rf ii tifei'
mv> *ltl4rir
afttl llir vrl
mi Ilir
II l*!il I S
tti
*"iic
Thb
antl iiiiiilri, inti
t>f
lit if;i Is*
Tti
lO
t
PRESSURE COMPOUNDING
493
Fio. no.
In Fig. no an attempt is made to avoid axial thrust on
the vanes, and at the same time to retain a fair efficiency
by making the
delivery angle of
the guides constant.
A calculation like
that on page 492
indicates that an
efficiency of 0.76
might be expected
in this case. It is
quite likely that
in practice there
might be difficulty
in making the delivery angle of the guide as small as 30,
but it appears as though the common idea that it is practically
impossible to make an economical turbine on this principle is
not entirely justified.
Pressure Compounding. The second method of compounding
impulse turbines with a number of chambers each containing
a single impulse wheel like that of the de Laval turbine requires
a large number of stages to give satisfactory results. For sake
of comparison with preceding calculation we will take the
same initial and final pressure and the same angle for the nozzles,
namely, 150 pounds by the gauge and 26 inches vacuum, and
a  30.
Nine stages in this case will give approximately the same
speed of the vanes as in the problem on page 490. The temper
atureentropy table which was made for work of this nature
is most conveniently used with temperature, and in this case the
initial and final temperature can be taken as 366 F. and 126 F.
At 366 F. the steam is found to be nearly dry for the entropy
1.56 and that column will be taken for the solution of this
problem. The heat contents is 1193.3 instead of 1193.6 as
found for 366 F. in Table I of the "Tables of Prop
erties of Steam." On the other hand the table gives at
4i)4 NT * AM n'Hi'lN**
13ff e far thr tint! tttltfftil'i */,*.S^, ami thr *i!rrciit'r i*
tf we ciivittt* liif tV4iiil>lr
fur rat It
mm j**rufu we
If Wr 14 kr V ".*,! %%iil It lii*i% t' r %( fanr in
tiiflrr, *I.H ttrtll tir rviilrlit, >W*!r t 4i,rf.f*iii flti..'/!!!
V V
fft'l frr '
Tltr tli
anil ilii* vrlitf'iiy f tin* V4r s s**
half f lilts tir ^?. frt! 'f ^r* nii
In lltittir for lfnli*rti mShrr I^
SifHC' %*'" h*tvr to <lrill ifll A
lifc'iUlSwf IftI 'iiflir?lr licr% afr
thfiJsi, all ilir tiii iii*iiis
i iifltl* *!* alf
wl lH* tf
,, , ,Hf., a _ ,,
.a *w <i,ncc
f
;p a , ttifa .** 
li b llil fif li* ii
tyj*' nf itirliiflr !}r
tilrndril A! Itl Itiit^
is allatttrti l* ir iff sti A <*tm\
i
M fc'ffijw'faf
lit
!
If!
If the Ji"fihrf.al '4j*nr! 4 ill
K of $s tikrly I li,r
f if tin irn m\}.'
*JO, litefc ?'
rf i lafffr f$vittl*i'f *{
r no ifii.fr ifto frrt
I* if* i ft4tft!j(f% itiilc.rtsi fif
?
i'KKSSUKK COMPOUNDING
495
This will give fur the avuilahlc heat for each chamber 8
thermal units, and using as before y 0,1 we shall have
T,  \ j X ^j X 778 X 8 X 0,9 600
feet IKT second. With n ~ jo the velocity of whirl is now 520
feel ami tin* veltKity of the vanes as stated is 260 feet per second.
The mxi tu<wtitm in the discussion of this turbine is the
cltHirihmion cf pressure. If the coefficients for friction and
cilhrr hissts arr laktn t 1 constant, then the pressure can be at
ont't drlrrmirirt! by I hr utliubatic mt'lhod.
In ihr problem alrrittly tliscusscd 33 n.T.u. are assigned to
w h s<i*r am) if lliis figure \w subtracted nine times in succes
sion frnm ihr heal contents 1104 at the initial temperature we
fthali have the vutues which may b used in determining the
ittfrrmrcltatfr lemfferatures from the temperatureentropy table.
Alnii frm that table or frm Table I in the "Tables of
Prupertir* f Suam/' the rrresjKnding pressures can be
tlrlrntiiiiiti, The work h arranged in the following table:
N <IF PRKSSURK.
4 *
tttn
!*.. *Mi
Ratiw *( prsur.
l*S
7.V5
47.
0.68
0.66
0.65
0.64
18.6
0> 01
o.fit
uJ
o!J7
i
0.
The taut t'olumn give* the ratio of any given pressure to the
preceding irrtirt% i.e. us : 165 0.68. These ratios indicate
that ftimplr utntral t'tm verging noxzicn will be sufficient for all
but ihr fast With the uutt! number of stages, twenty or
ronrr, thr nttiii* art* certain tci be larger than 0,6 in all cases,
indicating flit* uc of converging throughout,
sriufti
To determine the si,*r> of tin m.;4ir% or thr juvMKr* in ^
guicir* It U n**ff\%iry t rnt int^t** thr tju<t!iu f iSir it ram in
order t lind tin* sfwdftc vuluinr. Tt* 4 fin* wr may fontdcr
that, of the heal Mtf!f4icl i ^ f*rf;un niai?* ! iltr turtnm*, a
portiun w rSiAiignl tnl on thr !iiflinr vifir:i, arnr part b
railiatril ihr rcnvitttttrr b in ihr s!t ffum the
chamber tf llwt tifj if ilirrr t t]>rrt uhlr irak.igr, *fttvutl
lit" fciltrfl l It, l!l! l!li fit tlij! Hill rtlltf
can bt* Irft at *nr klr fr thr jrrvni.
Ntw ill thr 'i"* riifti4rfa!i(*!i, ' llicfnwl unili wrft?
to rarii %l4gi* in lite jMluJ*iit* t :i) uUtiun fir till?
(Ji?4lriS.lllkfl of firrswjfr, .!*> af! i%.i's 43.'iif!iri (* y li
ffic'lion ill lll.,il Ptllv .i l%,:'i ;t*lsn. ! flir , 4iilil,lltf
of vt*lority; of the
to IP
ill ittf i4 ilir
Iti I* rh.4 <! ltit h
further tin *.! r*,t .r ,o,n
i liit*lrfs i l lr th,t ;
tf 33 intu
, our c
will I* A til i he
tls it i HP !* la
the tin the
The of j*rr it
traded sucrrs'ilvrlf, ihr
a.H *irf tfwwfi lit llir latl"s. At we
** f #
thr quultt)* by Mtfitractiiiif i!t* l ittc the
control* the by tlir of r. 1
ari by ihr
but ft** sr it in all life f * *
PKKSSUKK COMPOUNDING
497
FIRST rOMI'trrvriONf OF QUALITIES AND VOLUMES.
5 i "i
f I IU,
S } t \i
1 1 ; 4 j ,y
i til ! jf
! 16?
V4jStfi
Miin
5S
y i S j w,$
yt*i i toio
Quality
0.078
0.076
a. 78
3.78
3QS
390
579
5,66
8 ft 5
8.44
'33
19.7
at .0
it). 8
34.1
31.8
55,8
52.2
1)7.0
88. 3
"75
158.0
By Ihr nid of thr trm[H*ratureentropy table, the qualities
iinil ^jit'tilir vcitumrn may lie determined directly with good
ftpprtuiinution. It bing nrcessary only t fallow the line of the
triit'fiiitirr tii an rntrupy column, having nearly the proper
.
llirrr i* u rtnt?4 cihjirtion to this method m applied, because
it tliM'?* mtt lakr any ut'cctunt of the fact that as the steam passes
from to Itwtiig Irwt heat than it would with adiabatic
Action, tlir rntroiy inrrraM^, and that with increased entropy
thr tjiffrrntrr of bent <"*ilt'nls lirtween two given temperatures
*!1ib will IH very aptmrvnt from inspection of a
ntrupy diagram or the temperatureentropy table,
Tlii* nt*tttrf will lit tlim:itl more at length in connection with
thr Curti* lypc* til turhint*.
It lias lti*t that the amount of heat should be
to fiit'lt for th adlalmlte calculation and that the
if y t allow for friction and remain constant.
to the wiliir* that nhoultl ht to y, we have very little
hlfohrt) infrroiitm; II may be noted in passing that our
for frktion in the noxxlra and guides is probably too
It will fa rvkiffil that there li no difficulty in maintaining
the to ritrlt In ite proper proportion even
,'
Li
498
STEAMTURBINES
though y shall be varied from stage to stage. For example, 01
choice of o.i for both y and y i gives
32 X 0.9 X 0.9 = 25.92 B.T.U.,
which ^multiplied by 0.75, the efficiency due to the angles ar
velocities, gives 19.44 B.T.U. as above. Let it be assumed f<
the moment that the above product shall be kept constant, so i
to obtain the same velocity of jet in each stage. Then tl
following table exhibits a way of accomplishing this purpo
while varying y and y 1 :
Stage
i
2
3
4
s
6
7
8
y
0.08
O.oSi;
o.oo
O.OQC;
O. IO
O. IO?
O. II
o. ii<;
O. I
y
0.088
O.OOI
O.O04
O.OQ7
O. IO
O. IO3
o. 106
o. 109
O. I
(iy) (iyj
0.839
0.832
0.824
0.817
0.81
0.803
0.796
0.787
0.7
B.T.XT
309
31.2
315
317
32
32.3
32.6
33o
332
The last line shows the proper assignment of thermal uni
for this condition. For simplicity both y and y l are assume
to vary uniformly, but other variations can be worked out wi
a little more trouble. Evidently the sum of the figures in tl
last line should be equal to
9 X 32 = 288;
it is a trifle larger in the table.
Now it is probable that the best values of the factor for frictic
and resistance are to be derived from investigations on turbin
rather than from separate experiments on nozzles and vane
and it is evident that the use of the methods of representii
the friction by a factor y is rather a crude way of trying to atta
in a new design favorable conditions found in a turbine alrea(
built.
Since the general conditions of this problem are the same
those on page 481, the efficiency due to adiabatic action will 1
the same as is also the efficiency due to the angles and velocitic
Taking the factors for friction in the guides and blades as eai
PRESSURE COMPOUNDING
499
o.i, the corresponding factors are 0.9 and 0.9. The efficiency
due to velocities is 0.75, and the mechanical efficiency may be
estimated as 0.9. The combined efficiency of the turbine is
0.262 X 0.75 X 0.9 X 0.9 X 0.9 = 0.143.
A computation like that on page 483 with this efficiency gives
for the probable steam consumption 16.2 pounds per brake
horsepower per hour.
Assume that the turbine is to deliver 500 brake horsepower;
then the steam consumption per second will be
16.2 X 500 ? 3600 = 2.25 pounds.
We can now determine the principal dimensions of the turbine
to suit the conditions of its use. Suppose that it is desired to
restrict the revolutions to 1200 per minute or 20 per second
then with nine stages and a peripheral velocity of 520 for the
vanes the diameter will be
520 s 207T = 8.28 feet.
For a turbine of the power assigned this diameter will be
found to be inconveniently large. If, however, the number of
stages can be made 36, the velocity will be reduced to 260 feet
per second as computed on page 495. This will give for the
diameter
260 * 2o?r =4.14 feet.
The remainder of our calculation will be carried out on these
.assumptions, namely, that the power is to be 500 brake
horsepower, and that there are to be 36 stages. If the method
of the table on page 497 were applied to a turbine having the
full 36 stages now contemplated, it would have 37 lines; namely,
the ten already set down, and three intermediate entries between
each pair of consecutive lines; but the temperatures found in
that table would be found in the more extended table together
with their specific volumes. We can, therefore, use that table to
calculate areas and lengths of vanes for 9 out of the 36 stages,
FttV
vH
t'lj
/M
ii. ffj*tfiifii, ills
Mtnjnllr.il if *;
wr Likr r f
sr l$r rllr live **fiffirtri
li*f*lr Is, !4 list r f r  ;
i> ken S*i bt
'', llic isr 5
;iiftiis.'nifi 1**
Iltr ?!ilc 41 ,!n.r tf
l.KAKACiK AND RADIATION
Conversely, If desired, the thickness of the vanes could be
adjusted^ give the same length. Such a construction as this
leads to if* likely its give UKJ sharp a curvature to the backs of
the vanes, and it may !x better to givp only the thickness
demanded for strength and take the chance that the passage
between the vanes shall nut IK* filled. If allowance is made for
f rift ion and the consequent reduction in velocity the lengths of
the vane* should br correspondingly increased.
The lengths of the guides fur the other stages will be directly
proitortional to the sx?ine. volumes in the table on page 497,
because the velocities have lieen made the name for all the stages.
Fur example, at too." the length far full admission will be
1.45 *. .p.H i 148  0.31 a inch,
whh'h will In the prux<r length ftr the twentyfourth stage. If
il h rttrtHttlrml tsrttltmsrablr t further reduce the length we may
resort to admitting slimm through guides for only a portion of
the jKTiphery. Making the are of admbsdon vary an the specific
volume*, the fourth stage (line i of the table on page* 497) will
have adnu**ton fr
t fo x J.J * 31.8 43.
Intermectintr length* of vanctt antj urm of admission may be
ciiylI by tilling out a litble like that on page 497 for all the
or a lit? drawn from which the required
information inn be had by interpolation; the values on the line
numbered o art* for thin irMe, then* being of course no corre
ximltng 1ft fact thi* method of computing at convenient
interval* ami IntrrMlittIrtg from curveit is likely to be more accu
rate is well n rr t'onvenir.nt t as the error of acliabatic calcula
tions for with *mail of temperature is liable to be
excessive,
ad Radiation. This type of turbine, as will be seen
In the description f iht* Raltmu turbine, hus a number of wheels
each in it* own chAmbrr mrici the rhamtx^n are separated by
stationary dink** thai extend to the shaft. Reduction of leakage
be tttlMinnl by a small clearance between the disk and the
shall for a rojT Iit.iiing r slulhm: ln * .inhui In* fl.tmt in so
inariTssihK' a J'lair, "I'ltr l%*ka>*r * ,ifi la r.<fitfui! hy aid of
Riinkimvi. rptoit**ii tm la^r 4,4* r fru tt,iir4t!
on gr i.y; J'tit l*th tw'i!*h ;r*' hkh i jr r
t> l<if#r, iifiti *i f*u!r Irv, liwn mull ^imtiSii U ailjril; Siyf
thr vjtlui' tf Niirh a iwir K*r 4 I*K mfri., ;tfinut*tr *ii4gi' ig
nttl kmwn, uml any riisnuii' mirt I ifwdr. Fir ,i lurhim* til
till* Eiilriill tVJ llir r.lLig in likrll !* lr Irvi ilfctft l$%r J*rf i'rni
til tlir tiigli irr*Afr ritsl, \*w llir lr^k.i*r r,
nrarty to lltr riillrrrllrr sif jrcvajfr fwl%%rrft surv
ami .i 8 * lilt* lisllrrrflt r rt fr.4'"i '* 4l' l**vi ill*" Scai,ir tl) II
iff II* iiiitiiilll ill llir Imici rfi. '!* dllitA ft^f irtkil
t*
In IM." any
lilt* l
fr
arr Ir*'+ fur llir
slritlilrngiftrs llir ratls
rrni, Fr iiirlilfifB l ih* K;iir
f I*iflt.itlitfi in IP rW!fr
itl lltr irr ! *tirr rtitl,
ivi*iii!ift frni strata
ts
'S ;Sft*t
V
Ulwrrn llsr
srt til ir
vdtH'ity i> iittlfiiy if ttwt
entrr* nti a*
i"* rtff4tii' It WUIllii fftf l
fftilf!r r fl!i*t/,lr' arr j*ti* r,
funrr U aliiiiiiiil i Iin4ling ll
whctl .sltiitl titn*ily iniu
lllfrtitlir liffir tn r (hf
vant'Jt, tllr *irrtftt will 1  !iiif'i'
4iiie al whit If it W*IH rr< rivrrl am! ihr
U It *iiriii ihr iiiftiifjc
rtiiifin,
*tir rt
ihr
%d*ii>, If aiiioi
i ft'jc*iri1< r llli
I i
it ai
ill!
p ?lifrt
KATKAU TURBINE
503
Let
**/* represent a vane which has steam entering it
ily with the veltKity V y while it has itself the velocity
r. .Witming that the relative? velocity is
constant we may divide the curve into a
nitmfirr f ecjual *malt parts that are approxi
mately straight. From b lay oil
r*
lll*  till
will U
Y
In lik
a Ktim in the trajeetory of the particle of steam.
. V
The i will dlfVif / may lie taken as the trajectory of the steam, and
r/ in the Ir.ttl *s defined almve. I*ro{a>rly a similar construction
TthnuUt t*r made *il*o fur the bark of the vane, and the mean path
fthnultl fir taken to e*!atiti*h the lend, Kxtremi? refinement is
protfciMy neither net > e.H?ary nor justifiable in this work.
r t'oniitrurtton of this turbine, which is
* *** of the pure pressurecompound
tyjH 1 LH represented by Fig. 113,
whirh is a half section through
the shaft, wheels and caeing.
The wheels are light dished
plates which are secured to
hubi that are pressed onto the
jthaft and which carry the
moving vanes. The chambers
are neparated by diaphragms
of plate steel, riveted to a rim
ami to a hub casting* The
htiliM are bushed with and
friction metal that is expected
to wear away if it by chance
tcmrhra the shaft. This tur
?* bint* b sometimes divided into
twit Mt tlitfi*. ! imnitlv 4 middle tearing for the shaft, which
ha iiiiis!irrlir Irfmili and should preferably have a small
tiianu'Ur IP rnliiM Iraktgir. Thr hurh pivvuw urtmn
ktVI'ii Mttallrf tluffKlrr l* frt illUti ,iff4f1>rntiiif tf *Wili am}
Viinr*. SomHimr* ftirfr ifr ttlfc tit,ifllrfrf ; ff lltr aillr nr
HM\ lint iitllr frtifa ttiHJlitai* t4 ttiinjntuitMfi iitlrlttil
y filli'Sl t haJ?r f tliiimrlrr, .ill i' llrriVHifl H Its
ll*r iriittfi l Iiiliiil4r llf.if }*T n!.ir lafgrr Hi in
the Ifti;rM" in Hrihrral ?Kr*l.
tl.vi"'. i*\ li.iri. .ir tt
s
I ft
i i s i
Tttt" iitcfittfiiiiyiii gi%'ra irtilfa i.4 t%ia on st
turtnm* by t*rft***tr Siiwluk, TM iiifi**ifr iviih rr^utis
*, lltr*r %liwli ! fctfc*i ii*
, 4 MI) rifciritti l .^4 I .jo.
Thi* ly* t( iiiftiifir fyjt dj*lir4 ^mtr^ftiUy I II?*
!f
Hi jifr^aiifr til a j**r is
fr, i*r liwt Jm^I f *i* nicfif.it!
1 ; 'llr fr4*!*!!* r i
ti ftiialiilt  if.;ii t^ll i
fttrci Jiiifln: llfaf, ilwl tllir !* fhr fll*lltl . llir i
srcflllfl, lltii! illtr l< llir 4* liwlt *4 llic i,ift s Ilk It h#Vr
From it i*tf4iirif,:
4m ly I
*
SIDE THRUST 505
its casing, and from tests of his own, Professor Stodola gives the
following equations for the horsepower required to drive smooth
wheels and to drive wheels with vanes forward :
Smooth wheels v
H.P. =0.02295 a. D 2>s (} 7.
\ioo/
Wheels with vanes
H.P. = [0.02295 a. D 2  5 + 1.4346 a. I 1  25 ] (
\ioo
where D is the diameter in feet, L is the blade length in inches,
V is the peripheral speed in feet per second, and 7 is the density
of the medium. The values of the other factors are
a 1 = 3.14 a 2 = 0.42.
These formulae explain why the backing turbine for marine
propulsion is always run in a vacuum when idle.
Turbines which have only a partial admission must be affected
by some such action for that part of the revolution during which
steam is not admitted; but this matter is obscure and such a
resistance must be combined with friction and other resistances.
It is therefore very difficult to assign the proper value to the fric
tion factor y for steam in the vanes or in the guides and vanes of
a velocitycompound turbine. In particular any change of the
angle 7 (Fig. 103, page 480) to avoid end thrust must be made
with caution and should be checked by experiment.
Side Thrust. If admission is restricted to only a part of the
periphery of a turbine, then in order to preserve 'a balance and
avoid unnecessary pressure on the bearings of the shaft, the arc
of admission should be divided into two equal portions, that are
diametrically opposite. Some builders, however, prefer to
ignore this effect, and concentrate the admission at one side,
because there is tendency for the steam to spread which will have
double the effect if the arc is divided as suggested. The amount
of side thrust can be estimated from the powers developed at*
the several wheels, having partial admission, together with the
dimensions and speed of revolutions, making allowance of course
for the distribution of the torque over an arc of a circle.
tttft Vtlocity A f,vr;
linn nwy In Hi.itlr f lli< iw trilt,b .4 umjw,ii
iliMiixHvtl; ilwi is ihr rr**ii
**tif
twt or im >r
. lt 'alr mtltt Ili
cf tfifumii
Siiur ihr jrim
iilmnl)% will i
rlU
Lrl u* likr fr
Walls ill rtoifka
tif 0.i, wti
1*1 ihr ifitikl
! 3* ffll'tfti f llt
far tf * '30 s *. Th*' 4hwlMl
and IHIF nlr*iMli%
arc toy 4 !*. Ilry
mill twvu nrarly 1 4^ nii
nr wt
t*nh
lit* j4i< .ui.n
 t
ill
j** i'
m 4i ilir i*
jia ih it** ir
ill th
of f, i* "O ** t' lrW'fattifr
to l ftei n.r.t?,
Thr rttkirttcy tif r*
for any w
f* '
thr
l$t>?'tr.j*iwrr jnr
Ttic rfluirnt'y for
L I s * t" 4
by the
PRESSURE AND VELOCITY COMPOUNDING 507
the combined effect of losses in the vanes may be taken to be
equivalent to making y equal to 25 so that i  y is 0.75; this
is in effect the efficiency factor for the vanes as affected by friction.
If, further, we take the mechanical efficiency of the machine as
0.9, then the combined efficiency for the turbine will be
0.285 X 0.883 X 0.85 X 0.75 X 0.9 = 0.144.
This corresponds to
42.42 ^ 0.144 = 295 B.T.U.
per horsepower per minute. Now it costs to make steam from
water at 102, and at an absolute pressure of 165 pounds, 1123
( r i + & ffa) thermal units, as already calculated in the deduc
tion of the efficiency of adiabatic action. Consequently the steam
per horse power per hour will be
295 X 60 5 1123 = 15.7
pounds per brake horsepower per hour. To this should properly
be added a fraction, to allow for leakage and radiation, amounting
to five or ten per cent; this added amount of steam will affect
the size of the high pressure nozzles only in this case, and as
extra nozzles are sure to be provided we will take no further
account of it than to say that the steam consumption may amount
to 16.5 to 17.3 pounds per brake horsepower per hour.
The heat contents which have already been found give for the
adiabatic available heat
1193  871 = 322,
and if this be divided equally we have 161 thermal units per
stage. Using 0.15 for y in the nozzles, the velocity of the jet
becomes
V =V 2 x 32.2 X 778 X 161 Xo.85 =2610
feet per second.
Assuming that we may use three sets of moving vanes the
velocity for them will be
2610 f (2 X 3) = 435
feet per second.
St'tUM Tt'Kl!\'fcS
If wi' rhixwe a iltiitm'lrr ( if f<*'t for t
v;tnrs il will lr;tii to litr ' *f iM*;j r*t*i
To tiro I fill* iKirffliriifiitf" ff'vttifr Wr
umtrnt* al that rr'*%iifr
* jntth '.isrinr of
tMrti i mimiir.
liir r thr t
which In llw* !rnirr*iitifr rirjiy l,iilr *iTrtj*m*h In 3j/*f,
Of iH,i mnth. Stmr ihr IM* k fr viiifr If f Sir nuwJri i frli
lively MnaU in railt t4 itu n './!* il! li.nr ihrn^lt for
thr V*!IH ilii"% itttt%i I* lrirriiiiiu'*! in r*rr f^i the
Hit* throat ifr*'4ttrr4 itwy ! t,ikrft I !
till' Srfii*'l'4lMfr.* 4f
SiniT lilt* f it"' flt,*.?lr ?'}
for friiltMfi tsiiitnt
liai'ljtrrsiiifr, wr
tn*i nllfw ihr niifr % : iiitir **f
ttir rxil, Tlit* **r4r* l* a
mtlrs givr m'*irl> Cult ittr
by i he trmH*ralurr 14 hit*
." 4 It* I S*/" I'*.
nj
Tlw
with
fr
lit*
vutumr U 44S rilttir frrt. The 4
iiii 114*1 ** 44 .
II f
I** thr
Ttlt* f thr utlt(
PRESSURE AND VELOCITY COMPOUNDING 509
The specific volume is
v= (xu + <r) = 0.902 (21.6  0.016) + 0.016 = 19.5.
With 15.7 pounds of steam per brake horsepower per hour
and 770 horsepower the steam per second is
w = 15.7 X 770 ^ 3600 = 3.36 pounds.
The combined area of discharge of all the first stage nozzles
is therefore, with the velocity at exit equal to 2610 feet,
3.36 X 19.5 X 144 * 2610 = 3.62 square inches.
The nozzles of turbines of this type are sometimes made square
at the exit so as to give a continuous sheet of steam to act on the
vanes. If the side of such a nozzle were made half an inch
there would appear to be fourteen and a half such nozzles; the
turbines would probably be given 16 or 18 of them, which could
be arranged in two groups. Since the angle of the nozzle is 20
the width of the jet measured along the perimeter of the wheel
will be
0.5 4 sin 20 0.5 ~ 0.3420 = 1.46 inch.
Allowing onefourth of the width of the orifice for the thickness
of the walls, the width occupied by eight nozzles would be
1.46 X 1.25 X 8 = 14} inches.
The combined throat area of all the nozzles will be
3.36 X 4.45 X 144 5 1480 = 1.41 square inch.
Dividing by 14^, the number of necessary nozzles, gives for
the throat area of one nozzle
1.41 f 14.5 = 0.0972 square inch,
so that the diameter will be about 0.35 of an inch.
A method of calculation for the second set of nozzles consistent
with the method of determining the intermediate pressure is as
follows: The pressure in the throat has already been found to
be 10.6 pounds, corresponding to 196 F., for which the tem
peratureentropy table at 1.56 units of entropy gives for heat
vfKAM Tl'
content* tuiS, Thr itr.it umtrnti .it t,*vj fumh ())$} has
alrraily Utn futiml to !<r H.JJ ^ that llw availaMr heat for
atlwballi' tUw ,q*j*ari ! l* ,14 tt.r.t'., whi h K* V '* f ur the
vrl(H:ity In ihr throat
I"  \ f j x jj.j < ;;M *. u ~ Jf* ^*ri,
Thr nrsl ^li" U ihr ilrlrrniuuitiun of thr *juiitilir^ at ihr thro&t
ami rxit, itnl frt iltrtii iln* %*fciitr vnlum**^. Now f the
a {tart Iww aittially Itfrii ittsit c *i it* work, !'***. llirrr
ulluwrti o.tji lr fritin in its*' im/./.i*, iniil <,*.$ (r lu\w. In the
llilrs lifltl ViinrH, whitr ihr rUuiru'y lut" ?* iif$.Ir'*, 4iii vcUi.itim
1,883, Thr hrat ini. work w..i> ihrrrfrr
161 *: >:' o,?i *: .*iS ~ tjM,f ii. t ,r.
ihr Ml W lh* lr<m *!> it fi*it:ttrs
w
I till  i ti.M ,t.f,
per fwiiritl. N*w r liit* lh? valur tj^j i! ^j,i I',, sitwl y it iti
that tlw* quality t
,f  (itaj  tit i :  iiy *>,^v*
If thu flow from thr t ih tlif*.;i! 34 ,f,t?,
to jf iftlri
wwl as f ii* tt 4iil f it t<r4 *t*
.* fteftM ' if 14 1  i
it thr throat f thr wt*ml nw/^lc,
Alipwifipl us lwftrr si, ic If ihr lri*!i*
In*
III I
PRESSURE AND VELOCITY COMPOUNDING 5ll
at exit from the second set of nozzles. The volume of saturated
steam at 102 is 335 cubic feet, and with x equal to 0.858 the
specific volume is 288 cubic feet. Consequently, with a weight of
3.36 pounds per second, and a velocity of 2610 feet, the united
areas of all the nozzles at exit will be
3.36 X 288 X 144 s 2610 = 53.4 square inches.
Now the perimeter of a circle having a diameter of 4$ feet is
about 170 inches. Allowing for the sine of the angle 20 and
onefourth for thickness of guides there will be about 43.5 inches
for the united width of passages between guides so that the
radial length will be
534 5 435 = 123 inch.
The specific volume of saturated steam at' 197 is 35.5 cubic
feet, so that with x equal to 0.925 the specific volume is 32.9.
Now the areas are proportional to the specific volumes and
inversely as the velocities, consequently the length of guides at the
throat is
. . 2610 . J 32.0
1.27 X X *rr
1300 288
0.29 inch.
The length of the vanes and guides can be found by the method
on page 500, using relative velocities for the vanes and absolute
velocities for the guides. The velocities decrease as indicated
by Fig. 107, page 487, and the lengths must be correspondingly
increased. In this case, however, there are two considerations
which influences the lengths that should be finally assigned to the
guides and vanes, (i) The thickness may be diminished, which
tends to decrease the length. (2) Friction reduces the velocity
which tends to increase the length. Friction of course diminishes
all velocities including the peripheral velocity of the wheel, but a
proper discussion of that matter would be both long and uncertain.
Attention has already been called to the defect of this method
of making all the calculations at a single value of entropy and
trying to allow for friction and other losses by simple factors.
The difficulty is aggravated in this case by the fact that the
512
STEAMTURBINES
second set of nozzles or guides have proper throats. The proper
method after having selected a set of intermediate pressures
appears to be to calculate the turbine step by step. The steam
supplied to the second set of nozzles (or guides) has been found
to have the quality 0.950, and this is probably a good approxima
tion to the actual condition, even if allowance is made for radi
ation and leakage. The temperatureentropy table gives for
steam having that quality and the temperature 223, the
entropy as nearly 1.66. At that entropy the heat contents at
the initial, throat and exit pressures, are given in the following
table with also the quality and specific volume at the throat;
the table also gives the quality and specific volumes at exit with
y equal to 0.15.
Pressure.
Temperature
Heat contents.
Quality.
Specific volume.
i8.a
223
IIOO
095
10.6
196
1063
0.92
327
I.O
1 02
927
0.85
245
The apparent available heat for adiabatic flow to the throat
is now
noi  1063 = 37,
which would give a velocity of
V = V 2 X 32.2 X 778 X 37 = 1360,
instead of 1280 as previously found. The apparent available
heat to the exit with 0.15 for the friction factor is now
(noi 927) 0.85 = 147,
which gives for the exit velocity '
V = V2 X 32.2 X 778 X 147 = 2710,
instead of 2610 previously computed.
This comparison shows that the intermediate pressure deter
mined by the customary method will be too high, and that to
obtain the desired distribution of temperature the factors for
imvr Htagi* must he modified arbitrarily as may be deter
mined ly rofttfutkmi with practice.
Curtis Turbine. Fig. 1 1 4 shows a partial elevation and section
of ihr rs*rwiiil failures of a Curtis turbine, which has four
rhamlKT!. *intl lw wts of moving vanes in each chamber. The
n*it uf liiiMurbinr is vertieal which demands an end bearing,
the tlitliftiltie* nf whirh construction appear to have been met by
oil umirr im^iMurt* into the bearing, so that there is
ciwijiktr liilirknitttn without contact of metal on metal. The
umtirntrr i* >Uil tlimlly under the turbine, and the electric
grnrrattr b aUw tin a tontinuation of the shaft, The arrange
afiftcitr* in IM convenient, and in particular to demand
Hjiair only.
iwrij for marine propulsion the Curtis turbine has a
hftfl from and has a large number of stages.
514
STEAMTURBINES
A turbine developing 8000 horsepower has seven pressure
stages, each of which but the first has three velocity stages, that
one has four velocity stages. The diameter is ten feet and
the peripheral velocity is 180 feet per second.
Tests on Curtis Turbines. The following tables give tests
on two Curtis turbines, having two and four pressure stages,
respectively; both were made by students at the Massachusetts
Institute of Technology.
TESTS ON A TWOSTAGE CURTIS TURBINE.
DARLING AND COOPER.*
Duration, minutes
I2O
120
I2O
I2O
60
Throttle pressure gauge
146. 3
ixc; . i
142 . 2
143.
I4Q . 7
Throttle temperature F
eia
?2O
464
"JO2
t !l2
Barometer inches
20.8
20 .0
20.0
20.0
30.0
Exhaust pressure absolute pounds . .
Load kilowatts
0.82
161 .4
079
2<< . 7
0.92
374O
0.84
512. o
0.85
731 .0
Steam per kilowatt hour, pounds . .
Thermal units kilowatt minute . . .
21.98
440
I963
396
19.98
39 2
18.43
3 6 9
1775
357
If the efficiency of the dynamo is taken at 0.9 and one kilowatt
is rated as 1.34 horsepower, the steam and heat consumptions
per brake horsepower are, for the best result,
1 1. 8 pounds 239 B.T.U.
TESTS ON A FOURSTAGE CURTIS TURBINE
COE AND TRASK.f
Duration minutes
60
60
60
1 80
I2O
Boiler pressure) pounds
TC2
IAD 6
I <J2 I
ICO
ICQ A.
Vacuum inches . .
28 *
28 2
28 8
28 4
28 1
Load kilowatts
282
380
C27
ega
788
Steam per kilowatt hour pounds . .
21.4
203
18.8
195
193
Thermal units per kilowatt (minute) .
394
37
352
360
357
* Thesis, M. T. T., 1905.
f Thesis, M. I. T., 1906.
TURBINKS
515
&
iraiure
the ertitiemy of the dynamo as 0.9 and a kilowatt as
i,,i4 horse jHiwrr, the liexi result is equivalent to a steam con
sumption uf u.o jHumcU ami a heat consumption of 237 thermal
units,
Rttctton TurbittM. The. essential feature of a reaction
turbine, in a fall of pressure and a consequent increase of veloc
ity In fiir (Mintage* among the vanes of the turbine. Since
surh wheel* rommonly are affected by impulse also they are
sometime, railed impulsereaction wheels, but if properly uncler
fittiiwl litr horter name neetl nut lead to confusion. In consc
tjuemr of the feature named the
relative e*it vrliH icy I', is greater
than I',, Another ron*equenee in
thai sir'tm Irnkn part the entls
i>f I fir viinr* whit It tin* usually
t.tt llir irifirr eruU f the
whtt h art l.o o(H'n; ihi*
to '4itiwft hy Fig. 1 1 5.
Tlu* reafiion turbine in always
made tomKmmi with a large
msfiiin*r f Htage*one set of guides
ami flir following set of vanes
IK ing counted as a stage. In
ctifisjtit'rii:i' tlir exit pressure either p w , n$,
frti the guide* or the vanes is
only 4 lltilt? Sr ihun the enlrantc prtmsure, and the passages
Thrrr h mi uttrmpt to awld axkl thrust, and therefore the
rxil 7 from tin* vams* may be made small; it is commonly
rtjtiat ui the rxit angle a from the gulden. A common value
for lltrir angles is Ji**.
llir giiitlr% ami vanw follow alternately in close succession
leaving only the nrersHary flearancp; the kinetic energy due to
thr ntiiliiir cxli vrluc'ity from a given set of vanes is not lost but
I in the nrt''t of guides. The turbines are usually
if I
nuidr in twt or
ami ii ' inly *tt
lu llir ,ltm*lis!r
tltis kinrtii rtit
ftttrcr M un^ in shown lv t>'s?. 11
im mil 4 *i >**! *u UMI ihr iiitrfis inrrgv ttttt*
M! wU*a> . firjirt !<<!, at ihr rm M 4
lirfr ifr 4i'*Wj%
illliiit'ilt " **( lltr ilfirli.* *'rf>t* l'.'
lt%T *rf i'rfi! it f;i% f'il'i
thr giitfli"'! ami tiin* 1  fiUj in?hnri r
tf Iir;t! sill** mrl 4 i*l*i!*:4 !<i *Jsr !tlsfif
of
m* rrdiir lite
r til Hfr^m .;!! lll*!";i\ifr,
ilir rill iil*%ilUt!r %rl<.$!%
driving ilir >l*'aiii ttti** tlir '%,! ^
SH V*J*nllV l
an
lilt*
tin ititli
 lltr
Tlw* *lrifll rflirfa a ?rl #l if
till' al*%*tr grimily lf*
I III w iltr lt*i tf j*frA*
uf k
tif VfttMtlV I* I** S
r%il vrl'ily * life It i** *j t^mftr
Stitr VfltifiU iKfllitiflni Ilic
t'lirfgi, ill !$r
tr rntifc
:r til
ill lilt
<! s n 4)>!nt) It)
i*t r i 3 R, tUrrti
4;r, i! r*
r to
't* i
* rsl$f ; ir
*4 hral
<
CHOICE OF CONDITIONS
517
the gain of velocity in the vanes is equal to the gain in the
guides.
In Fig. 116 let 7 1 be the velocity of the steam leaving the
guides and V the velocity of the vanes; then F 2 is the relative
velocity of the steam entering the vanes. V a is the relative exit
velocity which is greater than F 2 on account of the change of
heat into work. F 4 is the absolute exit velocity from the vanes
with which the steam enters the next set of guides. If the con
ditions for successive stages are the same, V 4 is also equal to the
entrance velocity to the set of guides of the stage under discussion,
and if ce is laid off at ac' then cfb is the gain of velocity in the
FIG. 116.
guides. Consequently to construct V s we may lay off ce' equal
to ac and e'd equal to c'b. Now a and 7 are commonly made equal,
and therefore the triangles abc and cde are equal. Consequently
the angle 3 for the entrance to the guides is equal to /? at the
entrance to the vanes. In fact the guides and vanes have the
same form.
Choice of Conditions. The foregoing discussion shows that
the designer is given a wider latitude in his choice of conditions
for the compound reaction turbines than appeared possible
for impulse turbines, though if the restriction of no axial thrust
were removed from the latter the comparison would be quite
different.
Ttlr II!
in prat li'r '
in a jarr !
mation in
I**
fl'ii'liwtl krfiv.iifr
w'9&$a * ^ $.'JSMki3*' j ' $&
fHUlCK OF CONDITIONS
PARSONS TURBINE  MARINE WORK.
Hift* **mt
Intrrmwlifttr wall *ir*wrr*
t'hAttwt 'sirawrt^ . . ,
titttirhin tttl
Smatt * f tir*
Prf, fal .
p stwntl.
Ratio of
velocities,
Number
of
H.P.
L.P.
vanw to
steam.
ahafls.
70Ho
110130
0.450.5
4
iteq
110135
0.4705
34
ijotoj
130150
0.370.47
3
83100
USMS
0.480.59
4
105110
130160
0.470.5
34
t 10130
160310
o. 470.51
34
The VVrattnghouHr 0<>m(mny have used much higher veloc
ities f vane for I'ltt'triful work than given in the above tables;
m mut'K an 170 fi.Ht IXT sct'ond for the smallest cylinder and
375 for iltt* krgrst cytimittr,
Tttr liliiclt* liright nhouUl t % tit least three per cent of the
elkftiricr of ftir tytlmlrr In orcUfr to avoid excessive leakage
over iitr lifw, Mr, SjRitkinan siys that leakage over the tips
til the liliitlrs U M'rha not so detrimental on account of actual
lew by as tKrcnuatf it upsets calculations regartoig
by inrrnt^inK the steam volume,
The ftilliiwlng equation reprcnenta Mr. Speakman'a diagram
for ttearaerrs over ill of vtnes.
rlearance In
inchen
0,01 + diam. in feet.
The t>roxirtmn f may be taken from the Mowing
table ;
" ' ~ HCHE8.
WMih
at
24
Mr. i*a n%* i\et for the efftricncy of the steam in the
turbine ttltti** themielvr* 0.70 to 0.80.
* /nil. ,V<*wl 4rA., 1903,
S !
1ft iiiti ! tt !* ilw Ir4ijt" JM'** llu
fa ft fit *S in fiitllir tic 9rn.il 1 iilnl ill
tlirfr U likrJv S K~ A *cM'istlrr*it*h?
fI'iiH wliis It uU ! t"*H i iW*! in
Tlii"* iligr i"4 in iSic m* iUrr*l i* tit*
firnl IK f si ill llir ti**nfti nf l
but alltiWiinrt* 'ltll t*c i i jfti
i frsiilt'i i4 trsfv.
f**r A Rwctifttt Tutfein*. I <"
.11* <
*hr I
ltl ft F. Thr
irfiry wf ,$riia ..i,
fi.f.f 4 , lwr%r*irf
lilt* fiiflitflr y, left f*"f
riciksliwll, ili" *M l
l t ftufii
we In? fltr Ht'Mrrt* % *l *h" iMftilftr
*l B $fe f
ffi.j
iff tt tir
tl lr*U f
tf llir f sir
tltf
ffir l
f*r? 14 
 mr*! ill
ir
rl ihr  lit*
lift J*rf sci'i.ifltl, r! iltr
FOR A REACTION TURBINE
521
cylinders be i and aj times the diameter of the small cylinders.
Let the {teripheral s>eed he 0.75 of the steam velocity, then the
latter will ! joo feet per second. If the exit angles for guides
and vanes tie taken us ao* and if the degree of reaction, is 0.5,
the velocities ami angles will be represented by Fig. 116, page
517, In that figure
$b y $ CO8 20 o a 0,940 F t ;
ami as V is 0,75 K t ,
we have <' ^ (0,040  0.75) V v 0.190 7 r
Hut J?  y, sin 20 0.343 V t ;
Ian ^ * o.j4^ J " 'P ^ 1800 ,\ )9 61.
The angle p is given to the Iwfe of the blades, and the angle at
the totes is somewhat larger, as will appear by Fig, 115, page 515 ;
in fnnsrquemr there b some* impulse at the entrance to the vanes,
To get the relative, velocity we have
F,/  a? F (044? + oiigo 1 ) F, 3
.', V,  o..y>a V,.
But ii is shown on frngr 517 that for the conditions chosen the
fnfiif of vdwity in Hlher guulot or vanes is equal to
V  F,  (t  0.392) F t  0.608 X 300  182
the ctmtki for vcknity when h thermal units are avail
ablr is
and i'onvtTM?ly
33.2 X
(64.4 X 77)
Th w lltr amount with allowance for friction and leakage
imut the rtttit* nf the which hai been aanigned the factor
0.0, m that fir the preliminary adkbatic computation we may
take for one **t iA blades
O.Mtf ! 0.6 I.I B.T.U.,
522
STEAMTURBINES
and for a stage, consisting of a set of guides and vanes, we may
take for the basis of the determination of the proper number of
stages 2.2 B.T.U. per pound of steam used.
It appears on page 507 that adiabatic expansion from 165
pounds absolute to one pound absolute gives 322 thermal units
for the available heat. If this is to be distributed to the stages
of a turbine with 2.2 units per stage, then the total number of
stages will be
322 4 2.2 = 146
stages,. This is under the assumption that the turbine has a
uniform diameter of rotor with 225 feet for the velocity of the
vanes; we have, however, taken the intermediate diameter i
times the highpressure and the lowpressure 2% times. The
peripheral velocities will have the same ratios, and the amounts
of available heat per stage will be proportional to the squares of
those ratios, namely, 2.25 and 6.25. Consequently the amounts
of heat assigned per stage will be as follows :
Highpressure Intermediate Lowpressure.
2.2 495 1375
If we decide to use ten lowpressures and twenty intermediate
stages they will require
10 X 13.75 + 20 X 495 = 2365 B.T.U.,
leaving 85.5 thermal units which will require somewhat less
than 39 stages. Reversing the operation it appears that one
distribution calls for
10 X 13.75 + 20 X 4.95 + 39 X 2.2 = 322 B.T.U.
For convenience of manufacture it is customary to make
several stages identical, that is, with the same length of blades,
clearances, etc. ; this of course will derange the velocities to some
extent and interfere with the realization of the best economy.
That part of the cylinder which has the same length of blades
is known technically as a barrel. Let there be three barrels for
each cylinder, making nine in all, which may be conveniently
numbered, beginning at the highpressure end and may have
DK8IGN FOR A REACTION TURBINE
523
the number of stages assigned above. In that table is given also
the number of the stage counting from the highpressure end,
which is at or near the middle of the length of the barrel, for
which calculations will be made. The values of the heat con
tents AT I q are readily found for each stage given in the table
by subtracting the amounts of heat changed into kinetic energy,
down to that stage, allowing 2,2 for each stage of the high
CC IMPOUND REACTION TURBINE.
It
t it
tjft 7
t>t 8
As 7
II?J
iMV.,1
1 1 JO . ?
+ o
nr.7
wo
184
MU
toy
ft7
UHfl
jmft
.001
984
075
ft3
OS
037
,00
Sped Ac
vmumw.
J. SO
4 SO
6. !)
004
j 6. o
34.8
47.t
190,4
S7
3,97
I S B
0.38
0S7
15
333
230
0.415
o.fiio
4.673
pifHsure cylinder, 4.05 fr tmch intermediate stage and 13.75 for
each lowirwwu; stage. For example, the fiftieth stage has
its heat content* found by subtracting from the initial heat con
lents f 193, the amount
to X 2.2 + ii X 405 " r 403
%! f
leaving for the heat contend after that stage 1053 thermal units.
Thr pwbable heat conttnt* allowing for friction and leakage IB
founcl by subtracting the product of the above quantity by the
factor 0.6. (living
1 103
X 0.6 * ii OQ B.T.U.
Having the values of *r 4 g obtained in this way the values of
y can be fount! by subtracting the heat of the liquid q, and
524
STKAM I
dividing thr frtwtirjtlrr by **. Finally lltr "ijitrttir volume an
by I lit* rqu;ittttn
but in fiRtrtki* * itwy In: ntrgUi'lctl
Ijecnune we have either x nearly e*}tul !* unity nr t*! 1 will be
wrttjanrt with ,
llir strain velnt ily for I tie I'm! rylindrr r> " Irrl jvr s
tlt" weight of Htenni jer 'u*'n*l i** .}.t4 ptifili in(i th<*
vulume at the seventh niagi', i.e., ihr itH*l<llr *! tlir ftr%t barrel
h ,31 Ctllik frrl, Thr rile* fjvr .ifra itiu^l !h'rrfure lit*
T IK* a ffiiilirtfi nf csi".!lut4 ,nr *inr.firih tf
ItlliiW for the lliit'kilr"** i thr tsiiilrs, >ini flir r*"ll bt
ring thruugh whi*'h the *tr^im
far ttit: fratiitift In thU a j % ^*
iH.f <wii,tff in* ttrs,
ll I* llir
of lilt* li*r ill*'
tinefount
It* 4
Tilt" iliiittirtrrm <i ihr iiiirffftnliaf* and Kw f r^s
'ill l*r
n.
tlir tif ii! Itir ^rvr
DESIGN FOR A REACTION TURBINE 525
ant! this length will be assigned to all the blades of the first
barrel. The blades of the second and third barrels will have
their lengths increased in proportion to the specific volumes at the
middle of those barrels, as set down in the table. The effect '
of increasing the diameters of the intermediate and lowpres
sure cylinders is to increase the steam velocity, and the peripheral
length of the steam passage, both in proportion to the diameter.
Consequently the lengths of the blades for these cylinders are
directly proportional to the proper specific volumes and inversely
proportional to the squares of the diameters. Thus the length
of the bladeM at the fortysecond stage, i.e., the middle of the
fourth barrel is
0415 X o41 v
J  J  I ,* 0,5^2 men.
3.27 X 1.5
The lengths are computed for the other barrels in the same way,
using 2.5 for the ratio of the lowpressure diameter.
Since the diameter of the small cylinder is 13.85 inches and
the sum! of the vanes on it is 225 feet per second, the revolutions
per minute are
HlJlJ925 Ia ...
laSs'ff "* 37S '
Partons Turbine. The essential features of the Parsons
turbine are shown by Fig. 117. Steam is admitted at A and
In succesHtun through the stages on the highpressure
cylinder, awl thence through the passage at E to the stages of
the intermediate cylinder; after passing through the intermediate
it through G to the lowpressure stages and finally
by B to the condenser.
The axial throat is counterbalanced by the dummy cylinders,
C C, C, the first receiving steam from the supply directly, the
second from the fiassage between the high and intermediate
cylimifrs through the pipe F, and the third through the pipe near
If from the between the intermediate and lowpressure
cylinders. Leakage pant the dummy cylinders is checked by laby
rinth packing, which is variously arranged to give a succession
IT X MINKS
U
 A
f i , f !<
gli whtfh llw* ^traits ttni'il M'^ wii
lltftilllr llir *4ra? . $1 jM*n?4
lwr, fltir is It* ki tirtff."% 'slrijitt *if hftivt int
lh<* sUffiirr w! llir fvliftilrr rtfiil ilif* ill*' nit km if list*
?w* thill till" ;4**iifH i'* ilfiififtlv lllftsilli'4 &>. ll  M .'j.w
IH rritrtt'il lltiil llir Uhvrtttiti *rfann* ti rnttrrly
rrtiiistfig liir 1cakar llir fvlintjrf !* a ammin
It i> {ifiiniit) mil ly Mr, Jmlr iln i'ti cilrtitwr thruitltn
fa al llir k.st *t titfii f llir labyrinth, lltr trtlirf srtliof
rr t't}IHira!i%"rly intliitiriil. Thit riltifr mill ttr rvidrnt If a
I'* In lUlll tif*tir llir l*r\ t >i*{U(.'4tit4l t
Miifiktfii?'* sji, t>( mrr i%nii A t
but TIIt!i% yet il> itltiilttfi*s Itr
Irakagr whii It >hmiM I** ^m*i){.
Wlirfi a4inl I ifnjni'ii}fs Jir
tiittitteti ami llir *ibl lliri^l i? iiwlnlli" ;ii*!fn It* the
iliafl, Stmr at! alrwiltilt" liaLtmr t*mt*t lr tsliiaificil, a
to rtviU) Irtil if fffcii' lfci%r iiciif *ft,f Wi
hiAVr litlt lilllr ffittiwft, Sutititury lufbillr."* 4!" h^vr
IttT ufiliakfirwi lliiti'tl,
A irM <n A
TEST ON A PARSONS TURBINE
5*7
Parsons turbine in Savannah was made under the direction of
Mr. B. R. T. Collins and reported by Messrs. H. O. C. Isenberg
and J. Lage,* which is interesting because the steam consumption
of the auxiliary machines was determined separately. The
data and results of tests on the turbine are given in the following
table.
The tests made at full load with varying degrees of vacuum
show clearly the advantage obtained in this machine from a
good vacuum, which amounted to a saving of
289 279 _
TESTS ON WESTINGHOUSEPARSONS TURBINE.
COLLINS, ISENBERG AND LAGE.
J load.
} load.
I
ull load.
ii load.
i load.
60
60
60
60
60
45
4 1 !
Steam pressures, gauge . . .
131
129
128
127
128
127
"5
28.1
28.1
2?. 7
26.7
28.0
26.7
26.6
Revolutions per minute . .
3616
3601
3602
3612
3562
3540
3537
Load kilowatts
260
370
493
501
499
629
733
Steam consumption, pounds
per kilowatthour ....
243
21.2
20.7
19.8
19.7
19.8
20.2
per electric h.p. per hour .
18.1
iS
150
14.8
147
147
ISI
Heat consumption B.T.U.
per kilowattminute
per horsepower per minute
462
345
403
301
494
289
375
284
374
279
373
278
3*i
283
A great importance is attributed by turbine builders to obtaining
a low vacuum, in many cases special airpumps and other devices
being used for that purpose. Unless discretion is shown both
in the design and operation of this auxiliary machinery, its size
and steam consumption is likely to be excessive, and what appears
to be gained from the vacuum may be entirely illusory.
* Thesis, M.I.T. 1906.
A i
Tt'RHINHH
Ttir steam ionsumptiim in
auxiliary roarhiw** was <i* f!l
(VntrtfuK'il juntj fwf lir
Ury Viif tin in jum$* ..
I tot well jiiifiii ...
KT hour fur the
HHi
at J
This Ulal was riftiiv^ilrtt! l o.t i%
of iltt* turbinr at fwll I,nl am! with
f turhint* iitailitl$tto
f lit*' rtm*umtfon
imhr* vai ttttw, S<ic
<jr tliii
INDEX.
Absolute temperature 56
Absorption refrigerating apparatus 41 1
Adiabatic for gases 63
for liquid and vapor 100
lines *7
Adiabatics, spacing of ..... 31
After burning 3 X 9
Aircompressor, calculation ... 377
compound 3^6
cooling during compression . . 360
effect of clearance 363
efficiency 37
friction 3 6 9
fluid piston 359
moisture in cylinder 361
power expended 362
threestage 3 68
Air, flow of 429
friction in pipes 380
pump 374. 375
thermometer 3^8
Alternative method 49
Ammonia I2 3
Automatic and throttle engines . 276
BellColeman refrigerating ma
chine 413
Binary engines 180, 280
Blastfurnace gasengine .... 335
Boyle's law 54
British thermal unit 5
Biichner 437
Calorimeter 191
separating . . . *94
Thomas  '95
throttling 161
Calorie 5
Callendar and Nicolson .... 231
Carnot's engine
function
principle
Characteristic equation
for gases
for superheated vapors ....
Chestnut Hill, engine test . . . .
Compound aircompressor . . .
airengine
Compoundengines
crosscompound
directexpansion
indicator diagrams
lowpressure cutoff
ratio of cylinders
total expansions
with receiver
without receiver
Compressedair
calculation
compound compressor . . . .
effect of clearance
friction, etc
hydraulic compressor ...
interchange of heat ....
storage of power
temperature after compression
transmission of power . . .
Compressedair engine ....
calculation . . "
compound
consumption
final temperature .....
interchange of heat
moisture in cylinder . ' . . .
volume of cylinder
Condensers
cooling surface
ejector
5 2 9
22
28
26
2
55
no
239
366
384
156
169
163
162
161
162
1 60
159
158
.358
377
366
363
369
372
365
39 2
3 6 4
39i
384
388
388
385
385
386
3<5i
386
149
15*
Carburetors ....
Creusot, tests on engine
Critical temperature
Cutoff and expansion
Cycle, closed .
nonreversible
reversible .
Delafond .
Denton
Density at highpressure
Drynessfactor
Designing steamengines
Diesel motor
economy
Differential coefficient dp/dt
Dixwell's tests
Dynamometers
INDEX
Entropy Contimied.
due to vaporization .....
expression for ........
of a liquid ........
of a liquid and vapor . . .
of gases .........
scale of .........
Exponential equation ....
First and second laws combined
First law of thermodynamics .
application of
245
257
256
255
268
23?
247
99
35
9/
application of vapors 8
Flow in tubes and nozzles
Biichner's experiments
Economy, methods of improving.
compounding
expansion
increase of size
intermediate reheaters ....
of steamengines
raising pressure
steamjackets 261,266
superheating 2 7
variation of load 2 74
Effect of raising steampressure, 148, 247
Efficiency 2 5
mechanical 2 7
of reversible engines 33
of steamengine !3> X 44
Efficiency, maximum . .
of superheated steam .
Ejector
condenser
Engine, Carnot's
compressedair
friction of
hotair
internal combustion . . .
oil
reversible ....
Entropy
39
us
470
4?i
22
384
285
335
24
3 2
43
43
design of a nozzle 44
experiments
friction head
Kneass' experiments
Kuhhardt's experiments . . 
Lewicki's experiments ....
Rateau's experiments ....
Rosenhain's experiments . .
Stodola's experiments . . .
Flow of air, Fliegner's equations
in pipes
maximum velocity
through porous plug . . .
Flow of fluids
of gases
of incompressible fluids . .
of saturated vapor
of superheated steam . .
French and English units . . .
Friction of engines
distribution
initial and load
Gasengine
after burning
blastfurnace gas . .  
economy and efficiency . .
ignition
starting devices . .
temperature after explosion
valvegear
water jackets
3 20 >
INDEX
53*
Gasengines Continued,
with aimprejtHlon in cylinder . 308
with .separate compression . . 305
Gasengine* fourcycle 337
two<ycl . 338
Gase* 54
adiabatic equations 64
characteristic equation .... SS
characteristics for gasengines . 314
entropy 6?
general equation* 6t
Intrinsic energy 66
iKoenergic equation 63
isothermal equation 61
special method 60
specific heat* S ( )
speciik volume* 57
Gasoline engine 334
Gasproducers 33 1 >3S 3
Gauges iH6
GayUwmc's law 54
Graphical representation of change
of energy . ao
of characteristic equation ... 4
of efficiency 33
Grashoff 1 * formula 432"
Hall's investigations 23
Halltuer's tests 219
Heat of the liquid 8a
Heat of vaporisation 85
Him engine, teat* on sao
Hirn'i analysis 305
Hotair engine* 298
Ignition 3 2 9
Indicators 187
Influence of cylinder walla ... 199
Callendar and Nieoluon , . . 331
Hall 330
Hirn'a analysis 205
representation 202
Injector 447
combiningtube 45$
deliverytube 459
double 4^1
Injector Contintted.
efficiency of 459
exhaust steam 467
Ktirting 462
lifting ........... 460
restarting 464
selfadjusting 462
Seller's 460
steamnozzle 458
theory 448
velocity in delivery tube . . . 455
velocity of steamjet 452
velocity of water 454
Internal combustion engines . . 298
Internal latent heat 87
Intrinsic energy 14
of gaxcn 66
of vapora 95
Inocnergic or iuotlynamk line . . 17
for gaiwa 63
Isothermal lines 16
for gases 61
for vapors 94
Joswe, tests on binary engine . . 282
Joule and Kelvin's experiments . 69
Kelvin's graphical method ... 29
Keroseneoil engine 335
Kilogram S 6
Kneass . 44045 2
Knoblauch no
Kuhhardt 443
Latent heat of expansion .... 6
Law* of thermodynamics ... 13, 22
application to gows 59
application to vapors 88
Lewicld 443
Lines, adiabatie 17
isoenergic *7
isothermal *6
of equal pressure *6
of equal volume ....... 16
Meyer 35
Mass. Inst. Technology, engine
tests 262
INDEX
533
Steam turbines Continued.
t'urtln . ......... 513
effect t>! friction .... 481, 491
impubr .......... 473
" general cure .... 477
frkticm til rotating tUnkn . . 504
lead , .......... ^oa
ami radiation .... 501
thrust ,.,.,.. 480
Rateau .......... 503
reaction ...... 4?f'i 5 "5, S^o
.Stirling's hotair engine .... agy
Stcxiciln . . ..... .... 441
Sulphur dioxide ,.,...,. 117
Su{rrh?atet! vapor* ...... no
t"haritrtrrSl!c et]untU>r) .... lai
rnirtipy ... ..... . . 115
sHi'ifk"hrt ........ u a
hrut .......... 1(4
ttlm*lutr wale
3
diagram
35, 104, 131, J7
.,., iud, 139
Testing steamengines 183
Teats of steamengines 237
examples of economy .... 238
marine engines 241, 242
simple engines 250
steampumps 244
superheated steam .... 270, 273
Thermal capacities i, 7
of gases 61
relations of . 9
Thermal lines 16
and their projections .... 19
Thermal unit 5
Thomas 112
ThuraUm 294
Total heat of steam 84
of superheated steam .... 114
of vapora 85
Tripleexpansion engines .... 172
Tumlire in
Value of R 57
Wwitchcttt engine 357
Wdrs ipx
Zeuner'i equations
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.Burr and Falk's Influence Lines for Bridge and Roof Computations 8vo, 3 oo
Design and Construction of Metallic Bridges 8vo, 5 oo
.Du Bois's Mechanics of Engineering. Vol. II Small 410, 10 oo
.Foster's Treatise on Wooden Trestle Bridges 4to, 5 oo
Fowler's Ordinary Foundations 8vo, 3 so
Greene's Roof Trusses 8vo < x 2 5
Bridge Trusses 8v i 2 SO
Arches in Wood, Iron, and Stone 8vo, 2 50
Grimm's Secondary Stresses in Bridge Trusses. (Tn Press. )
Howe's Treatise on Arches 8vo 4 o
Design of Simple Roof trusses in Wood and Steel 8vo, 2 oo
Symmetrical Masonry Arches 8vo, 2 50
Johnson, Bryan, and Turneaure's Theory and Practice in the Designing of
Modern Framed Structures Small 4to, 10 op
Merriman and Jacoby's Textbook on Roofs and Bridges:
Part I. Stresses in Simple Trusses 8vo, 2 50
Part H. Graphic Statics 8vo > 2 So
Part HI. Bridge Design 8v . 2 5<>
Part IV. Higher Structures 8v . 2 So
7
Morison's Memphis Bridge. , 4to, 10 oo>
Waddell's De Pontibus, a Pocketbook for Bridge Engineers . . i6mo, morocco, 2 oo
* Specifications for Steel Bridges ismo, 50
Wright's Designing of Drawspans. Two parts in one volume 8vo, 3 50
HYDRAULICS.
Barnes's Ice Formation 8vo, 3 oo
Bazin's Experiments upon the Contraction of the Liquid Vein Issuing from
an Orifice. (Trautwine.) 8vo, 2 oo
Bovey's Treatise on Hydraulics 8vo, 5 oo
Church's Mechanics of Engineering 8vo , 6 oo
Diagrams of Mean Velocity of Water in Open Channels paper, i 50
Hydraulic Motors 8vo, 2 oo
Coffin's Graphical Solution of Hydraulic Problems i6mo, morocco, 2 50
Flather's Dynamometers, and the Measurement of Power lamo, 3 oo
Folwell's Watersupply Engineering 8vo, 4 oo^
FrizelPs Waterpower 8vo, 5 oo
Fuertes's Water and Public Health lanio, i s
Waterfiltration Works I2mo. 2 50
Ganguillet and Kutter's General Formula for the Uniform Flow of Water in
Rivers and Other Channels. (Hering and Trautwine.) 8vo, 4 oo
Hazen's Clean Water and How to Get It Large I2mo, l So
Filtration of Public Watersupply 8vo, 3 <>'
Hazlehurst's Towers and Tanks for Water works '. . . .8vo, 2 50
Herschel's 115 Experiments on the Carrying Capacity of Large, Riveted, Metal
Conduits 8vo, 2 oo
* Hubbard and Kiersted's Waterworks Management and Maintenance.. .Bvo, 4 oo
Mason's Watersupply. (Considered Principally from a Sanitary Standpoint.)
8vo, 4 oo
Merriman's Treatise on Hydraulics 8vp, 5 oo
* Michie's Elements of Analytical Mechanics 8vo, 4 oo
Schuyler's Reservoirs for Irrigation, Waterpower, and Domestic Water
supply Large 8vo, 5 oo
* Thomas and Watt's Improvement of Rivers 4 t( > 6 oo
Turneaure and Russell's Public Watersupplies 8vo, 5 oo
Wegmann's Design and Construction of Dams, gth Edition, enlarged. . .4to, 6 oo
Watersupply of the City of New York from 1658 to 1895 4to, 10 oo
Whipple's Value of Pure Water Large i2mo, i oo
Williams and Hazen's Hydraulic Tables 8vo, i 50
Wilson's Irrigation Engineering Small 8vo, 4 oo
Wolff's Windmill as a Prime Mover 8vo, 3 oo
Wood's Turbines 8vo, 2 50
Elements of Analytical Mechanics 8vo, 3 oo
MATERIALS OF ENGINEERING.
Baker's Treatise on Masonry Construction 8vo. 5 oo
Roads and Pavements 8vo, 5 oo
Black's United States Public Works Oblong 4to, 5 oo
* Bovey's Strength of Materials and Theory of Structures 8vo, 7 50
Burr's Elasticity and Resistance of the Materials of Engineering 8vo, 7 S
Byrne's Highway Construction 8vo, 5 oo
Inspection of the Materials and Workmanship Employed in Construction.
i6mo, 3 oo
Church's Mechanics of Engineering 8vo, 6 oo
Du Bois's Mechanics of Engineering. Vol. I Small 4"> 7 go
"Eckel's Cements, Limes, and Plasters 8vo, 6 oo
Johnson's Materials of Construction . . . . . . Large 8vo 6 OCT
Fowler's Ordinary Foundations ;. .....; 8vo, 3 50
Graves's Forest Mensuration , .'...'.....'.'..'..'. 8vo,' 4 oo
* Greene's Structural Mechanics 8vo' 2 50.
Keep's Cast Iron '.'.'.'.'.'.'.'.'.'.'.'.'.'. .8vo', 2 50
Lanza's Applied Mechanics 8vo, 7 50
Martens's Handbook on Testing Materials. (Henning.) 2 vols. ...... .8vo, 750
Maurer's Technical Mechanics 8vo, 4 oo
Merrill's Stones for Building and Decoration 8vo, 5 oo>
Merriman's Mechanics of Materials Svo, 5 oo>
* Strength of Materials ismo', i oo
Metcalf's Steel. A Manual for Steelusers iamo, 2 oo
Patton's Practical Treatise on Foundations 8vo, 5 oo
Richardson's Modern Asphalt Pavements 8vo, 3 oo
Richey's Handbook for Superintendents of Construction i6mo, mor., 4 oo
* Ries's Clays r Their Occurrence, Properties, and Useo 8vo, 5 oo
Rockwell's Roads and Pavements in France I2mo, i 25
Sabin's Industrial and Artistic Technology of Paints aci Varnish 8vo, 3 o
*Schwarz's Longleaf Pine in Virgin Forest ., izmo, i 25
Smith's Materials of Machines I2mo, i oo
Snow's Principal Species of Wood 8vo, 3 50
Spalding's Hydraulic Cement izrno, 2 oo>
Textbook on Roads and Pavements 12010, 2 oo
Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 oo>
Thurston's Materials of Engineering. 3 Parts 8vo, 8 oo
Part I. Nonmetallic Materials of Engineering and Metallurgy 8vo, 2 oo
Part II. Iron and Steel 8vo, 3 50.
Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their
Constituents Svo , 2 50
Tillson's Street Pavements and Paving Materials 8vo, 4 oo
Turneaure and Maurer's Principles of Reinforced Concrete Construction.. .Svo, 3 oo
Waddell's De Pontibus. (A Pocketbook for Bridge Engineers.). . i6mo, mor., 2 oo
* Specifications for Steel Bridges i2mo, 50
Wood's (De V.) Treatise on the Resistance of Materials, and an Appendix on
the Preservation of Timber Svo, 2 oo'
Wood's (De V.) Elements of Analytical Mechanics Svo, 3 oo>
Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and
Steel 8vo, 4 oo.
RAILWAY ENGINEERING.
Andrew's Handbook for Street Railway Engineers 3x5 inches, morocco, i 25
Berg's Buildings and Structures of American Railroads 410, 5 oo.
Brook's Handbook of Street Railroad Location i6mo, morocco, i 50
Butt's Civil Engineer's Fieldbook i6mo, morocco, 2 50
Crandall's Transition Curve i6mo, morocco, i 50
Railway and Other Earthwork Tables Svo, i 50.
Crockett's Methods for Earthwork Computations. (la Press)
Dawson's "Engineering" and Electric Traction Pocketbook . . i6mo, morocco 5 oo.
Dredge's History of the Pennsylvania Railroad: (1879) Paper, 5 oo.
Fisher's Table of Cubic Yards : Cardboard, 25.
Godwin's Railroad Engineers' Fieldbook and Explorers' Guide. . . i6mo, mor., 2 50.
Hudson's Tables for Calculating the Cubic Contents of Excavations and Em
bankments 8vo > J 001
Molitor and Beard's Manual for Resident Engineers. i6mo, i oo.
Nagle's Field Manual for Railroad Engineers i6mo, morocco, 3
PhiJbrick's Field Manual for Engineers i6mo, morocco, 3 oo.
Raymond's Elements of Railroad Engineering. (In Press.)
fl
Searles's Field Engineering i6mo, morocco. 3 oo
Railroad Spiral i6mo, morocco, I 50
Taylor's Prismoidal Formulae and Earthwork. gvo, I 50
* Trautwine's Method of Calculating the Cube Contents of Excavations and
Embankments by the Aid of Diagrams. 8vo, 2 oo
The Field Practice of Laying Out Circular Curves for Railroads.
i2nao, mor.occo, 2 50
Crosssection Sheet Paper, 25
Webb's Railroad Construction i6mo, morocco, 5 oo
Economics o.f Railroad Construction Large I2mo, 2 50
Wellington's Economic Theory of the Location of Railways Small 8vo., 5 oo
DRAWING.
Barr's Kinematics of Machinery 8vo, 2 50
* Bartlett's Mechanical Drawing 8vo , 3 oo
* " " " Abridged Ed 8vo, i 50
Coolidge's Manual of Drawing 8vo, paper, i oo
Coolidge and Freeman's Elements of General Drafting for Mechanical Engi
neers Oblong 4to, a 50
Durley's Kinematics of Machines 8vo, 4 oo
Emch's Introduction to Projective Geometry and its Applications 8vo, 2 so
Hill's Textbook on Shades and Shadows, and Perspective 8vo, 2 oo
Jamison's Elements of Mechanical Drawing 8vo, 2 50
A'dvanced Mechanical Drawing 8vo, 2 oo
Jones's Machine Design:
Part I. Kinematics of Machinery 8vo, i 50
Part II. Form, Strength, and Proportions of Parts 8vo, 3 oo
MacCord's Elements of Descriptive Geometry. 8vo, 3 oo
Kinematics; or, Practical Mechanism 8vo, 5 oo
Mechanical Drawing 4to, 4 oo
Velocity Diagrams 8vo, i 50
MacLeod's Descriptive Geometry Small Svo, i 50
* Mahan's Descriptive Geometry and Stonecutting 8vo, i 30
Industrial Drawing. (Thompson.) 8vo, 3 50
Moyer's Descriptive Geometry 8vo, 2 oo
Reed's Topographical Drawing and Sketching 4to, 5 oo
Reid's Course in Mechanical Drawing 8vo, 2 oo
Textbook of Mechanical Drawing and Elementary Machine Design. 8vo, 3 oo
Robinson's Principles of Mechanism 8vo, 3 oo
Schwamb and Merrill's Elements of Mechanism 8vo, 3 oo
Smith's (R. S.) Manual of Topographical Drawing. (McMillan.) 8vo, 2 50
Smith (A. W.) and Marx's Machine Design 8vo, 3 oo
* Titsworth's Elements of Mechanical Drawing Oblong 8vo, i 25
Warren's Elements of Plane and Solid Freehand Geometrical Drawing, izmo, i oo
Drafting Instruments and Operations i2mo, i 25
Manual of Elementary Projection Drawing I2mo, i 50
Manual of Elementary Problems in the Linear Perspective of Form and
Shadow lamo, i oo
Plane Problems in Elementary Geometry I2mo, i 25
Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50
General Problems of Shades and Shadows 8vo, 3 oo
Elements of Machine Construction and Drawing 8vo, 7 50
Problems, Theorems, and Examples in Descriptive Geometry 8vo, 2 so
Weisbach's Kinematics and Power of Transmission. (Hermann and
Klein.) 8vo, 5 o o
Whelpley's Practical Instruction in the Art of Letter Engraving 12 mo, 2 oo
Wilson's (H. M.) Topographic Surveying 8vo, 3 50
10
Wilson's (V. T. ) Freehand Perspective g vo 2 _ o
Wilson's (V. T.) Freehand Lettering '.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.I'. .8vo, i oo
Woolf' s Elementary Course in Descriptive Geometry. .Large 8vo,' 3 oo
ELECTRICITY AND PHYSICS.
* Abegg's Theory of Electrolytic Dissociation. (Von Ende.) . . . 12010, i 25
Anthony and Brackett's Textbook of Physics. (Magie. ) Small 8vo, 3 oo
Anthony's Lecturenotes on the Theory of Electrical Measurements xarno, i oo
Benjamin's History of Electricity. 3 VO , oo
Voltaic Cell .'.'.'.'.'.'.'.'.'.'.".'.'.'.'.';:.' .'.'svo.' 300
Betts's Lead Refining and Electrolysis. (In Press.)
Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood.).Svo, 3 oo
* CoUins's Manual of Wireless Telegraphy i2mo, i so
Morocco, 2 oo
Crehore and Squier's Polarizing Photochronograph 8vo, 3 oo
* Danneel's Electrochemistry. (Merriam.) i2mo, i 25
Dawson's "Engineering" and Electric Traction Pocketbook. i6mo, morocco", 5 oo
Dolezalek's Theory of the Lead Accumulator (Storage Battery). (Von Ende.)
I2mo, 2 50
Duhem's Thermodynamics and Chemistry. (Burgess.) 8vo, 4 oo
Flather's Dynamometers, and the Measurement of Power i2mo, 3 oo
Gilbert's De Magnete. (Mottelay.) gvo, 2 50
Hanchett's Alternating Currents Explained i2mo, i oo
Bering's Ready Reference Tables (Conversion Factors) iomo, morocco, 2 50
Hobart and Ellis's Highspeed Dynamo Electric Machinery. (In Press.)
Holman's Precision of Measurements 8vo, 2 oo
Telescopic Mirrorscale Method, Adjustments, and Tests Large 8vo, 75
Karapetoff's Experimental Electrical Engineering. (In Press.)
Kinzbrunner's Testing of Continuouscurrent Machines 8vo, 2 oo
Landauer's Spectrum Analysis. (Tingle.) 8vo, 3 oo
Le Chatelier's Hightemperature Measurements. (Boudouard Burgess.) I2mo, 3 oo
Lob's Electrochemistry of Organic Compounds. (Lorenz.) 8vo, 3 oo
* Lyons's Treatise on Electromagnetic Phenomena. Vols. I. and n. 8vo, each, 6 oo
* Michie's Elements of Wave Motion Relating to Sound and Light. 8vo, 4 oo
Niaudet's Elementary Treatise on Electric Batteries. (Fisbback.) i2mo, 2 50
Worris's Introduction to the Study of Electrical Engineering. (In Press.)
* Parahatt and. Hobart's Electric Machine Design 4to,half morocco, 12 50
iReagan's Locomotives: Simple, Compound, and Electric. New Edition.
Large I2mo, 3 50
* Rosenberg's Electrical Engineering. (Haldane Gee Kinzbrunner.). . .8vo, 2 oo
Ryan, Norris, and Hoxie's Electrical Machinery. Vol. 1 8vo, 2 50
Thurston's Stationary Steamengines 8vo, 2 50
* Tillman's Elementary Lessons in Heat 8vo, i 50
Tory and Pitcher's Manual of Laboratory Physics Small 8vo, 2 oo
dike's Modern Electrolytic Copper Refining 8vo, 3 oo
LAW.
* Davis's Elements of Law ". 8vo, 2 50
* Treatise on the Military Law of United States 8vo, 7 oo
* Sheep, 7 SO
* Dudley's Military Law and the Procedure of Courtsmartial . . . Large 12010. 2 50
Manual for Courtsmartial i6mo, morocco, i 50
Wait's Engineering and Architectural Jurisprudence 8vo, 6 oo
Sheep, 6 50
Law of Operations Preliminary to Construction in Engineering and Archi
tecture 8vo 5 oo
Sheep, 5 5
Law of Contracts 8vo, 3 oo
Wintbrop's Abridgment of Military Law . xarno, a 50
11
MANUFACTURES.
Bernadou's Smokeless Powder Nitrocellulose and Theory of the Cellulose
Molecule I2mo  2
Bolland's Iron Founder lamo, 2
The Iron Founder," Supplement Tamo, 2
Encyclopedia of Founding and Dictionary of Foundry Terms Used in the
Practice of Moulding izmo, 3
* Claassen's Beetsugar Manufacture. (Hall and Rolfe.) 8vo, 3
* Eckel's Cements, Limes, and Plasters . 8vo, 6
Eissler's Modern High Explosives 8vo > 4
Effrotit's Enzymes and their Applications. (Prescott.) .8vo, 3
Fitzgerald's Boston Machinist lamo, I
Ford's Boiler Making for Boiler Makers i8mo. i
Herrick's Denatured or Industrial Alcohol. . . 8v , 4
HoDey and Ladd's Analysis of Mixed Paints, Color Pigments, and Varnishes.
(In Press.)
Hopkins's Oilchemists' Handbook 8v o. ^
Keep's Cast Iron 8vo > :
Leach's The Inspection and Analysis of Food with Special Reference to State
Control Lar S e 8vo  
* McKay and Larsen's Principles and Practice of Buttermaking 8vo, :
Maire's Modern Pigments and their Vehicles. (In Press.)
Matthews's The Textile Fibres, ad Edition, Rewritten 8vo, .
Metcalf's Steel. A Maunal for Steelusers iimo, .
Metcalfe's Cost of Manufactures And the Administration of Workshops . 8vo, ;
Meyer's Modern Locomotive Construction 4to, i<
Morse's Calculations used in Canesugar Factories i<5mo, morocco,
* Reisig's Guide to Piecedyeing 8vo, 2:
Rice's Concreteblock Manufacture 8vo,
Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo,
Smith's Pressworking of Metals . 8vo >
Spalding's Hydraulic Cement "mo,
Spencer's Handbook for Chemists of Beetsugar Houses i6mo, morocco,
Handbook for Cane Sugar Manufacturers i6mo, morocco,
Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo,
Thurston's Manual of Steamboilers, their Designs, Construction and Opera
tion 8vo 
Ware's Beetsugar Manufacture and Refining. Vol. I Small 8vo,
" " Vol. II 8vo.
Weaver's Military Explosives 8vo,
West's American Foundry Practice lamo,
Moulder's Textbook ismo,
Wolff's Windmill as a Prime Mover 8vo,
Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel . . 8vo,
MATHEMATICS.
Baker's EFaptic Functions 8 vo,
Briggs's Elements of Plane Analytic Geometry ismo,
Buchanan's Plane and Spherical Trigonometry. (In Press.)
Compton's Manual of Logarithmic Computations lamo,
Davis's Introduction to the Logic of Algebra 8vo,
* Dickson's College Algebra Large lamo,
* Introduction to the Theory of Algebraic Equations Large 12010,
Emch's Introduction to Projective Geometry and its Applications 8vo,
Halsted's Elements of Geometry  8 vo,
Elementary Synthetic Geometry 8vo,
* Rational Geometry . izmo,
12
3 So .
3 o
<>o
Oo _
* Johnson's (J. B.) Threeplace Logarithmic Tables: Vestpocket size. paper,'
100 copies for
* Mounted on heavy cardboard, 8 X 10 inches,
10 copies for
Johnson's (W. W.) Elementary Treatise on Differential Calculus . .Small 8vo,
Elementary Treatise on the Integral Calculus .............. Small 8vo,
Johnson's (W. W.) Curve Tracing in Cartesian Coordinates . . . ...... lamo,
Johnson's (W. W.) Treatise on Ordinary and Partial Differential Equations.
Small 8vo,
Johnson's Treatise on the Integral Calculus .......... ..... . .Small 8vo,
Johnson's (W W.) Theory of Errors and the Method of Least Squares . i2mo,
* Johnson's (W. W.) Theoretical Mechanics .......... ............. tamo,
Laplace's Philosophical Essay on Probabilities. (Truscott and Emory. ).i2mo,
* Ludlow and Bass. Elements of Trigonometry and Logarithmic and Other
Tables ................................... ...... . ....... 8vo, 3 c>o
Trigonometry and Tables published separately ...... . ............ Each, 2 O o
* Ludlow's Logarithmic and Trigonometric Tables ...... ............. 8vo, i oo
Manning's IrrationalNumbers and their Representation by Sequences and Series
lamo, i ^s
Mathematical Monographs. Edited by Mansfield Merriman and Robert
S. Woodward .................................... Octavo, each t oo.
No. i. History of Modern Mathematics, by David Eugene Smith.
No. 2. Synthetic Projective Geometry, by George Bruce Halsted.
No. 3. Determinants, by Laenas Gifiord W<ild. No. 4. Hyper
bolic Functions, by James McMahon. No. S. Harmonic Func
tions, by William E. Byerly. No. 6. Grassmann's Space Analysis,
by Edward W. Hyde. No. 7. Probability and Theory of Errors,
by Robert S. Woodward. No. 8. Vector Analysis and Quaternions,
by Alexander Macfarlane. No. o. Differential Equations, by
William Woolsey Johnson. No. 10. The Solution of Equations,
by Mansfield Merriman. No. n. Functions of a Complex Variable,
by Thomas S. Fiske.
Maurer's Technical Mechanics ..................................... 8vo, 4. oo>
Merriman's Method of Least Squares .............................. 8vo, 2 oo
Rice and Johnson's Elementary Treatise on the Differential Calculus. . Sm. 8vo, 3 oo
Differential and Integral Calculus. 2 vols. in one ........... Small 8vo, a 50,
* Veblen and Lennes's Introduction to the Real Infinitesimal Analysis of One
Variable ................................................ 8vo, 2 oo
Wood's Elements of Coordinate Geometry .................. . : ...... 8vo, 2 oo
Trigonometry; Analytical, Plane, and Spherical ................ izmo, r oo
MECHANICAL ENGINEERING.
MATERIALS OF ENGINEERING* STEAMENGINES AND BOILERS.
Bacon's Forge Practice .................................... ..... i2mo, x 50
Baldwin's Steam Heating for Buildings ............................ i2mo, 2 , 50
Barr's Kinematics of Machinery .................................... 8vo, a so
* Bartlett's Mechanical Drawing ............................ ....... 8vo, 3 oo
* '< " " Abridged Ed ................. . ...... 8vo, i So
Benjamin's Wrinkles and Recipes ................... . . .......... . .isrno, 2 oo
Carpenter's Experimental Engineering ................... ........... 8vo, 6 oo
Heating and Ventilating Buildings .............................. 8vo, 4. oo
Clerk's Gas and Oil Engine ............................  ...... Small 8vo, 4 o
Coolidge's Manual of Drawing ............................... 8vo, paper, i oo,
Coolidge and Freeman's Elements of General Drafting for Mechanical En
gineers ........................................... Oblong 4to, 2 so
Cromwell's Treatise on Toothed Gearing ........................... I2mo, i so
Treatise on Belts and Pulleys ..................... ...:... ..... iamo, I S<>
13
II
Durley's Kinematics of Machines 8vo, 4 oo
Flather's Dynamometers and the Measurement of Power i2mo, 3 oo
Rope Driving lamo, 2 oo
Gill's Gas and Fuel Analysis for Engineers xamo, i 25
Hall's' Car Lubrication i2mo, i oo
Bering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 2 50
Button's The Gas Engine 8vo, 5 oo
Jamison's Mechanical Drawing 8vo, 2 50
Jones's Machine Design :
Part I. Kinematics of Machinery 8vo, i 50
Part II. Form, Strength, and Proportions of Parts 8vo, 3 oo
Kent's Mechanical Engineers' Pocketbook i6mo, morocco, 5 oo
Kerr's Power and Power Transmission 8vo, 2 oo
Leonard's Machine Shop, Tools, and Methods 8vo, 4 oo
* Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean.) . . 8vo, 4 oo
MacCord's Kinematics; or, Practical Mechanism 8vo, 5 oo
Mechanical Drawing 4to, 4 oo
Velocity Diagrams 8vo, i 50
MacFarland's Standard Reduction Factors for Gases 8vo, i 50
Mahan's Industrial Drawing. (Thompson.) 8vo, 3 50
Poole's Calorific Power of Fuels 8vo , 3 oo
Reid's Course in Mechanical Drawing 8vo, 2 oo
Textbook of Mechanical Drawing and Elementary Machine Design. 8vo, 3 oo
Richard's Compressed Air izmo, i 50
Robinson's Principles of Mechanism 8vo, 3 oo
Schwamb and Merrill's Elements of Mechanism 8vo, 3 oo
Smith's (0.) Press working of Metals 8vo, 3 oo
Smith (A. W.) and Marx's Machine Design 8vo, 3 oo
Thurston's Treatise on Friction and Lost Work in Machinery and Mill
Work 8yo, 3 oo
Animal as a Machine and Prime Motor, and the Laws of Energetics . I2mo, i oo
Tillson's Complete Automobile Instructor i6mo, i 50
Morocco, 2 oo
Warren's Elements of Machine Construction and Drawing 8vo, 7 50
Weisbach's Kinematics and the Power of Transmission. (Herrmann
Klein.) 8vo, 5 oo
Machinery of Transmission and Governors. (Herrmann Klein.). .8vo, 5 oo
Wolff's Windmill as a Prime Mover 8vo, 3 oo
Wood's Turbines 8vo, 2 50
MATERIALS OF ENGINEERING.
* Bovey's Strength of Materials and Theory of Structures 8vo, 7 50
Burr's Elasticity and Resistance of the Materials of Engineering. 6th Edition.
Reset 8vo, 7 30
Church's Mechanics of Engineering 8vo, 6 oo
* Greene's Structural Mechanics ..8vo, 2 50
Johnson's Materials of Construction 8vo, 6 oo
Keep's Cast Iron 8vo, 2 50
Lanza's Applied Mechanics 8vo, 7 50
Martens 's Handbook on Testing Materials. (Henning.) 8vo, 7 50
Maurer's Technical Mechanics 8vo, 4 oo
Merriman's Mechanics of Materials 8vo, 5 oo
* Strength of Materials 121110, i oo
Metcalf's Steel. A Manual for Steelusers i2mo, 2 oo
Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 oo
Smith's Materials of Machines I2mo, i oo
Thurston's Materials of Engineering 3 vols., 8vo, 8 oo
Part II. Iron and Steel 8vo, 3 50
Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their
Constituents 8vo, 2 50
14
Wood's (De V.) Treatise on the Resistance of Materials and an Appendix on
the Preservation of Timber 8 VO> a oo
Elements of Analytical Mechanics 8vo, 3 oo
Wood's (M. P.) Rustless Coatings; Corrosion and Electrolysis of Iron and
Steel 8 VO> 4 oo
STEAMENGINES AND BOILERS.
Berry's Temperatureentropy Diagram izmo, i 25
Carnot's Reflections on the Motive Power of Heat. (Thurston.) I2mo, i 50
Creighton's Steamengine and other Heatmotors 8vo, 500
Dawson's "Engineering" and Electric Traction Pocketbook. . . .i6tao, mor., 5 oo
Ford's Boiler Making for Boiler Makers i8mo, i oo
Goss's Locomotive Sparks Svo, 2 oo
Locomotive Performance , 8vo, 5 oo
Hemenway's Indicator Practice and Steamengine Economy tamo, 2 oo
Button's Mechanical Engineering of Power Plants 8vo, 5 oo
Heat and Heatengines 8vo, 5 oo
Kent's Steam boiler Economy 8vo, 4 oo
Kneass's Practice and Theory of the Injector 8vo, i 50
MacCord's Slidevalves 8vo, 2 oo
Meyer's Modern Locomotive Construction 4to, 10 oo
Peabody's Manual of the Steamengine Indicator lamo, i 50
Tables of the Properties of Saturated Steam and Other Vapors 8vo, i oo
Thermodynamics of the Steamengine and Other Heatengines 8vo, 5 oo
Valvegears for Steamengines 8vo, 2 50
Peabody and Miller's Steamboilers 8vo, 4 oo
Pray's Twenty Years with the Indicator Large 8vo, 2 50
Pupin's Thermodynamics of Reversible Cycles in Gases and Saturated Vapors.
(Osterberg.) I2mo, i 25
Reagan's Locomotives: Simple, Compound, and Electric. New Edition.
Large 12010, 3 50
Sinclair's Locomotive Engine Running and Management I2mo, 2 oo
Smart's Handbook of Engineeririg Laboratory Practice I2mo, 2 50
Snow's Steamboiler Practice 8vo, 3 oo
Spangler's Valvegears 8vo, 2 50
Notes on Thermodynamics .'i2rao, i oo
Spangler, Greene, and Marshall's Elements of Steamengineering 8vo, 3 oo
Thomas's Steamturbines , 8vo, 3 50
Thurston's Handy Tables r 8vo, i 50
' Manual of the Steamengine ; 2 vols., 8vo, 10 oo
Part I. History, Structure, and "theory. 8vo, 6 oo
Part H. Design, Construction, and Operation 8vo, 6 oo
Handbook of Engine and Boiler Trials, and the Use of the Indicator and
the Prony Brake. 8vo, 5 oo
Stationary Steamengines 8vo, 2 50
Steamboiler Explosions in Theory and in Practice I2mo, i 50
Manual of Steamboilers, their Designs, Construction, and Operation. 8vo, 5 oo
Wehrenfenning's Analysis and Softening of Boiler Feedwater (Patter'sdn) 8vo, 4 oo
Weisbach's Heat, Steam, and Sterimengines. (Du Bois.) .8vo, s oo
Whitham's Steamrenglne Design. .'. 8vo, 5 oo
Wood's Thermodynamics, Heat Motors, and Refrigerating Machines . . .8vo, 4 oo
MECHANICS AND MACHINERY.
Bur's Kinematics of Machinery 8ro, a so
Bovey's Strength of Materials and Theory of Structures 8vo, 7 50
Chase's Th Art of Patternmaking. xamo, a 50
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Spangler, Greene, and Marshall's Elements of Steamengineering 8vo. 3 oo
Thurston's Treatise on Friction and Lost Work in Machinery and Mill
Work 8vo, 3 oo
Animal as a Machine and Prime Motor, and the Laws of Energetics. 1 2mo, i oo
Tillson's Complete Automobile Instructor i6mo, i so
Morocco. 2 oo
Warren's Elements of Machine Construction and Drawing. , 8vo, 7 50
Weisbach's Kinematics and Power of Transmission. (Herrmann Klein.). 8vo. 5 oo
Machinery of Transmission and Governors. (Herrmann Klein. ).8vo. 5 oo
Wood's Elements of Analytical Mechanics 8vo, . 3 oo
Principles of Elementary Mechanics I2mo, i 25
Turbines 8vo, 2 50
The World's Columbian Exposition of 1893 4 4 <>> *
MEDICAL.
* Bolduan's Immune Sera 12mo, 1 50
De Fursac's Manual of Psychiatry. (Rosanoff and Collins.). . . .Large I2mo, 2 50
Ehrlich's Collected Studies on Immunity. (Bolduan.) 8vo, 6 oo
* Fischer's Physiology of Alimentation Large I2mo, cloth, 2 oo
Hammarsten's Textbook on Physiological Chemistry. (Mandel.) 8vo, 4 oo
LassarCohn's Practical Urinary Analysis. (Lorenz.) r2iro, i oo
* Fault's Physical Chemistry in the Service of Medicine. (Fischer.) . . . . i2mo, i 25
* PozziEscot's The Toxins and Venoms and their Antibodies. (Cohn.). I2mo, i oo
Rostoski's Serum Diagnosis. (Bolduan.) I2mo, . i oo
Salkowski's Physiological and Pathological Chemistry. (Orndorff.) 8vo, 2 30
* Satterlee's Outlines of Human Embryology lamo, i 25
Steel's Treatise on the Diseases of .the Dog 8vo, 3 50
Von Behring's Suppression of Tuberculosis. (Bolduan.) lamo, i oo
Woodhull's Notes on Military Hygiene i6mo, i 50
* Personal Hygiene izrno, i oo
Wulling's An Elementary Course in Inorganic Pharmaceutical and Medical
Chemistry iamo, 2 oo
METALLURGY.
Betts's Lead Refining by Electrolysis. (In Press.)
Egleston's Metallurgy of Silver, Gold, and Mercury:
Vol. I. Silver 8vo, 7 30
Vol. n. Gold and Mercury 8vo. 7 So
Goesel's Minerals and Metals: A Reference Book i6mo, rnor. 3 oo
* Iles's Leadsmelting I2mo, 2 50
Keep's Cast Iron 8vo, 2 50
Kunhardt's Practice of Ore Dressing in Europe 8vo , i 50
Le Chatelier's Hightemperature Measurements. (Boudouard Burgess. )i2mo, 3 oo
Metcalf's Steel. A Manual for Steelusers 12010, 2 oo
Miller's Cyanide Process lamo, i oo
Minet's Production of Aluminum and its Industrial Use. (Waldo.). , . . I2mo, i 50
Robine and Lenglen's Cyanide Industry. (Le Clerc.) 8vo, 4 oo
Smith's Materials of Machines I2moi i 6b
Thurston's Materials of Engineering. In Three Parts 8vo, 8 eo
Part II. Iron and SteeL 8vo, 3 50
Part HI. A Treatise on Brasses, Bronzes, and Other Alloys and their
Constituents 8vo, 2 50
Ulke's Modern Electrolytic Copper Refining 1 . 8vo, 3 oo
MINERALOGY.
Barringer's Description of Minerals of Commercial Value. Oblong, morocco, 2,50
Boyd's Resources of Southwest Virginia. , . ...8wo, i 3 oo,
17
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X 5
Chester's Catalogue of Minerals. g v o, paper, i o
Cloth, i 2
Dictionary of the Names of Minerals gvo, 3 5
Dana's System of Mineralogy Large 8vo, half leather, 12 5
First Appendix to Dana's New " System of Mineralogy." Large 8vo, i o
Textbook of Mineralogy g vo
Minerals and How to Study Them i2mo,
Catalogue of American Localities of Minerals. . . ' Large 8vo, i o
Manual of Mineralogy and Petrography lamp 2 o
Douglas's Untechnical Addresses on Technical Subjects I2mo, i o
Eakle's Mineral Tables 8vo, i 2
Egleston's Catalogue of Minerals and Synonyms gvo, 2 5
Goesel's Minerals and Metals : A Reference Book rbmo.mor. 30
Groth's Introduction to Chemical Crystallography (Marshall) I2*mo, i 2
Iddings's Rock Minerals gvo, 5 o
Johannsen's Key for the Determination of Rockforming Minerals in Thin
Sections. (In Press.)
* Martin's Laboratory Guide to Qualitative Analysis with the Blowpipe. lamo, 6
Merrill's Nonmetallic Minerals. Their Occurrence and Uses 8vo, 4 01
Stones for Building and Decoration gvo, 50
* Penfleld's Notes on Determinative Mineralogy and Record of Mineral Tests.
8vo, paper,
Tables of Minerals svo,
* Richards's Synopsis of Mineral Characters iamo. morocco,
* Ries's Clays. Their Occurrence. Properties, and Uses gvo, 3 <
Rosenbusch's Microscopical Physiography of the Rockmaking Minerals.
(Iddings.) gvo, 5 01
* Tillman's Textbook of Important Minerals and Rocks .8vo, 2 01
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MINING.
Beard's Mine Gases and Explosions. (In Press.)
Boyd's Resources of Southwest Virginia 8vo,
Map of Southwest Virginia Pocketbook form,
Douglas's Untechnical Addresses on Technical Subjects i2mo,
Eissler's Modern High Explosives .8vo
Goesel's Minerals and Metals : A Reference Book i6mo, mor.
Goodyear's Coalmines of the Western Coart of the United States i2mo,
Ihlseng's Manual of Mining 8vo,
* Iles's Leadsmelting i2mo,
Kunhardt's Practice of Ore Dressing in Europe 8vo,
Miller's Cyanide Process I2mo,
O'Driscoll's Notes on the Treatment of Gold Ores 8vo,
Robine and Lenglen's Cyanide Industry. (Le Clerc.) 8vo,
Weaver's Military Explosives 8vo,
Wilson's Cyanide Processes i2mo.
Cblprination Process '. umo,
Hydraulic and' Placer Mining, ad edition, rewritten izmo,
Treatise cm Practical and Theoretical'Mine Ventilation tamo,
3 o
2 o
1 o
4 o
3 01
2 5'
5 01
2 5<
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2 Ol
4 01
3 01
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SANITARY SCIENCE.
Bashore's Sanitation of a Country House umo,
* Outlines of Practical Sanitation isrno,
Folwell's Sewerage. (Designing, Construction, and Maintenance.) 8vo>
Watersupply Engineering .8vo,
18
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I
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Towler's Sewage Works Analyses _ ^ i2mD, 2 oo
JFuertes's Water and Public Health. .f .T. A . ! I2mo, r 50
Waterfiltration Works i2mo, 2 50
Gerhard's Guide to Sanitary Houseinspection i6mo, i oo
Sanitation of Public Buildings I2mo, 1 50
Hazen's Filtration of Public Watersupplies Svo, 3 oo
Leach's The Inspection and Analysis of Food with Special Reference to State
Control , .8vo, 7 50
.Mason's Watersupply. (Considered principally from a Sanitary Standpoint) Svo, 4 oo
Examination of Water. (Chemical and Bacteriological.) 12010, i 25
* Merriman's Elements of Sanitary Engineering Svo,, 2 oo
Ogden's Sewer Design i2mo, 2 oo
Prescott and Winslow's Elements of Water Bacteriology, with Special Refer
ence to Sanitary Water Analysis i2mo, i 25
* Price's Handbook on Sanitation 12010, i 50
.Richards's Cost of Food. A Study in Dietaries i2mo, i oo
Cost of Living as Modified by Sanitary Science 12010, i oo
Cost of Shelter 12010, i oo
Richards and Woodman's Air. Water, and Food from a Sanitary Stand
point Svo, 2 oo
* Richards and Williams's The Dietary Computer Svo, i 30
JRideal's Sswage and Bacterial Purification of Sewage Svo, 4 oo
Disinfection and the Preservation of Food 8vo, 400
Turneaure and Russell's Public Watersupplies Svo, 5 oo
Von Behring's Suppression of Tuberculosis. (Bolduan.) 12 mo, i oo
Whipple's Microscopy of Drinkingwater 8vo, 3 So
Wilson's Air Conditioning. (In Press.)
Winton's Microscopy of Vegetable Foods Svo, 7 50
Woodhull's Notes on Military Hygiene iCmo, i 50
* Personal Hygiene I2mo, I oo
MISCELLANEOUS.
Association of State and National Food and Dairy Departments (Interstate
Pure Food Commission) :
Tenth Annual Convention Held at Hartford, July 1720, 1906.... Svo, 3 oo
Eleventh Annual Convention, Held at Jamestown TriCentennial
Exposition, July 1619, 1907. (In Press.)
Ummons's Geological Guidebook of the Rocky Mountain Excursion of the
International Congress of Geologists Large Cvo, i 50
IFerrel's Popular Treatise on the Winds .8vo, 4 oo
Gannett's Statistical Abstract of the World 24010. 75
Gerhard's The Modern Bath and Bathhouses. (In Press.)
Haines's American Railway Management I2mo, 2 so
Ricketts's History of Rensselaer Polytechnic Institute, 18241894.. Small Svo, 3 oo
Rotherhara's Emphasized New Testament Large Svo, 2 o o
Standage's Decorative Treatment of Wood, Glass, Metal, etc. (In Press.)
The World's Columbian Exposition of 1893 4to, i oo
Winslow's Elements of Applied Microscopy I2mo, i 50
HEBREW AND CHALDEE TEXTBOOKS.
Green's Elementary Hebrew Grammar I2mo, i 25
Hebrew Chrestomathy 8vo, 2 oo
Gesenius's Hebrew and Chaldee. Lexicon to the Old Testament Scriptures.
(Tregelles.) Small 4to, half morocco 5 oo
Letteris's Hebrew Bible ' .8vo, 2 25
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