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Thermodynamics of the Steam-engine and other 

This work is intended for the use of students in 
technical schools, and gives the theoretical training 
required by engineers. Fifth Edition, Rewritten, 
vi + 633 pages, 117 figures. 8vo, cloth, $5.00. 
Tables of the Properties of Steam and other 

Vapors, and Temperature-Entropy Table. 
These tables were prepared for the use of students 
3n technical schools and colleges, and of engineers in 
general. Seventh Edition, Rewritten. 8vo, vi + 130 
pages, cloth, $1.00. 
Valve-gears for Steam-engines. 

This book is intended to give engineering students 
instruction in the theory and practice of designing 
valve-gears for steam-engines. Second Edition, 
Revised and Enlarged. 8vo, v 4- 142 pages, 33 fold- 
ing-plates, cloth, $2.50. 

By Prof. Cecil H. Peabody and Prof. Edward F. 
Miller. Nearly 400 pages; 142 illustrations. 8vo, 
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Manual of the Steam-engine Indicator. 

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>O I J 

'. ^C' 

COPYRIGHT 1889, 1898, 1907 



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 steam-turbine has changed adiabatic 
calculations for steam, from an apparent academic abstraction, to 
a common necessity. To meet this changed condition, the Tables of 




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 steam-turbine. 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 blast-furnace gas. A chapter is given 
on the thermodynamics of the steam-turbine 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 steam-engine, steam-tur- 
bine, compressed-air and refrigerating machines, may be read 
separately in the order that may commend itself. 


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 text-books, either in substance or in manner q 
presentation, and may require a few words of explanation. 

The general theory or formal presentation of thermodynamic 


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 steam-engine. 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 compressed-air 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 foot-notes, to aid in more extended investigations. 
It does not appear necessary to add other acknowledgment of 



assistance from well-known authors, further than to say that 
their writings have been diligently searched in the preparation 
of this book, since any text-book must belargely an adaptation of 

their work to the needs of instruction. 

C. H. P. 

May, 1889. 


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 text-book. 

C.H. P. 

July, 1898. 


























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 steam-engine 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 

As an example, we have from the combination of the laws of 
Boyle and Gay-Lussae the general equation for gases, 

pv RT, 

in which f is the pressure, v is the volume, T is the absolute 
temperature by the air-thermometer, 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 no-called first and second laws of 
thermodynamics, which will be stated and discussed later. 


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 


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 steam-engine 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. 


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 freezing-point 
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 


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 boiling-point of water. A centigrade thermometer 
has the volume of the stem between the reference-points divided 
into one hundred equal parts called degrees. The Fahrenheit 
thermometer differs from the centigrade in having one hundred 
and eighty degrees between the freezing-point ;md the boiling- 
point, and in having its zero thirty-two 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 air-thermometer, 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 
air-thermometer. To gel a conception of what is meant by this 
expression we may imagine the air-thcrmomctcr 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 freezing-point 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 


shown later that there is reason to suppose that the absolute- 
zero of temperature is 273 centigrade below the freezing-point 
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. 


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 air-thermometer 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 


Graphical Representation of the Characteristic Equation. 
Any equation with three variables may be represented by ft. 
geometrical surface referred to co-ordinate axes, of which surface 
the variables arc the co-ordinates. In the case of a perfect gas 
which conforms to the equation 

pv = RT t 



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 co-ordinate 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 Gay-Lussac. 

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 steam-engine 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 reference-points on the thcrmometric scale; 
this is especially true for air, Rut ihe properties of water change 
rapidly at and near freezing-point 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- 

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 


If the specific heat varies the amount of heat must bo oi 
by integration that is, 

Q - fcdt, 

and conversely 



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 = 


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 


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; 


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 


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 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 light-haml 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 



and consequently we may write 


which substituted in equation U) gives, 

c v (!l -I- 




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 


. Sv ,,\ 

,'. c p ** c 9 -\- i -jr (0) 

Also, equating the remaining 


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, 

+ m 4, = e > 

= c n 



From equations (2) and (3) 

c p dt + mdp = fw 


and from an equation 


which latter substituted in equation (11) gives 

t, j ' JA i J 

p &V O/> 

Equating coefficients of dv, 

C = Cn R 




Finally, from equations (i) and (3), 

c v dt -h Itlv ='iidf -t- odv (13) 

Substituting for dt as above, 


-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 


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. 



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 well-deter- 
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 foot-pounds 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 foot-pounds. 

i calorie -126.9 metre-kilograms. 

This physical constant is commonly represented by the letter 
/; the reciprocal is represented by A. 


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 


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 


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) 


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 fluid-pres- 
sure; consequently 

rflK- pdv 



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 / 


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 so-called 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 tracing-point 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 



= p I 


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 tracing-point 
moves from a t to o a . The temperature usually 
increases meanwhile. Since dv is zero, 




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 non-conducting 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 air-com- 
pressor or a compressed-air engine are very nearly adiabalic. 
Adiabalic changes never occur in the; cylinder of a steam-engine 
on account of the rapidity with which aleam is condensed on or 
vaporized from the cast-iron walls of the cylinder. 

Since Ihcrc is no transmission of heal to (or from) ihc working 
substance, equation (19) becomes 


, ~f- / ' fitto) 




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 or|iuuion. 

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 Gay-Lussac, 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 


umi.a. jjt-giiiiinig 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 





v ) 






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 

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 


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 


Heat-engines 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 heat-engines 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 steam-engine arc 
he furnace and the condenser. The boiler is properly con! 


to cliscuss a 

Pro. ro. 

v .,-._.... ^M.iuui with non-conducting 

s fitted a p,ston, also of non-conducting 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 


(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 a-ABb, be the external work, the 
hca( received from A will be 

Flo . . 

Q-A (>- 

( 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 

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 


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 heat-engine 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 smoke-box, 
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 smoke-box injure the surfaces of the valves and 
cylinders. Some locomotives have been arranged so that the 
exhaust-nobles can be shut off and steam and water supplied 
to the exhaust-pipe, 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, 


(?* - (? - (?* 

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>X-f 1'\ V *f* 4 J ( Tl f~* J "*/*' t i 

or A]tCl'CJ)hCrA) or, ngain, ABCJ'UA -f- 

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. 



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 



Q - Q 



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 

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 self-acting 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- 

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 


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 belwcc-n 
such n scalp of temperature and the scale of the air-lhcnnomcter 
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 freezing-point. 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- 
ing-poinl to boiling-point. 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. 


The absolute- xcro is consequently 273 C. below frccxing-poinl. 
VuruVr discussion of the ubsohile scale will be deferred till 
a comparison is made with the air-thermometer. 

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 


upward, and if adinbnlics ft re spuci-d 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'm-nccK 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 bt-nealh 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 non-conducting 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 




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 

tlO <ll 

ii . i 

Q V 

or, integrating between limits, 




and the efficiency for the cycle becomes 



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 rt-it- 
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 heat-engine. 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. 



BC. First it will be shown that all the srmill arc-as 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 fool-pounds 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 inn-paw** 
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 (T-r) w - </>) r - 

-"- J- - v_ j . . 




as found by equation (35). The deduction of this 
integration is more simple and direct, but the uraphlcnl 

* * n i ^ 



I-' HI. 31. 

is interesting and may give the student additional light on (hi.s 

Temperature-Entropy Diagram. Thermal diagrams are com- 
monly drawn with pressure and volume for. (he co-ordinates, 
but for some purposes il is convenient to use other properties 
as co-ordinates, 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 lure-entropy 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) 


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. 


which should for any particular case either be integrated 
between limits or else a constant of integration should be 

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 




" 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 



- 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 
u-ork. ,Sup|KWt' 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 tntciriK-poim 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 non-reversible. The cycle represented by Fig. 23 in purposely 
drawn like a sieam-cngine 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 



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 

o-Q' _ T - r . Q 








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, 




Fig. 25 represents the simplified ideal diagram of a hot-air 
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- 



jcctccl at 20 C., the combined dlinumy of the diagram 
computed to be 



3 5 'I' 2 73 3 


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 " 

Non-reversible Cycles.-- If a process or a cycle is non-re 
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 



i < 



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, 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 non-reversllilc 
engine had a greater eflu-ienry than a n-vcrsiblc engine working 
between the same lemperalures. 

Some non-reversible operation*, like the /low of gus through 
an orifice, result in the development of kinetic energy of motion. 
In such 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 non-concluciing 
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 non-reversible 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. 


A non-reversible operation in non-conducting 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, thm-forc*, ctl 
possible to represent any changes of a fixed weight f w. 
stance, by a diagram drawn with temperatures and ertlf 
for co-ordinates. 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. 



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 



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 gctm-al 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 iiu-iliod, 
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 In-furr 
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 ct-riuin 
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 u-mji 
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 parlii-ulur chiiraclerisiir equation, ami for that reason, it 
nit ilu:r, the Ainu of (lie inu-gral equation connecting K with 
fiindiu-iinnul 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 

Application of the First Law. ..... - The first Kctienil principle 

may be lulu-n u> be rrprcsi-nli-;! by njuutiuu (i), 

inul ilu- law of lluTmodyiiiunicH by t-ciuation (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 


U h cvltlcni tlmt 

Now equation (,|,|) Is an abbreviated way of writing Iho 
for continun] tllRcrvnilm'wn which may be expanded 




or replacing the first pnrtial clilTcrenlial coefficients by 




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 


Making use of Ihc equation 

v * 




Uui llu- ithhum|ii(oti of u diimu-U-riHiii 1 . ajvmtitm c 
f>, Vt ami / uirrii-s willi ii ilu- usHumpliun llmL 


in, fnnii tc|uiiluih (.0 \vi* tntiy have 

tl{> - A ((//; | {Hlr} - ml ft ! tnlv. 


Appllcfliion of Iho Second Law. Tin 1 ht-itnu! inw of 
clynnmici inn be cxprfwii'il liy ctjuwlion (.^H), PHKC 37i 

T 1 '^ 
J ^ 


which rmikrm -* (trdtfi n t*xit<( dirfcrc-nlln), i that we may 

$v> ^v- 

' Daa _ "* . 

'I'd prrpnrr rt|imi[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 




T \8v/f ~YS 

' 8 A ~ ( Sc \ i 

W. UvA" T 



( 2 ) we haw 


m, from cquation 


First and Second Laws Combined _Th 

th the first and thc sccond -- To 

to the 


iilioriK (1)1 ('*), nnd (3) may la- oUainrd hy ctimliinin^ ilu- 
ei|iuuinns rmillmtf from tin- application nf llu- laws M-purtiU'ly. 
Thus ^illations (-15) ami (.|c)) give 

' ' 



and (so) uiv 
t ' 

i tu 





ft is uitwiuVnl tn [ntn-f(irin thU fa^l ri|iialinn Ity L 
valuta of n and ti front pii^r i j, yu-ldiiij! 

The- rquntirin* (lctlticcl in tlin tliuptrr uluiw tlu- rt 
rctatiunn aiming lilt 1 lluTinal Mipmilin if llu- U\VH of llirnno 
dynarniri rr nur|i(rd, Simtr itf iltrin, nr rttu.-iliunn rlnltiinl 
freim llu-m, liavi* IKTH MH| liy wrllrrt un ihrriiUHlyimitiut in 
(-HlahlKli rrkilinn*! nr (ini|HHr Jirtiprrlir-, llml i-iniu.l In- rnitlily 
olilaincd liy dim l r*|K'rinu'm*>. 

i-'tir llic niudt-nl familmriiy with the jir<nr^*-. ii nf murv 
imptirlitnrr ny nf \\w rriulu. 

Alternntlve Metlmtl. Stunr uriirr* cm ilu-rrtHKlynnmlt^ rr 
HTVC iln- di-it ii'rtjcin of ifn|H-T(iiiirt' until tin.-) arc rt-ady tu 
dflinc- (if ii'^umr nil al^nluti- wtilr jtidt'|wndrni nf liny it 
iinil dt-pindiri^ unly nn tttr hinduim-mal unit, nf length 
wri|(|il. Hf tin- ihrrr i-rllrral ri|unliimi (i), (j), and (0 lhr\ 
Uhf ill lirAt tmlv tin- latter : 



No\v from equation (16), representing the first law of thermo- 

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 


may be integrated directly; we may then consider that we have 
a scries of thermal lines represented by making 


; const., etc. 


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 



heat Q during the operation AJi t and reject- 
ing the heat Q' during the operation CD, will be 



(10 . 

But - is an exact differential, and depends on the state of 


the substance only, and consequently is the same at the end as 
at the beginning of the cycle, so that for the entire cycle 


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 


*= s = o, 
S S' 

.0-0' 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, 


-^, + g* 

so that 

n BE o BE 

A~Sj' A-*7 
These properties Zcuner writes 


Solving equation (54) first for o and then for w, 



= w~ 

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, 


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. 



THE characteristic equation for a perfect gas is derived from 
a combination of the laws of Boyle and Gay-Lussac, 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. 

Gay-Lussac's Law. It was found by Gay-Lussac that any 
volume of gas at freezing-point 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 air-ihcrmomclcr, and the law therefore 
asserts that the expansibility or the coefficient of dilatation of 
perfect gases is the same as that of air. Gay-Lttssac's law may 
be expressed by the equation 

v- v c (i + a/) (57) 

in which v is the original volume at freezing-point, 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 freezing-point. 




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- 


-f- /) ^ 

- (5 s ) 

If it he assumed that a KIW conirucls a- purl (if its volume ut 
freexing-point for each degree of tempuniture below free/an^ 

then the ulj.solule xern of the ir-ll)ermomi'U.'r will be -degrees 
below freezing, and 

may be replaced Ijy T, Llio absolute icmpcrnlurc b) r the air- 

The usual form of the characteristic equation for perfect 
gases may be derived from equation (58) by fuibstltuting T , 

the absolute temperature of freezing-point, 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 



' r 1 



Absolute Temperature. Recent investigations of the prop- 
erties of hydrogen by Professor Cullender* indicate that the 
absolute zero is 273.! C. below freezing-point. 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 30-3? 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 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. 



Specific Volumes of Gases, --I'rom rm*m (Iclcrminiilioiw of 
(Icnttilit's of KIISC.X by Li-due, Mnrlcy, untl Kiili'igh il appears tlitil 
[he most probable values of UK- specific volume of the i-onimuna- 

ses ii rr 


AimospliL-rit air ....... .... 

Oxygen .... 

1 1 . ? 33 

: Tin- correspond! UK (juanlilies fur Kn^li-h unit* an- ^iveii in 

^ tin- ne.xt (able. 

VOI.UMKS IN rnnr I-\-:KT <H- ONI: 
Aimctsphrrir air . ........ 

i j . 31; 
178. a 

To iht'si- may In- addi'd tin- valw for uirlion tlioxitlt 1 , 0.506 
culm- mi'lri: per kiltigrnm r t-ubir feel per pound; but 
us llic cHiic/il u-mfM'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- n|imliim for ti giiH iTpn-HrniH thu 

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. 


Solution of Problems, Many problems involving the proper- 
tics of air or other gases may be solved by the characteristic 

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 gftuge-prcssurc and at 100 F. Assuming a 
barometric pressure of 14.7 pounds per square inch, 

V tea 

S.V3S (450.5 'I- TOO) 
(1,1-7 + 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 
volume at 200 C. and at 10 atmospheres. Here 

i X 2 

10 V 

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 


.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 N|uri;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[ llu-rmodynanii(s lo a 
jierfecl gas, and also wilh a delerminiilion from ihr theory of 

SL-s 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 u-ilJumi ftny refcrc-na- (o Ilic law of 

Application of tho Laws of Tliormodyimmlcs. The prrrcd- 
in^ slutcmenlH concerninij; the Mpefific IICIUM iif [K-rfrci KIIHCA 
and their ratio would be alisfaclory were it delinilely deli-nnined 
by experiment, llwl the Hjiecific heal al con.slanl volume is IIH 
nearly constant na in the wptrilk' lu-til ut conslnnl preswire. 
None of the experimental delerminalions (not i-ven ihm by July ^:) 
din be considered as wtlbfiictory us Llu ML* for tlie speciCu heal 
ill conRlftnt prt'ssucc; roji.ser|tii'jnly iJicrt- is romnVlrrnbU' !m|>nr- 
lancu lo be attached to the application of the laws of thi-rmn- 
dynamics lo the (.'linrui'irrhtic equitlion for a jierfect HHH, and, 
moreover, this applicalinn furnislu-s 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, ). 



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 




.'. c,, 


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/wlierc-A/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 


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 

} f lL t f c \ , ., L t, .... , \ tr } f } ) 

' ' n t f /' 'i'> .. I'/' ''' ' \ UI V 





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, 



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\ - /), 

^' " ^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. 


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 frcexinx-polnt 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 foot-pounds. 



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 gauge-pressure. 

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 


V rr. 1 1 1 

' /'') l> 

or, .sulxslUulinK 

r l 

from equation (d,\ 
^ , ( . | 



A comparison of ec|imtion (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* lu-ul applied 
is chunRud into exlernul work, m> thill ihe intrinsic i-iu-rgy IK nni 
dmttgc'd. This ccincluslon i Imsc-d 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 jjlvi-s 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 





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 non-conducting 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 


' -&6.) 


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 


*- EH) 


so that 



T.v.*- 1 

* \ v [ 


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 


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 


M'7._XMfl X 

231140 fool-pounds, 



which Is considerably less than the work for tliu t-orres 
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: u-rm tc 
(00.405; if It bo admitted that (he 1 Jnst figure Is um-crirflft to 
oxlont of two iinllSj the error of calculation In-cmmcM half a 

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 


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 Hi-ldoni 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 isotlu-rmul 


Change of temperature during such an expansion may be 
calculated by the equations 



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 = 74-7, 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 



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 i-ntrupy 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 prt-Hsure 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 u-mpi'niluiv of i.,0F rit 
initial condition. As has nlruidv been suid, there is sold 
occasion in practice Tor usin^ UK- i-mropy f n K , !S . 

Comparison of the Alr-Thermomoter 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- HmrarK-nstir vt[Wl \i on O n 
assumption that the scale of the air thmno.m-U,- coincides 
inc^hcrmodynnmic scule, and it alTords a delicate method 
esung the (ruth of the characteristic equation, and of compat 
the two scales. 


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 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 i-lmn^e of temperature 
iminuU'il a dfviiiliiui fiin the ii^siimjilions of tin- ilu-ory 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 lempi-ratnrc of fi-ei'/in^-poinl 
JT^.'j C 1 , As the rrrtiili nf Inter exju-rimentst llicy Hinlecl that 
iht- KKilinw for a ttilferem-e of pressure uf 100 inches of mercury 
wits reprehemeil cm llu- lenliKracle wulc by 

From tliesc- expt-rinuMUH mid from other t'onHidi-mlionH con- 
cerning the i-nnMnni volume liyctroKc-n ihernuimelcr, I'rofcsBor 
Cidlendiir IIRH clflvrniinrd llml the nuwl prnbiiblf value for the 
aliM.lulc lenipiTiilnre of fnx-2lnf{ point !H yjjp.i C'., an nlrcotly 
Kivrii, iind nlvt' a liible <tf currc'ellnns (n the hydrogen liter- 
nuimt-HT 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. 



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 

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 


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 temper-own?. 
* Phil, Trans., t%(*>. pnrt !i, p. 573 , nml ifyd, jmri II, p. ,, 3( . 


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. Su|N-rhfutrrl vn|ir * luinifiiTunl hy u lurm'P vulumi- limn 

uilui';U(-il wi|ir fur 11 ((ivni tcnuH-ruHin 1 itiut proKsuri-. 
,|, t'tiin; near ilu* iriilml U'm|nTaluri' llu- ilrvlnllunH from 
llm-IrS Uw rr very liir^c, l lu^litT (t-inprrfiturc (he 
iU'iiiifiun-i iliminKh ami lirnuni- uniin|iiiriaiil. 
Critical Tmu|){milur<-'i, Tin- fulluwin^ Inltlr nf i rilkal 
Irnt)HTiUtirr'> ami uf Utility (HIJIIH nl ninio-tplu-rli prcvuirr h 
Ukfii in | ',u i friim t'rrMnn'?! "'I'hrnry *>f Unit," ny.*.\, 


.' I' 


Sulphur tlin 

KlIltT . 



I f HI {n 4 

h Fri^aure. If ihr ihtul mcilu&h (Klwn on 
fur llir .iiluUMii sif prntilrm* InvnlvliiK ihr proprrllei 
air <i|j<l(Yl with vrry hifjh prcvturc, rrrr nmotintin^ 
In UVH nr ihrrr |-f irni wrr li(ilj|t' (u U- inturml, uwlitg lu I he 
[|r\int!im from |tn>lr\ Uw. In Hmr iawn, ihU crrnr may lie 
if,flnrnl in r-tiginrrrinK 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,, 


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 


IJI .. 

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; amm|iicn(ly 


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 slop-cock 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. 



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 

6, A gas-receiver 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. 6-|f)<| fool-pounds. 

9. Whal would have been the external work had Ihe air 
expanded ntliabalically? AIIB. 4450 fool-pounds. 



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 fool-pounds. 

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- 

15. Find the intrinsic energy of one pound of nitrogen undfif 
the standard pressure of one atmosphere and at frcczlng-palNt 
of water. Ans. 66,500 foot-pounds. 

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 foot-pounds; .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 



increase of intrinsic energy 1,420,000 foot-pounds; increase in 
entropy 3.29; heat 2570 JI.T.U. 

20. Suppose a hot-air 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 horse-power if the engine is doublc-acling and makus 30 
revolutions per minute. Ans. 8.3 horse-power. 



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!. 



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 |KIUIU|H [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 


. 7^3076 


\og i o-oau-IS^l 

ft at I J|J 

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; 






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 

y. 13751 Ho 









T. 0011907 


/ -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~ 5,3085-119; 

loj(/i(\" -l-o. 531 376(1 0.00361,18 (j 
logc/J" 0.96.15333 0.0315501 /. 

Differential CoefAclant '-f-. 


equation (94) we have 

mm the general form of 


>/ being the modulus of the common system of logarithms. 

7?, - 7T '' lf) K " "!- TT c lo K ^ ^"! 
put M M 

or, reducing to common logarithms, 


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 - 6-3493' - 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 sc|iuiro 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 


by dividing a small difference oC pressure by the corresponding 

difference of temperature; that Is, by calculating rr^. With tt 


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 

- o.ooiQHi / 1 a 0003701 0500515' 


wo.oojsHso I | -j.oGfiji 3,1-0.01.3 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 freexing-poinl 
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 wipor-s, 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 freezing-point 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 foot-pounds. 

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 freezing-point 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 one-tenth of 
one per cent. 





1 !.* lulllfJOH 












I .0094 




































o . 99806 




I6 7 


1 6O 

i So 


39 a 







" s 






* Physical Review, vol. xv, p. 71, 1903, 



Heat of the Liquid. The heat required to raise one unit of 
weight of any liquid from freezing-point 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 

Alcohol ............. 


Carbon bisulphide 
Carbon UilrnchlorHlc 

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 - I- o.oojj.ufi/ \ 

Total Heat. --This term in defined n* tl % lwl r|wat\ 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 ic-mporatura, 
The experiments made by Rt-gnnull wcrr in ll- rr verse onlotj 
that is, slenm wns U-cl from n \ioHcp into llw tflUmmeli-r and 
there condcnswl. Knowing the Initial nml final wrtghu of 
the calorimeter, the temperature of ihc nit-nm. nnil the initial 
and final temperatures of the water in llu- i-Jilnrimrlcr, 
able, after applying the m-ceswiry corriTtiunH. id 
lovn\ hciUs for the acvernl i-xpt-rimt-nis, 

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 ft|cclfc 
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 

fj-l + 0-45/ - o. 00055556 (' 

67 -1-0.1375* 

-I- o. i.\(>o\ t 0.0004133 /' 

52 -I- o.i,)6aj;( 0. 000172 / l 

Accton 11 => 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: 


Alcohol ..... 

Kihcr ....... 

Chloroform . . . . 

Carbon hlaulphklc , 

Sulphur dioxide . 




Specific Volume. 

with Wftlov 

nl < C. 

Cubic Meirei. 

Cubic Keel. 


o oat a<|O 


o. 736 

o 001350 

1-5 = 7 



o 00077,1 

l .6iao 




i.. 1336 









Experiments were made by Him* to determine me volumes 
of liquid at high temperatures compared with I he volume at 
freezing-point, by a method which was essentially to use them 
for the expansive substance of a thermometer. The results arc 
given in the following equations: 


Loja Hi Kntiit 

6.0361445 - 
.).. 1781868 - 

i..l5 B 3'Hfl " 


100 C. 10 200 C. 

(Vol. at 4 = unity.) 

v - i -I- 0.00010867875 / 
-H 0.0000030073653 (' 
-) 0.0000000387304331' 
0.0000000000066457031 /' 

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 /' 


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* 

0-7849494 - 

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' - 


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 + 


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-.iu|ji_-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 



so thai the above equation reduces to 


Application of the Second Law. - The second law ol thermo- 
dynamics makes 


for a reversible process, so that the general equation (103) may 
be reduced to 



Si ?' 

First and Second Laws Combined. -The combination oJ 
Uons (io. ( ) and (105) gives 


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 

T- (r~ Ar) AT 

'T "" 7' ' 

so that the heat changed into work will be 


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 = 




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 


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 KnnbUuu-h, 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). 

Hv Knoblauch, fjmlf, aiul Kiel*. 

Volmno On. M. 





i . -i i 3 

1. 674 


i, til 


1 20 







Volimia t"n. M. 




o . 50 j i 
o. ,1-105 
o . 3880 




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 

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 


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- 




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 



,1 2 76 


i . 30 


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, whrri-u|M4i 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 rx|-rimrntallyby 
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 cut-off 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 


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 freezing-point 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 freezing-point 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 freezing-point. 
It is customary to consider that 



-I- <?) 


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, 

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, 


The initial and final specific 


The converse problem requiring llir prt^urr KiriTH|K.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 rc|uniinn 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* cx|Kmrni 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 


> 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 




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 


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 



Tne nrst term ciin 
second term, which is small, nm be. delermined graphically, 
that the expression Tor entropy of water bmimes 



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- free-sing. 
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/mg-poinl 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%ing-poim of 
water may be obtained by aid of equation (113), which gives for 

ether with the French system of units, 


.52901 -|- 0,OOOS9l8 


0.0005918 r//); 

' ^=0-0005918 (T 1 - 373) + 0.3670 
.-. 0= 0.0005918 /-h 0.3670 log, 

.... ( M 6) 

For temperatures below the freezing-point 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 


',** 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- 
ing-point to the temperature; t and then vaporizing x portion of 
it is 


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 freezing-point, 

The change of entropy in passing from one stale to another 


'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. 



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 tht-r lw|iiWi will bo 
found on page 85. 

*V fl**itt^c, one pound of dry Mcnm 
pressure will have the values 

/ * K, r, - 884.0, C, - 


IE the final prcasurc is 15 pounds n 
(, - ai3.o I 1 '., r a 965.1, 






The initial and final volumes nre 



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 

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 non-conducting 

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, 




- ~ 

72.26.V. . 

' -- * -I- 

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 non-conduct- 
ing cylinder is accompanied by a partial vaporization. 



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 cliom-n, 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 non-conducting 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 

W - 778 (297.9 - 181.8 -I- i X Hoa.8 -. 0.894 X 
W - 120.2 X 778 - 93,500 fuot-imimcla. 

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 

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 indicator-diagram is instructive, since it shows 
to the eye Ihc difference between the expansion in an actual 
engine and that of an ideal non-conducting cylinder; but it can 

be iiHcingcnuy uruwn umj - ..... ...... -"- -" -^ 

general purposes ilic hyperbola w I he lit-sl 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 


Temperature-Entropy 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 



Via. ion. 

and the temperature-entropy diagram is* ihc equivalent of such a 
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. 


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 temperature-entropy 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 team-engines 
nnd steam-turbines. 

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 

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 

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 temperature-entropy 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. 

Temperature-Entropy 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 
steam-turbines, 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 temperature-entropy 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- 



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 ,1-39 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 

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. 



I. WftU-r HI loo I-', H fed in ei Uiilt-r 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 inrfiM-ir 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 - 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; H|MI the eslprnal wnr k f 
3,68 cubic feel and goto faai-pnumU. 

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*.; 




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 cut-off 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 cut-off 62.2 pounds by the indicator, 
and at release 0.2 pounds; the mixture in the cylinder at cut-oft 
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 cut-ofT 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- 



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 so-called 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 
right-hand 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 



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, 


centigrade Ihcrmomclcr. The constants have ihc following 

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 

/v-85.85 7 l -~/.(i-|-o.ooopo 97 6/o -0.0833 

The following equation may be used with ihc pressure in 
pounds per square inch ; 

/w-o. 5962 T-p (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. 



In the English system with the pressure in pounds per square 
foot and the volumes in cubic feel, for ubsoluie temperatures 

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). 


... . ., , 150,100,000 
Vnluva of llic forlnr -- -- o.ofljj. 














67-1 5 










a .15 

604 5 





















730 -5 


a ?5 










7-J9 -5 





T a nip oral ura. 








75') -5 











3 '5 








4 jn 







0.3 id 




0.31 t 












o. 105 




O. [1)0 



8 j.i. 5 





o. iSo 












o.i 66 




o. 163 





85'). 5 

811,. 5 


()0-| . 5 
()<.*) . 5 




o- 15.1 
o- 1. 10 
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 










070. S 


1010. s 



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 


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. 

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 cross-curves 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. 



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. 

Thomas and Short. 

1'rewure Lb. pet S(|, In. (Absolute.) 

Superheat Falir. 















o. 6.19 































o-55 f > 


















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 


+ 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- 


polation, as a small variation does not have a very large 

The total heat or heat .contents of superheated steam in the 
temperature-entropy 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 freezing-point 
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: 


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 


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 + 459-5 


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- <f59-5 

+ O -I- 459-5 

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- 

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- 
turc-cnlropy 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 


)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 lulu-n from 
c (cmpcmturc-enlropy inhle, nnd tlic quimiity 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 temperature-entropy 
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'ligmec-ring 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 fliipt-rhenUfl vn^Ktrs 
found in the approximate calfiiliilion of [troperiien of eerluin 
atilc liquids which arc uaetl in rcfrlKcrailng-machlnw, iintl for 
Ich we have not suflicienl txprrimrnial tlain loconalruct inhli-a 
Ihc manner explained in the chapter on saturated vaporn. 


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 and at atmospheric 

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 

p-nT-cf ./.... (125) 

proposed by Xcuner has commonly been used, and it is con- 
venient to admit that it may take the form 

- Cf 


* M&moires tie I'lnst'tlttt da France, tonic xxl, 
t PliysHtalische-clieinlsclie Tabellan. 
f Wall'a irnnstnifan, p. a8o. 


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 


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 right-hand 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. 



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. 


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. 


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 -t-i 


-I- .10 C. 

In which u ** s <r. 
The results arc 

t - 30 C. o 

r 106.9 w.Go 00-5'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 derivi-d by ihr fuUnwitiu 
device. First assume that llu- entropy of the Mipi-rltntlrd vn|Hir 
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 pt-rfeci 

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 


factor a, so that it may read 


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 

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 

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 


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 ting-machines 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 4a6-9 X 
and the coefficient of /* is 

5fr.3.><. a Lz 


so that the equation becomes 

pv - 54.3 T 



'* 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 1435-3 mm - of mercury, 

and at 8.i C. the ratio 



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 /? 9-99397 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 S-7 3-*5 277-5 

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, 


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 cut-off 
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 foot-pounds. 



THE steam-engine is still the most important heat-engine, 
though Its supremacy is threatened on one hand by the steam- 
turbine and on the other by the gas-cnginc. When of large size 
and properly designed and managed its economy is excellent and 
con be excelled only by the largest and best gas-engines, 
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 by-products. 

It can be controlled, regulated, and reversed easily and posi- 
tivelyproperties which are not possessed in like degree by 
other heat-engines. It Is interesting to know that the theory 
of thermodynamics was developed mainly to account for the 
action and to provide methods of designing steam-engines; 
though neither object is entirely accomplished, on account of 
the fact that the engine-cylinder 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 steam-engine 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 indicator-diagram from some actual engines, 
but it differs in essential particulars. 


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 ^ 

797-1 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: 



Initial Pressure 
by the Gauge, 
above the 




i-S bounds 




o. i8t) 
















The column lor atmospheric pressure may be used as a 
standard of comparison for non-condensing engines, and the 
column for 1.5 pounds absolute may be used for condensing 

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 



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 one-half, 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 one-half, 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 




ylinder at o; but there is no necessity for such assumptions, 
nd they in no way alTcct the efficiency. 

The temperature-entropy diagram (or Ounol's cycle for a 
team-engine 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) 


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 heat-engines. It is of course apparent 

lhftl ^ g. - Q a ^ L-T-Za. 

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 


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..! 369.36 873-I- 3 

19-7-1 0.3035 Q..I.M9 0-0343 

. 57 8 -7 '19-1-3 6 3-i3 5-53 

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 (i|o) 

7' T" 

n _ /}_.. - i - * n . 


= 137 calorics, 


- a x 0> 

and for steam 

while for chloroform 

(2, - Q, 50-53 X 0,377 "' 14 calorics. 

After acliabalic expansion the qualities of the fluid will be, 
from equation (137), for stenm 

* - 


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 "- 0-000655) 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. 



Even if we consider that the difference of pressure lor chloro. 

8734-2 - 369-3 = 8364-9 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 

184-9 + 273 


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 heat-engines 
as any other saturated fluid; in practice, the cheapness and 
incombustibility of steam indicate that it is the preferable fluid 
for such uses. 

Non-conducting 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 steam-engine 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, 


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 non-conducting material, 

though no such material proper for making cylinders is now 


The diagram representing the operations in a non-conducting 

Under for a steam-engine (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 



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 exhaust-steam 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 



If values are assigned to fa and p 9 and the proper numerical 
calculations arc made, il will appear that the efficiency for a 
non-conducting 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 ^.U-nl 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 Temperature-Entropy Dlngrnm. Tin- Kiuikinr 
cycle is drawn with a varying quiinlily nf HIHIIII in HIP iylimli-r, 
beginning at a, Fig. 33, wilh the u-am nuiKlu in llu- tlmntmr 
and finishing at ft, wilh ihut wi-iKlU pliw llu- wriKlu ilmwn fn.m 
llic boiler; consequently ft proper u-in|rnUiirr cjnr..jy 
which represents ihc changes of oni- ]>untl of ilu- 
stance, cannot be drawn. 

We may, however, use ihc u-mpmituri' (-nlntpy 
(like Fig. 30, page ro,(, or the plfitc in tJir ent\ of ihr 
solving problems connected wilh lhal i-yclf inntcAd of n|iin(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, (- 


for a volatile liquid. From ihc Inner 


we have 


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 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 ndo-p}. 

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 
non-conducting 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 temperature-entropy 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 non-rcvcrsible 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 


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. 

Temperature-Entropy Table. The lempcralurc-cntropy 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 non-conducting engine 
may be incomplete because the expansion is not carried far 
enough to reduce the pressure to that 
of the back-pressure 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 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 hcat-ccf! 
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 


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 t-lVicirnlly. 
Finally, the efficiency of the cycle is 


r _ 


If ^ fl is made equal to />j in Iho prtrerlinK t'f|UiiliM, it will 
reduced to the same form as uijimlinn (i.|.()i IHTKUM* lln* 
sion in such case becomes complete. 

Steam-Consumption of Non-conducting Engine. A 
power is 33000 foot-pounds per mmuie or 60 X .13000 fimi 
per hour. But the hu changed inlo work pt-r pound <if 
by a non-conducting engine with complete expansion h, liy 
equation (143), 

'i + ffi " ( h - -V' 
so that the steam required per horse-power per hour is 

778 (r, H-ry, - j,- v,) 

j the steam )>cr horac-powcr 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 horse-power per hour in of course the work done im- 
pound of steam, and the parenthesis without the 


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* n-3 ' ............. " v ..i * 




is the efficiency for the cycle. 

Actual Steam-Engine. The indicator-diagram from nn aclual 
steam-engine differs from the cycle for a non-conducting 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 slow-moving 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- 

When steam enters the cylinder of an engine, some of it is 
condensed on the walls which were cooled by contixct whh 
exhaust-steam, thereby healing them up nearly lo the tempera- 
ture of the steam, After cut-off the pressure of the steam is 
reduced by expansion and some of the water on the walls of 
the cylinder At release the pressure falls rapidly 
to the back-pressure, 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 steam-engine with a non-conducting cylinder can lead only 
o confusion and disappointment. 

The most apparent effect of the influence of the walls of the 
cylinder on the indicator-diagram 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 cut-off 
: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 

It may be mentioned that the fluctuations of temperature 
in the walls of a steam-engine 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 steam-engine is commonly stated in 
pounds of steam per horse-power per hour. For example, a 
small Corliss engine, developing 16.35 horse-power when 
running at 61,5 revolutions per minute under 77.4 pounds 
boiler-pressure, used 548 pounds of steam in an hour. The 
steam consumption was 

548 4- 16.35 = 33-5 
pounds per horse-power, per hour. 



This method was considered sufficient in the curlier history 
of the steam-engine, and mny now be used for comparing simple 
condensing or non-condensing engines which use saturated 
steam ami do not 1m ve u steiim-jaeket, 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 steam-engines may bu more exactly 
slated in British thermal units per horse-power per minute. 
This method, or some method equivalent to it, is essential in 
making comparisons lo discover the advantages of superheat- 
ing, steam-jacketing, and compounding. For example, the 
engine just referred to used steam cunluiumg two per cent of 
moisture, so that .\\ at the steam-pressure of 77-1 pounds was 
0.98. The barometer showed the pressure of the atmosphere 
to be 14.7 pounds, and ihis was tilso the buck-pressure during 
exhaust. If it be assumed thai the feed-water 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 horse-power per minute were 


Efficiency of the Actual Engine. When the thermal units 
per horse-power per minute are known or can be readily cal- 
culated, the efficiency of the actual steam-engine may be found by 
the following method : A horse-power corresponds Vo the develop- 
ment of 33000 fool-pounds 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 horac-power 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 Mi-sun 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 supply-pipi* luul liu- pre-war 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 Hlcnm-jnekHfi wn wlihclrnwn 
at the temperature due to the pressure find could Jmvc \wcn 
returned to the boiler at that temperature; raniiec|Urnily 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 horse-power per minute, and the efficiency WAS 
e ( |a.,ja *- 333 0,183. 



The efficiency of Carnot's cycle for the range of temperatures 
corresponding to 157.7 anc ^ 4-5 pounds absolute, namely, 821.^ 
and 6i7.2 absolute, is 

'/', - 7 ' a 821.7 ~ 617.2 



The efficiency for a non-conducting engine with complete 
expansion, calculated by equation (1*14), is for Ibis case 

0.821 X 1004.1 

* I 

858.6 -1-333-9 ~ 120 - 
where *a is calculated by the equation 



1004,1 \82i.y 


) * 0.821. 

During the lest in question Ihe terminal pressure at luccntl of 
ihe cxjMinslon in Vhc low-pressure cylinder was 6 pounds tvbso* 
hite, which gives 

.,. 0,5189 - 0.2475) - 0.832, 
- / 

995.8 \82i-7 
and the efficiency by equation (148) was 

jn^ l _ *>?* "I* +? ~ A (P* " ^^j 
r, H- ff, - q, 

0.8-12 XooS-8-138.0 -I- 126.0-1- \n (6-4.5)0.833x63 

u-j v __ . ....... i *r. ....... ^.^-W -. . \t ..... --- -*- ..... ' " l* ""- 

333-9- I2 - 


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 





But jf we take for our standard an engine with a cylinder of non 
conducting material the ratio for complete expansion is 





For incomplete expansion the ratio is 
e 0,18 

= 0.807. 


= 0.824. 

To complete the comparison it is interesting to calculate 
the steam-consumption for a non-conducting steam-engine 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 + 333-9 126.0) 
and for incomplete expansion 

60 X^ 33000 

= 10.5 pounds, 

778 X 0.222 (858.6 + 333-9 - 126.0) 

per horse-power per hour. 

But if these steam-consumptions arc compared with the 
actual steam-consumption of 13.73 pounds per horse-power 
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 
non-conducting 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 well-designed engine running under favor- 
able conditions. Improved economy must be sought cither by 
increasing the range of temperatures (raising the steam-pressure 

= 10.7 pounds 



or improving Ihc vncuum), or by choosing .some oilier form of 
hciil-molor, such us the gas-engine. 

Attention should be called to the {act that the real criterion ol 
Ihc economy of u heat-engine is the cosl of producing power by 
that engine. The cost may be expressed in thermal uniis per 
horse-power per minute, in pounds of steam per horse-power 
per hour, in coal per horse-power 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 steam-engines. 
If the same fuel can be used for different engines, such as slcam- 
and gas-engines, then the cost in pounds of fuel per horse-power 
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 sicam-prcasurc above 150 pounds is alow. The 
same thing is shown even more clearly by the following Iftblc: 


I'roliHhla l'erlorinnce, 

lireiiura hy 

Kffl clenoy, 
Cut not 'i Cjtlt, 

H.'l'.U. [> 


II. P. per 

Ml mils. 














If. P. PM 



Slm |r 




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 non-conducting engine is assumed to be complete, The 


heat-consumption of the non-conducting engine is obtained l.y 
dividing 42-12 by the efficiency; thus for 150 pounds 

,}2.*|2 -r 0.272 - ' 156. 

The heat-consumption of the actual engine I'K assurm-d ( be 
one-fourth greater than that of the non-condiic'ting engine. The 
steam-consumption is calculated by the reversal of the method 
of calculating the thermal units per how-power per minute 
from tlic steam per horse-power 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 Hlcam-jackelcd. The adinil 
steam-consumption 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 
steam-pressure 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 steam-engine, known n jet-condensera nmt 
surface- condensers. The former fire commonly nun I f(tr 1/tnd 
engines; they consist of a receptacle having n volume i-quiil i 
one-fourth or one-third of that of the cylinder or cylinders llml 
exhaust into it, into which the ateiun passc-a 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 


where <j ( is the heal of the liquid at the temperature /, of tl\e 
injection-water as it enters the condenser. Each pound of steam 
will require 

G* "I"" / / * / \ 

* r^r~ Oso) 

pounds of injection-water. 

For example, steam at 4 pounds absolute lias for Ihe total 
heat 1128.6. If the injection-water 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 


pounds of injection-water. 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 jet-condensers cannot be used at sea when the boiler- 
pressure exceeds 40 pounds by the gauge; all modern steamers 
are consequently supplied wilh surface-condensers 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 sea-water is circulated. The 
condensed water is drained out through the air-pump and Is 
returned to the boiler. Thus the feed-water is kept free from 
salt and other mineral matter that would be pumped into the 
boiler if a jet-condenser were used, and if the feed-water 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 feed-water, even 
though attempts arc made to strain or filler it from the water. 

The water withdrawn from a surface-condenser is likely to 


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 surface-condenser 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 feed-water, 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 horse-power: 

AbiuUilo Termlnul PrtMiirt, 
I'OUTUU jiar Ki\\itte Inch. 

l f l 
|nr I. II. I'. 




i tii 


I . 77 


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. 

Air-Pump. The vacuum in ihc condenser is maintained 
y the air-pump, which pumps out the air which finch its way 
here by leakage or otherwise; the condensing water carries 



a considerable volume of air into the condenser, and the s 
of the air-pump can be based roughly on the average percent* 
of air held in solution in water; the air which finds its way i 
a surface-condenser enters mainly by leakage around the It 
pressure piston-rod and elsewhere. 

It is customary to base the si/.c of the air-pump on the ( 
placement of the low-pressure piston (or pistons); for exam] 
the capacity of a single-acting vertical air-pump for a mcrch 
steamer, with triple-expansion engines, may be about ^V of 
capacity of the low-pressure cylinder. 

With the introduction of steam-turbines, 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. Air-pur 
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 indlcator-diagn 
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 



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 piston-displacc- 
ncnt. The boiler-pressure 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 wire-drawing 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. 



Problem. Required the dimensions of the cylinder of an 
engine to give 200 horse-power; revolutions 100; gauge pressure 
So pounds; vacuum 28 inches; cut-off at stroke; release at end 
of stroke; compression at T ' ff stroke; clearance 5 per cent. 

The absolute boiler-pressure 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 Xo-35 foot-pound, 

and during expansion is 

# ! v 1 log e -* = 94.7 X 144 X 0.35 log. 


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 


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 + 94-7 Xo.35 log, 

V *J 

- i X 0.85 - i X 0.15 log, - 59.1 


The probable mean effective pressure may be taken as 
of this computed pressure, or 53.2 pounds per square inch, 



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 


2OO = 

2 X 53-2 X X X loo 

12 4 


.'. d = 16.8 inches, $ 33.6 inches. 

In practice the diamc-tcr would probably be made i6| inches 
and the stroke 33^ inches. 



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 back-pressure 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 
back-pressure 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 back-pressure 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 cut-off 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 




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 back-pressure 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 non-conducting 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 crank-pin. 

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 



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 low-pressure 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< 

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 steam-chests 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 indicalor-d 
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 back-prc 
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. 



At E the communication between the two cylinders is closed by 
the cut-off 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 cut-off 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 
low-pressure 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. 


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 high-pressure, intermediate, and 
low-pressure 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 triple-expansion 
engines; the customary arrangement has three cylinders with the 
cranks at r8o. 

Quadruple engines with four successive expansions have been 
employed with high-pressure 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 low-pressure piston dis- 
placement to the displacement developed by the high-pressure 
piston at cut-off. 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 multiple-expansion 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 
cut-off in the high-pressure 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 cut-oil, tak- 
ing account of clearance. And further, since the clearance of 


the high- and the low-pressure cylinders are different there can 
be no real equivalent expansion. 

If the ratio of the cylinders is R and the cut-off of the high- 
pressure cylinder is at - of the stroke, then the total expansion 
is represented by 


- = R 

This last equation is useful in determining approximately the 
cut-off of the high-pressure 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 high-pressure cut-off will be about 

- = 34 *- 10 0.35 
of the stroke. 

Low-pressure Cut-off. The cut-off of the low-pressure 
cylinders in Figs. 36 and 37 is controlled by the ratio of the 
cylinders, since the volumes in the low-pressure cylinder at cut- 
off is in each case made equal to the high-pressure piston dis- 
placement; this is done to avoid a drop. If the cut-off were 
lengthened there would be a loss of pressure or drop at the end 
of the stroke of the high-pressure 
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 non-con- 
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 cut-off of the low-pressure cylinder is shortened the 

FIG. 41. 

1 62 


pressure at C" will be increased because the same weight of steam 
is tnkcn in a smaller volume, The back-pressure DC' of the 
high-pressure 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 

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 crank-pins 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 slfam-prcsaurc the ratio 
is i: 3 or i! 4. For triple-expansion cn|(incs the cylinders may 
be made lo increase in the ralio r : a or i : air. 

Approximate Indicator-Diagrams. The indicator-diagrams 
from some compound and multiple-expansion 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 



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 

It will be assumed that there arc no losses of pressure due to 
throttling or wire-drawing; thus the steam line for the high- 
pressure cylinder will be drawn at the full boiler- pressure, and 
the back-pressure line in the low-pressure 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 slow-speed pumping- 
cngines the discrepancy is small and all irregularities are easily 
accounted for. On the other hand the discrepancies arc large 
for high-speed marine-engines, and for compound locomotives 
they almost prevent the recognition of the events of the stroke. 

Direct-expansion 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\ cut-off occurs at b, and be repre- 
sents expansion to the end of the stroke; be being a rectangular 


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 high-pres 
cylinder and admission to the low-pressure cylinder arc ussu 
la lake place, so that communication is opened from the 1 
pressure cylinder through' the receiver space into llio low-p 
urc cylinder. As a consequence the pressure falls from c \ 
and rises from it to h in the low-pressure cylinder. The 
O'P' Is drawn at a distance from OP, which corresponds Ic 
volume of the receiver space, and the low-pressure diagra 
referred to O'P' and O' V as axes. 

The communication between the cylinders is maintained 
cut-off occurs at / for the low-pressure cylinder. The lim 
and hi represent the transfer of steam from the high-pro 
to the low-pressure cylinder, together with the expansion d 1 
the increased size of the large cylinder. After the cut-off 
the large cylinder is shut off from the receiver, and the slcn 
it expands lo the end of the slrokc. The back-pressure 
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 


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 Hnilt-s depending* 
on the springs used in (he indicators. 

Some engines have only OIK* valve lo gi\v release nnd ami 
pression for the high-pressure cylinder and dmi.s.*mirt and itu 
off for the low-pressure cylinder, tn such nisi- llu-rr is nu 
receiver space, find the points t-nnd/roim-iiJi-. 

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 rect-ivi-i- in opened ui tlu- end nf iln- 
stroke. It is evident thai the drouo/ may U- rt-diucd li\ .-.Imri 
cninglhc cut-off of the low-pressure cylinder HO UK in j^ivi- inure 
compression from e to /nnd|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 .subHc-ri|rt lettcnt, nnd reprrseiU 
ing the volume of the receiver by i' f , we liavr ilu* following 

p a m, j) b initial pressure; 

PI ** pm** 

V f \ 



v n 

Pa - p k - ( 
P, - A A/ 



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 c-nn 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 low-pressure piston displacement 
equal to three limes the high-pressure piston displacement. 
Assume that the receiver space is half (lie smaller piston dis- 
placement, and that the clearance for each cylinder is onc-lcnlh 
of the corresponding piston displacement. Let the cut-off for 
each cylinder be at half-stroke, 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 back-pressure be two 
pounds absolute. 

If the volume of the high-pressure 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 


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 + 0-5) 

1.57 ^ = i-57 X 0.655 A* - 1-03 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 4-0.26^; 

A/ - 25.89 + 0.26 X 1.03 p a ; p tl - 35.36; 
A - A = 0.655 A/ = 0-655 X 35.36 - 23.2; 
Pt = 1-03 A. = 1-03 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. 


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 slow-speed pump- 
ing-engmc the multiplier may be as large as 0.9 or even more; 
for high-speed 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 high-pressure 
cylinder to the low-pressure cylinder as represented by de and /*. 
The net effective work during the transfer is 

pdv = 

= 144 

-f v r ) 

t , 

- 144x35-4(1.1 +0.3 

4120 foot-pounds 

;' , V ' *' 

u$ -f Vh f v r 

0.6 + 1.8 -f Q-5 

for each cubic foot of displacement of the high-pressure piston. 
This corresponds with our previous assumption of unity for the 
displacement of that piston. The increase of volume is 

1 1 


so that the mean pressure miring uiu 

4120 -HI X 144 " 28 - 6 


pounds per square inch, which acts on bolh the high- and the 
low-pressure 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 log. -- a8.6 <i.i -0.6) 

. . . , U.U V U.S 

21.2 (o.G -V- 0.5) iou ""*"' 
"" 1-14 X 33-26 4789 fool-i)oniuls. 

t x ' a 

This is the work for each cubic foot of the high-pressure 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 fool-jmundg. 

Since the ratio of the piston displacements is 3, the work for 
each cubic fool of the low-pressure piston displacement is one-third 
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- 



tribution can be improved by lengthening the cut-off 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. 

Cross-compound Engine. A two-cylinder compound engine 
with pistons connected to crunks at right angles with each other 
is frequently called a cross-compound 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 cut-oil of the large cylinder is earlier or later than half-stroke; 
n the latter case there ia a species of double admission to the 
ow-prcssuro 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 half-stroke. 
The admission and expansion of steam for ihe high-pressure 
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 Imlf-atroke; 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 low-pressure diagram. The cut-off 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 dead-point; 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 low-pressure 
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 crank-pin. 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 


crank is 90 behind or if ihe angle KyOR t in other than a 
angle. The actual piston position and crank tingles wlu-n 
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 & back-pressure; 

j>< t - A, 

A - A 

A C^ -I- t'rt t- r r ) 
-I- v,-) + (i>'M'r 
- /'* -I/'/ (^ -I- iv) I- y 



The pressures ^ and fa cun be found dirtrlly from il- iniliiil 
pressure and the hftck-prcssure, 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 aflt-r 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 low-pressure diagrnm, art- hypi-rlmJffi 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 

The work and mean effective pressure may be calculated in n 
manner similar to that given for the direct-expansion 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 cut-off of the low-pressure is earlier than half-stroke so 
as to precede the release of the high-pressure 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 high-pressure piston requires an additional unknown 
quantity and one more equation. 

Triple Engines. The diagrams from triple and other mul- 
tiple-expansion 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 
high-pressure, low-pressure, and intermediate, as shown by Fig. 
45; or in the order of high-pressure, intermediate, and low- 
With the cranks in the order, high-pressure, low-pressure, and 

Fl ' 



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 half-stroke. IE the cut-olT for that cylinder is later than 




twrlo I Inn 

it (mm 

Ihtla (0 

fin. 46, 

half-stroke, it is In communication with the first receiver when 
its crank is at /, and atcarn may poaa through the first receiver 
from the high-prcsaurc 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 cut-off for tho 

w uiC 

position c for the high-pressure 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 high-pressure 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 high-pressure to the Intermediate cylinder repre- 
sented by In and hit. At / the high-pressure compression ik 
begins, and is carried so far (is to produce a loop at k. After 
compression for the high-pressure 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 low-pressure cylinder. The remainder 
of the back-pressure line ol the Inlormcdmlc cylinder and the 
upper part of ihc low-pressure diagram for the low-pressure 
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 -1-f. -1-up) * (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 


JIL p, 

' /* = 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 *= back-pressure; 

The pressures at c and at ? can be calculated immediately 
:rom the initial pressure and from the back-pressure. 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, 


** 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 cut-off for the intermediate cylinder occurs before the 
release of the high-pressure cylinder, then the transfer represented 
by tie and op docs not occur. In like manner, if the cut-off for 
the low-pressure 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 low-pressure. The diagrams take 
forms which arc distinctly unlike those for the other sequence of 
cranks. In general, Ihc case solved, i.e., high-pressure, low- 
pressure, and intermediate, gives a smoother action for the 

For example, the engines of the U. S. S. Mnehias have the 
following dimensions and proportions: 



Djiurieicr of platan, Inches 
Piston displacement, cubic feet 
Clearance, por com 
Cut-off, 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 liIgh-proMura plslon din- 
placement .................. Ot g., 

Stroke, Inches .................. 

Boiler-pressure, absolute, pounds per sq. In ...... 

Pressure !n condenser, pounds per aq. In ....... 






1 80 







If the volume of the high-pressure piston displacement is 
taken to be unity, then the volumes required in the equations for 




y. i 



7J rf w I .06 


** I 1 3 

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 ^ 



'fa ^ ^H IHI1 ^'35 

V, ^ 2.O3 

t/ y M 3.6O 

ij(. isa T/ ( ** 4'0't 


. JJl V.3OU1 <-il 

m *- 


= A = 

150 A 

= 165 

A - A = 



= 112 


= 60.0 

A - 52-3 


= A - 

76.5 # ff 

= 5-5 

/> = 22.1 


= p p = 

67-5 A 

= p f = 28.3 

P& - I8. 5 


= 67.5 


= Py = 25.3 

P, = Pf = 



= 76.9 


= 25.1 

Ptl J?' 



= A = 

73-5 A 

= 29.0 


- # = 

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 indicator-diagrams 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 connecting-rod, 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 low-pressure 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 multiple-expansion engines should have at hand a well- 
systematized fund of information concerning the sizes, pro- 
portions, and powers of such engines, together with actual 
indicator-diagrams. 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 indicator-diagrams 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 indicator-dia- 
grams are at hand, and for the new design. He may then 
sketch diagrams for the new engine, using the approximate 


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 horae-piwr 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 Kit-esses on the members of that 

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 low-pressure 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: 


l)e*;rl|>iloii of Knn!n<i. 



Throe-cylinder triple, merchant ahi|ii 

0.6.1 [u o.Tifl 

O.6o to 0. 6 

Three-cylinder triple, gunluiuit And turi win -Ixinu 

0.6o lo o.f 

For example^ lei the boiler-pressure be 80 pounds by the gauge, 
or 94.7 pounds absolute; let the back-pressure 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 

<M-7 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 horse-power at 60 revolutions per minute is 



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 
horse-power 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 vapor-engines. 
At thai time the common steam-pressure was not far from thirty 
pounds by the gouge, corresponding to a temperature of 250 F. 
If the back-pressure of the engine be assumed to be 1.5 pounds 
absolute (115 F.), the efficiency for Cafnot's cycle would be 

350 -h 460 


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 


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,). 



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 cx|H'riini'ii(n MM 
binary engines using steam and .sulphur-dioxide. 

The practical arrangement of a binary rnginr sulisliliiu-i fur 
the condenser an appliance having somewhat llir winu- form n* 
a tubular surface-condenser, 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 
"water-tube" 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 surface-condenser which is cooler) with wnirr 
at the lowest possible temperature. 

An ideal arrangement for a binary engine avoiding llir UHC of 
air-pumps would appear to be the combination of a compound 
non-condensing steam-engine 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 hoillng-jKiint n( 
atmospheric pressure is 94 F t) consequently it would from 
necessity require a vacuum and an air-pump unlrwf tin- rilirr 
couid be entirely freed from air, and leakage inlo tlu- vacuum 
space entirely prevented. Sulphur-dloxldc givc-js 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 steam-engine with a vacuum of 22 inches of mercury 
or about 4 pounds absolute, which gives a temperature of 155 F., 
at which -sulphur-dioxide 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 fuel-con- 
sumption was not less than that of good engines of that lime, 
which appears to indicate that he could not secure favorable 


THE principal object of U'Hls of sicam-engmcs is Lo determine 
the cost of power. Scries of engine tests are made: to 
determine ihc elTccl of certain conditions, such as superheating 
and steam-jackets, 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-, llu-n, 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 steam-engine 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 dynunio-HirirU' 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 twenty-four 
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 surface-condenser 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 non-condensing and on jet-condensing 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 
feed-water should be long enough to minimizi 
uncertainly of the amount of water in a boiler 
an apparent height of water in a water-gauge: 
height of the walcr-lcvel depends largely on llu 
lion and the activity of convection currents. 

When the cost of power Js expressed in tl 
necessary to measure the steam-pressure, 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 


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 steam-jackets 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 steam-pressure 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 steam-pressure should remain constant 

limn that nil tests nl a given pressure should have identically the 
same steam-pressure, 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 freezing-points 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 gauge-makers 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. friction-brake. 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 


nust be freely lubricated with oil. An iron wheel running in a 
furnished with blocks of wood requires lialu or 110 lubn- 


To avoid the increase of friction on the brake-bearings clue 
o the lond applied at a .single brake-arm, 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 friction-brake, 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 electric-gem-ralnr may readily have 
he dynamic or brake-power deicnnim-cl from the electric out- 
mi, provided that the efficiency of the gcncralor is properly 

The only power thai can be measured far a Klwim-uirhinc is 
he dynamic or brake-power; when connected with nn oleelric- 
cncmtor this involves no difficulty. For marine propulsion i|: 
> customary lo dclcrmine lhe power of Hleam-turbinea by some 
3rm of lorsion-mcirc 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 torsion-metre 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 enginc-U-sling 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 .... .i-v, 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- 
ailor-pislon, pencil-motion, and pencil arc affected hy errors 
which may be classified us follows: 

t. Scale of the spring, 

a. Design of ihe pencil-motion. 

.V Inertia of moving parts. 

<|. Friction and backlash. 

Good Indicator-springs, 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 engine-cylinder. But a spring is appre- 
ciably weaker til high temperatures, so that when thus enclosed 
in the indicator-cylinder, It gives results thai are too large; the 
error may be two per cent or more. 

Oulsidc spring-indlcalors 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 pcncil-moiion, 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. 



When steam is suddenly let into the indicator, as at admission 
to the engine-cylinder, the indicator-piston and attached parts 
forming the pencil-motion arc set into vibration, with a natural 
time of vibration depending on the stiffness of the spring. A 
weak spring used for indicating a high-speed 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 cut-off 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 pencil-motion. 

The most troublesome errors of the indicator are due 
to friction and backlash. The various joints at the piston 
and in the pencil-motion 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 knife-edges 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 quick-opening 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 
exit-valve 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. 

Water-Meters 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 



on a by-pass through which the feed-water from the surface- 
condenser can be made to pass by closing a valve on the direct 
line of feed-pipe. 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 surface-condenser. 

Priming- Gauges. When superheated steam is supplied to an 
engine it is sufficient to take the temperature of the steam, in the 
steam-pipe 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 heat-measurers. Three of these will be men- 
tioned : (r) the throttling-calorimetcr, which can usually be applied 
to all engine tests; (2) the separating-calorimeter, which can be 
applied when the steam is wet; and (3) the Thomas electric calor- 
imeter, intended for use with steam-turbines to determine the 
moisture in steam at any stage of the turbine whatever may be 
the pressure or quality of the steam. 

Throttllng-Calorimeter. 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 half-inch pipe b, with a 
throttle-valve 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 boiler-pressure may be taken 
from a gauge on the main steam-pipe 
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 gauge-reading, making it less than tho 
real pressure. The reservoir is wrapped 
with hair-Mi 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 boiler-pressure 
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 

K|Q - <" 


{\J ISO! 

Example, The following arc the data of a lest made with 

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 = 943-8 + 212.7 -r- 0-48 (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 
:ondcnsing-cngine 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. 











'85! 3 







no. 3 






5 . 



In case the calorimeter is used near Us limit -thai is, \vhcn 
UK- superheating is u fi-w 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 n nmHidenibk- error in the. tcmpi-ailurc 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 gauge-reading 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 one-fourth of i\n 
inch in diameter under the pressure of 70 pounds by the gauge, 
stt thai if the throttle-valve be. replaced by such tin orifice the 
([iH'Htion of rudialion need not be considered. In such case a 
stop-valve 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 ihrollle-valve may be opened at first 
a small amount, ftnd the it-mpt-mUia- 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. 

Sflparatlng-Calorlmcter. 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 scparating-calorimctcr 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 
water-glass 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 

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 


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- 

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 
If W is ihc weight of steam flowing per hour through the 

PlO. JO. 



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 


3.42 E. E. 


= 3-42 CS 


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 steam-tables is 884, 


3=1 I "-* - ' - ' E=J O.Q<1 
88 4 93-0 

Method of Sampling Steam. It is customary to take a sample 
of steam for a calorimeter or priming-gauge through a small 
pipe leading from the main sicam-pipc. 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 steam-pipe, and which is closed at the end and drilled 
full of small holes. Il Is better to have the sampling-pipe 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 
sampling-pipe should be short and well wrapped to avoid 



IN this chapter a discussion will be given of the discrepancy 
between the theory of the stcam-cnginc 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- 

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. 






Ily Chlct-KnKlncrr IHIIKUWWW, Resetircliat !n llxl>erlir>itai Stenm 

Duntllnn, hiiu 


Revolution* |HT iiilnutr 

Holler prrawuir, 


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 n-lcnw . 


1 t/u 







In the firm |>|JUT tin- Jn-l cronomy /or thw engine ww 33. 
pounds inHlcntl of 36.5 pounds tin nilfiilatcd )>y the expression 

deduced on 


nl 60 
OnllMf* Jj*w04 of HAM)) 

77 (', ( q l - Ay, - qj 

:.)( fur iht> HiuiinvronHiirnpiitm /or a non-con- 

dueling engine with 
cnmplcic expansion, 
Thia result was ob- 
Uiincd with cut-oft at 
four-ninths of the 
slrolu- which gave a 
terminal pressure ol 
one pound above the 

Tin-manner of the 
consumption with ihc 
" cui-oft Is clearly 
shown by Fig. 51, in 

which the fraction of stroku tit cul-off fa ttikcn for absclssm and 

the atcum-eonhumptionti us ordlniitoH. 


Km. ii. 



To make the diagram clear and compact, the axis of abscissa: 
is taken at 30 pounds of steam per horse-power 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 cut-off; 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 back-pressure 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 
back-pressure 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 steam-consumption decreases 
as the cut-off is shortened till a minimum is reached, usually at 
i to stroke; any further shortening of the cut-off will be accom- 
panied by an increased steam-consumption, which may become 
excessive Jf Ihc cut-off 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 indicator-diagram. 
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 cut-off 
at -14 of the stroke to 45.1 per cent for a cut-off 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 cut-off, and the greater part 


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 cui-off 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 cul-tifT was lengthened to 0.689 of 
lire .slrnkc, llicre wus a?.y per mil of wuiw at cut-off and 23.9 
per cent ul release. The stulenu-nl 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 
cul-nff. On llu* ronirnry, there is more waler condensed in 
the cylinder when ihc rul-nft 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 icmpcralurc-ontropy 
diagnvin ua shown In 
WK- 5^ which is con- 
structed from the Indicator- 

diagram in Fig. 5-1, 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. ,*. 



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 slcam-lablc 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 piston-rod. 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 high-pressure 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 





.11 O.M,9A 

To plot the point e on the Icmpcrulurc-onirony 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 cui-otT. 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 rut-oft . This po 
readily included in the preceding investigation, no that x, 
determined. Locating n on the temperature-entropy 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 



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 indicator-pencil 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 
steam-pressure falls. It then lets go and falls sharply aomo 
little time after ihc valve 1ms closed at cul-olT. 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 steam-engine, 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/m-mnil of hi* 
method which will be given hero ia derived from a menmir by 

Let Fig. 54 represent the cylinder of a HlMim-enfflno 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 
cut-off, release, compression, and admission. 
The part of the cycle from o lo r, that in, 
from admission to cut-off, is represented 
by a; in like manner, b t c, and r/ represent 
the purls of the cycle during expansion, 


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 cul-iifT 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, 



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 cut-off 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 supply-pipe 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 freezing-point, is 

Q = M (q + xr] 


Should thu steam be superheated in the supply-pipe 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 heat-equivalent 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, cut-off, release, 
and compression we have 

7,= (M 
/ 3 = (M 

+.%vO; ...... (156) 

-f- *y> a )j ...... (157) 

in which p is the heat-equivalent 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 heat-equivalent of the fluid in the cylinder 
is /, and the heat supplied by the entering steam up to the point 
of cut-off 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 cut-off. The remainder must have been absorbed by 


the walls of the cylinder, and will be represented by Q a , Hence 
(?"<? -I- /,-/,- 4 W n . 

From cut-off to release the external work W L is done, and at 
release the heat-equivalent 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 cut-off 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 heat-equivalent of intrinsic energy T y So that 

6* - A 


-|- 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 heat-equivalent of the intrinsic energy is / . 

It should be noted (Fig. 54) that the work W n is represented 


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 repi-i-senled 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'.' - 



/UK, . (161) 


A consideration of Ihw eijuiUioiiH shows that all the quanti- 
ties of the righi-hnnd 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> cut-off and release bo 
V l and K 3 ; finally, let V t reprntenl ihe corresponding volume 
HI romprewiiim. Tlic spc-cilic 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). 


At the points of admission, cut-off, 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 i-uliU: 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 lia|i|*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- 

v .Y1L. 

2 M + M 

By aid of the temperature-entropy table we may find (by inter- 
polation if necessary) the corresponding temperature / 3 and the 
value of the heat-contents or total heat. The heat-equivalent 
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, cut-off, release, find 
compression are determined by the aid of the indicator-diagram, 
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 exhaust-steam in a surface-condenser and collecting 
and weighing it in a tank. If the engine is non-condensing, or 
if it has a jet-condenser, or if for any reason this method cannot 

be used, then the feed-water 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 jet-condenser is used, and the condensing 
water mingles with the steam, / 4 is identical with t k . The quality 
x of the steam in the supply-pipe must be determined by a steam- 
calorimeter, A boiler with sufficient steam-space 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 

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 


The heat Qj supplied by a steam-jacket 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 steam-pipe, 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 
right-hand 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 

If a steam-engine 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 non-con- 
densing engine or to the high-pressure cylinder of a compound 

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 hoi-air 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 slow-speed 
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 

Ilollcr-prcasiiri' liy KflURp 77.4 pounds, 

nanimeter 14-8 " 

Condition of steam, two per cent of moisture, 
Kvcnis of the stroke: 

Cut-off: 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- 



ttmi. HAII Bun. 


Cut-off . . 

Comnrcaslon . 
Admission . 


aR.i . a 
317. a 




803. a 



39. B 




863. 9 


a 6. -164 

* Thou vnliios nro tnkon from tho Jlrat edition of the Tables of I'rojwnlos ol 
Snturatfid Stonm. 


2I 5 




HBAD Eun. 

Man Prtsmrts. 

Equivalents of 

Mean Pressure). 

Equivalent! of 

Admission .... 
Kxpansion .... 







o. 1104 

Compression . . . 




At cut-off, V + V, 

At release, V -t- V t 

At (he boiler-pressure, 92.1 pounds absolute, we have 

r =. 888.4, q = 291.7. 

The steam used per stroke is 


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. 

,, 0.034-1 + 
* = 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 



2 X 3692 

= 1-973- 

fi'l (,\ 

" A 

. . __ 

* aooigX HiS-.M-l 1-13.664) 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. 


1 0.0761 X 4 (5-190 4 5.307) 63.4 X 4(5-19 -1-5-207) 
- 0.6336. 

3 "" (A/ 

' '0.0761X4(13.0344-13.804) 
* 0.7088. 

.'. /, - 4 X 0.0019 [201.5 + 319-0 + J- 00 ( 8 77'4 "I- 
^ 2.054. 

7, - (A/ I-A/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)] 

.'. 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 + 4-159) - - 7-09 1 ' 
Q e = /, - h - M& - C (ft - ?,) + <W e ; 

Qp = 63.311 2.041 0.0742 X 109.3 

- i-973 (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 (3.540-4-4.018 1.841 0.070) 
= 86.243 8.110 69.723-5.647 = 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 horse-power of the engine is 

778 X 5-647 X 3692 X s _ i6 IUV 
60 X 33000 

and the steam per horse-power per hour is 


= 33-5 pounds. 

For data and results of this test and others see Table IV. 

Effect of Varying Cut-off. 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 cut-off 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 
cut-off so that it shall not come earlier than one-third stroke. 
Unfortunately tests on this engine with longer cut-off than one- 
third stroke have not been made, and consequently the poorer 
economy for long cut-off 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 steam-jacket. 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 steam-jacket. 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 

H(U)I .Bill 

Until in j|i[ 

vjtunod 'aini 



*O "t 
>-. in 

6 ro 
1/1 i~ 

1^ Q O M K 

I-. (^O M OQ 


in i-wj in ci 
(i o> i- O 4 


O t* M M 

<O "" l-00 O 

M M M M P| 

M- irt-O 

t-k It N l> \f\ 

n O >O f >O N 

i o> M n in 

o *r 
O O 



O M "O 

fi M Q. 

I w 

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 cut-off is reduced from 52.2 per cent to 
27.4 per cent, when the cut-off is two-tenths of the stroke, by 
the use of superheated steam; with longer cut-off 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 cut-off, 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 
cut-off 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 cut-off 
Finally in lest 8 the exhaust waste is practically reduced to 
/cro by the use of .strongly superheated steam in a non-con- 
densing engine; tins shows clearly that the exhaust waste Q e by 
ilsi-lf is no erilcrum of the value, of a certain method of using 

Steam-jackets. If the walla of the cylinder of a steam- 
engine, are made double, and if the apace between the walls is 
filled with all-am, the cylinder is said to he steam-jacketed. 
Holh barrel and heads may be jacketed, or the barrel only may 
have a jarkel; less frequently the heads only are jacketed. The 
principal i-ffccl 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 u-fli 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 two-thirds 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 exhaust-pipe. 
Il appears, then, that the direct effect of a steam-jacket 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 Multiple-expansion Engines. The application 
jf Him 's analysis to the high-pressure cylinder of a compound or 
miltiple-cxpansion 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 the-ncxt cylinder, 
whether it be the low-pressure 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 heat-equivalent 
of the work clone in the cylinder, and Q e is the heat radiated. 
Suppose ihc steam from the high-pressure 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- 

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 low-pressure cylinder of a 
triple engine. 

It is clear that such an application of Kirn's analysis can be 
made only when the several steam-jackets on the high- and the 
low-pressure 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 triple-expansion engine in the laboratory 
of the Massachusetts Institute of Technology. 



It will be noted lhal the steam in the cylinders becomes drier 
in Us course 1 through the engine, under the influence of thorough 
steam-jacketing with steam nl boiler-iiressure, and is practically 
dry nl release in the low-pressure cylinder. All of the tcsu 
show superheating in the low-pressure 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 low-pressure 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 Hit-am supplied to [he 
cylinders in an, hour t and 3-15 pounds lo the Hlcam- jackets; so 
thai the steam per horse-power 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 heat-consumption 
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 non-conducting 
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. 






KRS, Q, ift, 

Traas- AM, .Sto. ^/<fc//. Kitgrs,, vol. xtl, p. 740. 

Durnltott of (cat, tnitititea . 
Total number of revolutions 
Revolutions per minulu . . . . . 
Steam-consumption dining leat, Mm.: 
Passing through cyliwlws 
Condensation in h.p. jacket 

in first receive r-jnckcl 

fn fnler. jacket . . . 

In second rccoivcr-jw:kl 

In l.p. jackal . . 


Condensing wutcr for lest, ll>n. 
Priming, by calorimeter . 
Temperatures, Fnhronhcli: 
Condensed s ten in . . . 
Condcnslng-wnU'r, cold 
Conrlcnsfng-wnicr, Jiot . 
Pressure of the ntmosplicr 
barometer, Iba. |>or nq. in. 
Holler pressure, Iba. jicr s({. in, 


Vacuum in condenser, liu 


EvcrUsof iltofllroke: 
Hlgh-pressuro cylinder 
Cut-oft, crank end 

liertd end .... 
Rclctise, bolli unda 
Compression, crnnk end , 

licnd end . . . 
Jjilcrmctlidle cylinder 
Cut-off, Ixilli ends 
Uclctisc, lx)lh ends 
Compression, cnink end 

bend end . . . 
Low- pressure) cylinder 1 
Cut-off, crnnft ond 
lieflt) end , , , 
Release, both cmla 





. . , , 




8-j i 

5 'H a 


cat, Ibis,: 

Cl ... 





( } 




L . . . . 








)H. ... 





. . . . 



96 6 


J0 5-3 

is, 1>y ihc 

111. ftllSO- 





} o( nier- 


a 3-9 


1 . . . . 





1 . . . . 








TAUUK VI Continued. 

lisiiluir hrr^urr* in lli<- yllmlr-r, 
IK nl in IN |nT B'|- III.! 
Hiltli-iirrsuturr i yUrnU-r 




.17 -^ 



i j.d 
t J..| 


A. j 


I 1,0. 





HI- IV. 

38.8 138,3 
to. J 140,6 
44-7 48.4 
'"5-7 ^9.8 

S4- S Ci.o 
7.a 3i.s 
86.7 57.8 

38.6 40.9 
,10-6 43.6 
1-1.7 16-0 
H.Q 16.0 

30-3 33.^ 
33.3 1 31.1 
3>1.3 1 90.; 

I2.-I 13- 3 
V' 5-1 

5.1) 6.4 
4-6 4-7 

7.00 8,19 
11 .33 1 11.09 

R..1-1 9-os 
0-73 - 

Q.(Jl 10.64 

10.37 n.H 





i J. i 
5' 4 

ft. ft 







rciiil|>rewtl"M, trunk rll<l . . 

MlmMun, \ rank rwl 

Irfivv-crruuirr < vllnilrr 

UrlniWt t ra\\"k n\t\ 

i rattk rin! - 

Hralii|ulvaU-itl* nf rtlrrnnl Wiifk 
H.T.U., frtun rctuiit Indii ni 

Utah prr&iurt 1 tylliultr 
ttunnu n(tm(aftlUi 

IturluK rx|innniun ( 

tlurliiu (timprrtoliiiip 

liilcrmrcllnlr tvllmlrr 
DurliiK in tin Union, 
/III/, iwnk mil .... 

fHirinu cxiwn^innj 



__ . 


TABLE VI Continued. 






Intermediate cylinder 
During exhaust, 


During compression, 



Low-pressure cylinder 
During admission, 
A\V t ", crank end 



8. 19 


During expansion, 





During exhaust, 






During compression, 

Quality of the steam in the cylinder. 
At admission and nt compression 
the steam was assumed to be dry 
and saturated: 
High-pressure cylinder 



Intermediate cylinder 

* # * 

* # * 

* * * 

I-ow-prcssurc cylinder 
A( cut-off 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: . . 
High-pressure 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 . . . () . . 

= 3-5-1 

- 8.36 




23- 43 
-19. 28 
- 7.22 
o. 5 i 


141. t i 
- 3-5 


- 2.38 


* Superheated. 



TAJH.K VJ -Continual, 





Jnlrrmnlitiir i ylimlrr 


HmviRlH In by siriitn . y - . KJ 




1 1. 11 

UuriK cxtmiialon . . . (_'' . 


i U u . 
1 ii . n.l 




(Hiring rximuti . . . . (V 

O. Jj 



Uurlitft (tirti|"rcftilnn . . ^'/ . 
Su|i|illr(( liy jiukrl . . (>/ . 






1.4 ml |i)' r<nlliHl"ii . . . ^V . . 

J - -15 

j , ,iK 

Set mill liilrrmcillntr rc-i river 

. Ji S' 

Supjiliril liy Jnikft . . ^'/' 
IJMI liy miiifiilim . . V*' 

-| JO 

I. Ju 

-I. o-l 

i . jj 



IXIH- |"MHifr r yllwlrr 


Hrmiglii In liy Pimm . t>" 
During nclml&sliin . . . (.V 


i .10 . 50 



I Hiring cxintiialoii . . . ^'*" 


7- (") 

n . fi< 

- 10 M 

f hiring oxniuiit .... (J," 



- 1.-14 

O.I I 

Ihirinu umi|irra't|ttii . . ^'j" 





Su|'|iHnl liy jmkrt . . ('/' 


ft. jo 

7. -II 


Ijitnt t>y mill ui lii ii . t't 

1 .1-1 

1 -i o 

.1 . je 

Tuinl li^t tty rn'lUil'in 


Hy (frrUfiilnary ir^ii . 3C(' 

1 f,ti7 

10. JO 


(0 ,- 

liy ntimllini (170 . . . 


10. M) 



I'covrr ftnn mummy; 


Hrwl ri|itlvAlcnu n( wurk \<rt 

M.l'. .yllti'li-r . . . . A\\' . 



u. 17 

fittrrtn. i vllmlrr. . . . AW 





1.. 1'. lyllmtvr /Ml"" 

y.f I 

1 o . of i 

10. B 7 

Tulnh . .... 

tf,. JH 


3?. Hi 


TotJt) h*fll fiirnlshnl ly jai \tet9 . . 

J? ^ 




Uimriliullnn n( wtirb 

Il'fifi (ift*iiirf f vldtrlrr . , . i 

t .ceo 




Init<rme<Unip tyUndrr 


a. Bj 



i.i i 

1. Ji 








Siritm iwr H P. |*r Iwuf ... 

1 4 . 65 

i -I - A ' 



iri'.r. j^r If I'. |-r mtmiir . , 




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- hiffh-prcflBurc cylinder 
nnd llinl a8..|j; n.t.u, ]n*r slrtikc iirr HUppIU'd hy llic siciim-JftckeU! 
and tfmi, funlu-r, jcj-vj n.T.U, lire c-hnngi-d 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 



was radiated; the other two-thirds may fairly be considered 
to have been changed into work, since the exhaust waste of the 
low-pressure 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 
exhaust-pipe, and found it to vary from 3 to 10 per cent. Professor 
Carpenter* says that the steam exhausted from the high-pressure 
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 exhaust-steam. 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 exhaust-pipe, 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. 



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 
thermo-electric couple, represented by Fig. 56. / is a cast- 
iron plug about three-quar- 
ters of an inch in diameter, 
which could be screwed lr*to 
the hole provided for attach' 
ing an indicator-cock to the 
The inner end of the plug 
which was assumed to act as 


FIG. 36. 

cylinder of a slcam-engme. 
carried a thin cast-iron 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 thermo-electric couple. 
Wires from / and W led to another couple made by soldering 
together cast-iron 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 Ihermo-clcctric couples there was placed a galvanometer 
and a circuit-breaker. The circuit-breaker was closed by a 
cam on the crank-shaft, 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 
steam-cycle were chosen for investigation, one immediately 
after cut-off and the other immediately after compression, since 


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 thermo-electric method. 

The wall temperatures were determined by a thermo-electric 
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 cylinder-head, 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 cylinder-barrel, 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. 


heiid toward llu- uank end. Thr U-mpi-nuuru ol Ihc sleam 
near \\w i-ylindrr 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 high-speed 
engine, with a halamed slide valve t-nnirolU'tl by a fly. wM 
governor. During ihr invi-sligiiliunH the eni-oft Wis sci at a 
fixed point lalitHil OIK- liflh Mrokr). and the speed was controlled 
i-Mi-trutlly. My ihi- addition of a u(Va-ic-iu amount of lap io 
pfi-vcnl UK- vatvt- front taking sinim at liu- ttank end Ihc engine 
was rniulc silicic at ling. Tin- normal f-pccd of the engine was 

from .jo in i/o rrvuhuion*. JKT ininutr. Thcdinrociorrfihe 
tyllndiT wan to."; imhi-H and tin- himke of the piston was n 
im IUT. Tlu* flt'iiram r wai tt-n JUT n-nl if tlu- piston displftccmem. 
From the indualor iliiigmnih an unalyiH, nearly equivalent to 
llirn'a imuly. 1 *^, ohuwnl tlu* In-al yic-ldnl to or ttikcn from tjic 
wiilU tiy thi* Mnim; *m (lit- oilit-r hnml (In- thermal mcflstircmcnts 
\r nit iruliudion of ihr JH-JI! gninnl )>y or yielded by the walls, 
an* ulu-n 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, 





] rni-: CVLJNDKR. 

if t'iv. 


tit r.^u 


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 


j old 

. <,| 


>-\ ( " 


| & *! 

. f 




' (HI 

1, ' 


t , t ta 

,, . -. 

.*. i 4 


41 r>f| 



- '-*'' " 


' Cl FlOlft 

71 4 

gi o 

o 10)4 

o o$j6 


0.040! i 
0.04)4 !(* 

0.0090 ' O.Ml 

0.0066 1 a.Hj 
I 0,0041 |0t4. 

0.0ll6 0.09 

'7.11 M 

jft-0 ' I) I 



The platinum thermometer near the cylinder-lira*! .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 fill-off, its 
of course it should; after ail-off it began again In show n trm 
peraturc higher than that clue to tin- indicated pressure, whit h 
shows that the cylinder-head probably evaporated all I hi- moist wr 
from its surface soon after cut-off. Jf this conduMim is rnrrn I. 
there would appear to be little advantage from steam jarkriititf 
a cylinder-head, 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 


POII loin of surface consMnreil. 

of inirlact, 
aqiiftrg fail. 



Cover face, 10.5 Inchw (Hnmetcr . . 

I'iston fnto, 10.5 fnchci diameter. . . 




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 H|IWH 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 steam-jacket lo the head than to the barrel of. a 

The exposed surfaces at the side of the cylinder-head 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 steam-tight 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 cylinder-head. 

Leakage of Valves. Preliminary tests when the engine was 
at 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 steam-chest 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 


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 horse-power per hour, so 
that the steam supplied per horse-power pet hour amounted to 
56.4 pounds. If it be assumed that the horse-power is propor- 
tional to the number of revolutions, then the engine running 
double-acting will develop about 44 horse-power, and the leak- 
age then would be reduced to 6.5 pounds per horse-power 
per hour. Such a leakage would have the effect of increas- 
ing the steam-consumption 23.5 to 30 pounds of steam per 
horse-power 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 quadruple-expansion engine, which 
had plain unbalanced slide-valves. 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 slide-valves: 

i i 
leakage = 


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 steam-chest in 
excess of the exhaust-pressure. The value of the constant 
in the above equation is 0.021 for the high-speed 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 piston-vivlve 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 
(i-jiti'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 port-opening wlicn the cut-off 
with Hhorienecl l>y llw Hy-wheel governor, and was faced off on 
both aklwi c> llial it could Midi' Iji-Uvuun the valve-scat and a 
massive covrr-pliLie. The cover-plule was rocossccl opposite 
tilt- Hlenm-porlH, 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 ollu-r it pnaswl into the cover-plate and 
thence Into tin 1 HU-am-port. Thi type of valve 1ms long been 
urnl tin Vlu- 1'orU-r -AUeu and Uw SiiulKUt-llne engines; the former, 
litiwcvcr, lw st'paraU 1 Hlcam- and exIuiUHl-vulvcs. Such a valve 
IUIH a very long perimeter which iiccounW for the very large cftcd 

of \\w leiikiiKC. 

Oillemlnr anil NicoUon ron.sidt-r that the leakage is probably 
in the form of water which is formed by condensation ot stenm 
on Uw surface of the valve-scat uncovered by the valve, and say 
further, that it h modified by the condition of lubrication of 
the valve-awil, OH oil hinders the leakage. 


IN this chapter an attempt is made to give an idea of the 
economy (o he expected from various types of steam-engines 
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 steam-engine 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 

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 
pumping-station 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 heat-consumption, 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 



Ty r ot 

l-rnvill |iilln|iirtK enflinr nl ('limliuil 11111 

Sul if r nillt-rli|ti'ic 'it Au|CMhurt{ 

Kx|trnmrnliil rnulnc< nl lltr 
JiiiliUiU* nf Yrihriulony 
M urine rriftliif limn 



Mnrlur vrififnr Rush . . . 
Mnrinr cnjtlnr }>uti Vnmn 


Curtis rriRlnt 1 wl Crruwil . . . 

Ciirtitui tltlf wUlmiil Jiukcl . . 

IliirrU Cnr l(w niftdtr nt C'lni (imnll 

Mnrine cnRinu tiallalhi .... 
Simple ruglnen, niiii-cnnilpnqin|( : 

C'urlliui PHKl'lP itl Crruwil . , . 

CorUss cnijfoti wlihmiL Jn kct . . 

llflrHe-Carliaa engine nl t'lm Irmull 

Ilattitt-C'ttrlt^ PtiKlnp nt \\w Mnwntlttiiwiib 
liisliiuleof 'i'cclinolofjy 

l)tm-t-aclli 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 



















n.. i 













pounds of Blcnm ftnd IQQ II.T.U. pt-r 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 cam-shaft; the cut-off for the high-pressure cylinder is 
controlled by a governor. Steam-jackets are applied to the 
heads and barrels of each cylinder, and tubular reheaters are 
placed between the cylinders. Steam at boiler-pressure is sup- 
plied to all the jackets and to the tubular reheaters. 



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 ......... ...... '4-9 

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 low-pressure jacket, pounds per square inch ....... 99-6 

Horse-power .......................... 575-7 

Steam per horse-power per hour, pounds .............. 11.2 

Thermal units per horse-power per minulc ............. 3 4-3 

Thermal efficiency of engine, per cent ............... 20.8 

Efficiency for non-conducting engine, per cent ........... aS.o 

Ratio of efficiencies, per cent ................... 74 

Coal per horse-power 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 low-pressure cylinders. The 
high-pressure cylinder and one low-pressure cylinder are in line, 
with their pistons on one continuous rod, and the intermediate 

cylinder is arranged in .similar way with ihc olhcr low-pressure 
cylinder. The engine hits iwti cranks at right angles, between 
which in i hi- lly wheel, grooved far rope-driving. Kach cylinder 
hiis four double acting poppet-valves, actuated by eccentrics 
links, iiinl lever* frm n valve-shaft. The admission-valves 
re i oiKrcilIcrl by the governors. Four teats were made on this 
engine, us recorded in Table XII, 


K iMAUKri^WS j.ij. ,\.\.$, AND TWf) OK 51/1 INfllKH; BTKOKK 78.7 

Hulli l,y SutJkK "( Wlnirrlltur, Mlvhrl/t tin Vt-rfins Deulsclier Iiigtniei ire 

vul, \l, ji. 5j.j, 

Urviillllliinn |r inlniUr ..... 

Slmm'|irrruuiir, |niini'li |wr wjltnrr Im It 
Vrttuuni, Imln-u <i( tnrrdiry . , . . 

?r hnrBF-iKiwcr |KT Imu 
Mcnn fr fniir tcotn .... 

CVial |njr Imrw jwiWf r |KT limir, 
\rean lir four (eaia .... 

Sirnm fwr IKJII nil nf fnl . 









' 5 ft - ' H 



i '1 5 ' * 

1-17 .0 



inJI' 4 " 1 



1$ t() 

i ' 5.1 

ii ..|() 

ll. .19 


' .17 




H. 7 H 




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 back-pressure 
auch an engine may be expected to give a horse-power 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. 



By Professor ALEXANDKR S. \V. KENNEDY, Proc. hist. Mech. Engrs., 1889-1892; 
summary by Professor H. T. BF.ARK, 1894, p. 33. 







ViUe de | 
Douvres. j 





50. t 






8 '.97 





= 73 




21 .t) 

i ft 


o. 70 


70 r 


rt i 










S (com -pressure above nimosphcrc, pounds per square 

Pressure in condenser, absolute, pounds per srjuare 

Ii nek -pressure, absolute, pounds per scjuarc inch . . . 




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 medium-sized 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. 




By F. T. MILLER and R, G. II 

Duration, hours 

Revolutions per minute ....,., 
Steam-pressure, pounds per square inch 


Vacuum, Inches of mercury . . . , . 


Steam per hone-power per hour, pounds 
Coal per horse-power per hciur, pounds 
B.T.U. per horse-power per minute . 

The horizontal mill-engine 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 




CYUNDftR 37.2 AMD 

By F. W, BEAM, TVww. Am. $ 




i Inttif 4 

l)iamrtt*rf ryiii 
Stroke t inche* .,...* 
Duration, hour* , , , 

Revolutions |er ttilmilf 
Stram-|t*JUH* lit ftt 

Vaeuumy itidtru*f mm wty 
Total * ... 

4 am! 


<*>, i 


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 


A of teg 

to by M, F. are 

XXX aid XXXI, are in 'I 

ami i 

in the 



The details of the tests on t 

cinnati, together with tests on 1 

Table XVIII. 





of fttrokii. 

01 utrokt* 

by f*u. 


u . 40 

10, IO 





55, ei 


1 1 . 49 




ic. fio 

II . IO 





47- J 







u . 70 




u . 66 

4ft. S 







By P. A, Engineer W. W, WHITK, 


* The two on the direct-acting flre-pumj 

Massachusetts Institute of Technology are fr 

XIX, and the on the few! and fire-pump 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 non-condensing 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 





5. Compounding. 




by the ideas that have be 
of thermodynamics, and i 
the steam-engine; 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 
non-condensing 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 steam-p 
but the steam in the cyli] 
and it is better to consid< 
cylinder condensation. 

It is interesting to cons 
steam-jackets were used b] 
he was limited in pressure 


that the theory has sometimes been misapplied, has 
erroneous opinion that the steam-engine has been d 
without or in of thermodynamics. And further, I 

all the then available has had a tendency tc importance, and It the more desirable to ; 

as given above. 

It Is now commonly considered that the steam-en 
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 



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* 
cut-off, 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 steam-consumption, 
35 pounds by the to 6 

without a Jacket, but i 

to 80 and 100 pounds 
sumption. The i 

the limit for non-condenHinj; 
on Fig. 58 are not quite KO 
figures give the following a 
simple of 


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; 

friction-brake 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 



58 represents tests with ste 
densation, at 50 pounds be 
curves are the per cents oj 
steam-consumptions in poui 





of test. 


tions per 

Cut-off in 
per cent o 






7 ! 





5 H 














































it. 5 


















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 < 


JIC*$ 4 j,jt INCIIVS 

ONIVJ NttNKtWttPNXfttt*. 

II? R im^AWNi*, lift Aft***, iKK$. 

Number <-* 









1 IJ 






















lit. 4 


ff ,4 

i-r i rtnf til 




aj | 







it, i 











radically from the 

at so early a cut-off is u 
probable error of 


on Fig. $8. It not appear worth while to try t< 

curve to reprencnt teats. 

The complement of raising the steam 




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 horse-power per h 
indicated steam by the m 
pairs of results became f 01 
non-condensing 26.9, and 
with steam in the jacket, 
from condensation was 

26.9 22.1 _ 

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 


pressure for a pumping-cngine or mill-engine may b< 

18 pounds per .square inch, ant! a difference of o 

vacuum (or half a pound of hark-prc&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 



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 

Bipuaslofiu - There are 

can be 

is by the o 

by the of 


which can be 
mcnts; compound and tri 
the tin 

employed. The \ 

a triple, or 


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 cut-off for 

Is a little less than one-fifth strok 

other hand, the triple engine at Chestnut Hill has a ] 

than for the ratio of the cylinders, an 

cut-off 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 ^ 


and two low-pressure cylinders was i 
ships. Many triple engines have t 
which with the high-pressure and 
make four in all. Again, some trip 
pressure cylinders and two low-pr 
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 


pounds with a steam-jacket ; with an allowable variation 

pounds. For a non-condensing 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 triple-expansion non-o 

About ten ago aa attempt was made to introd 1 

steam at about 250 p 

marine in conjunction with water-tube boilc 

can be built for high- pressures; but more recen 

has to to triple engines even where the 

has a high-pressure 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 . 





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 horse-power per hour, pounds . 

Gain from compounding, 

22 18.4 

= 0.16. 


Gain from using triple engine instead o 



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 steam-jackets, the co 
of steam-consumption* is not much in error. 

Staam-Jacktts. 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 low-pressure 

and is not ll would clearly be much me 

to the cylinder! of non-conducting 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 


the piping being so arranged 














V N 



4 "S, 



steam-jackets 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 steam-jackets; 
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 valve-gear is of the Corliss type with vacv 
which give a very sharp cut-off. The high-press 
mediate cylinders have only one eccentric and w 
"consequently cannot have a longer cut-off than hal 
the control of the drop cut-off mechanism. Th< 
cylinder has two eccentrics and two wrist-plates, and 
valves can be set to give a cut-off beyond half 
governor is arranged to control the valves for an; 
cylinders. Each cylinder has also a hand-gear : 
its valves. For experimental purposes the gove 
control only the high-pressure valve-gear, when 
running compound or triple-expansion. The 
used for adjusting the cut-off for the other cylinde 
usuallv the cut-off for such cylinder or cylinders i 



Clearance in per cent 

High-pressure cylindei 
Intermediate ' ' 

Low-pressure ' t 

Results of tests on tto 
order to form a triple- 
XXIII, and are represei 
cut-off of the high-press 
consumptions of therma 

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 





TVtf'ff. .-l 



' ! '4vittt ttwrtl 1ft pt i 


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a ti i iS , <* d* v -, J; } A f 



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4 || 

tt %i / *' 14* l * i it i , I * ft 

4 * 

I , 


uj (y % ^j M" W 1 * I- .- 4 | IH 4 , 
if ft; i * *| 4 ll t ' ' f li*<, 

l 1 

* , 


r & 

|| M f 4 14^ i <* -* ,<, i j t a ; 

W ft' rf | ' / i t * t 4 

II f 

1 f 1^ 



KT ',1 4 ij *i* i fc * it < 'MI; 



4 III ii ij iif J ! * * i it |i 
-** Mj << l s i - 4 * 1 tr* t i " M *j 

: ij 



ii* - 

ttt A*\ it* ll lf <^ M , ' f f, , 4 / f ^, , 

i 41 


III *' M *| I4| *,**. ,y | ^ ., |, j| f , , 4 

1 MI( to ii in i * i l<f . - ; ^ /i f . j 

It 4 

f | 


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 



^ I? *l |* M< *' ** 1 H / * ft f. 2 i ( 

j * ^ f B| 

1 ,' 


f ,i 

4 w! o i |f ^ fc ! |, v t 

4 / 



^4 i*t' M *ii <4I 1 * 4 , M i * ' , * 

W ^' 



*i ii; ** /' !- 1 M *' ' n * i * i ? r 

J l! *! 1 | i| *< . ** , , ,!" 




14 j* 

*** rt*,i *i | 14 1 | ! i^ 4 ?i| t | | , , t |j I 

Ii t| 



1 ,' 

I *j 


% (* S Ij *,,* 4 * # * v ' 



* i 

% to! i,* i til I III I , M fv , , 





Table XXIV givtxs tests 
In the jackets ami stea 

the results of these wil 


nilTSKTTS INS firm-. 



i* i 


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*m|H*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 c|i!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 



These heat-consumptions 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 


The corre8[K>ndence 
Callemlar and Nicolson ci 

has already 
From the 

to MIV 


are the Leavitt pumping-engines, 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 receiver-jackets the steam in 
pressure cylinder shows signs of superheating, whi< 
considered to indicate that the use of the steam-jacke 
too far. 

After the tests referred to were finished the engin< 
nished with reheaters made of corrugated-copper 
arranged that one-third, two-thirds, 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 reheating-surfao 
when steam was supplied to a reheater. 

For some reason the heat-consumption 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 heat-co 
for the engine without steam in the jackets and wit! 
in the reheaters (taken from Table XXIV) is assu 



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 
1863-64 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 





Proceedings of the Society of Arts, Mass. Inst, Tech., i8 


irated Stez 
















Revolutions per minute 
Boiler-pressure above atmosphere, pounds 
per souajre inch. 



5O. 2 



Back-pressure, absolute, pounds per sq. in 
Temperatures Fahrenheit: 





In cylinder by pyrometer . 





Per cent of water in cylinder: 
At cut-off 





At end of stroke . .... 






12. 7 



Steam per horse-power per hour, pounds, 
B.TJJ. per horse-power per minute. . . 

796 ' 


747 ' 


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 cut-off and release. 

The apparent gain by comparing the amounts c 
per horse-power per hour in favor of superheated 



we must compare instead tl 
giving a real gain of 

696 546 

This same Harris-Corlis 
consumption of 548 B.T.TJ 
supplied with saturated stea 
why the earlier attempts a 
so easily set aside when it ^ 

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 horse-power per 

The best results obtainec 
steam in compound engine 
in Table XXVI, for a 

T^m'l* 1^1 STUck-mf TTiTro f/aofc 


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 steam-pressui 

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 




%Ntt jj witt't; j;|,5 

tt'ft f*| P|i>4, 

By Pwfijt*r M. 

'' t > * 

i } 

*'| ft ' ; . . 

im iw p'i 


re^jf 1 w 


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 


I*, ? 11 D si 

i i' i t i 

i* 4 
i i 



one-third stroke when the 
about one-sixth 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 high-prmure 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 

The stationary comjxnu 
have about 20 expansions, 
that for highest economy 
quired. In practice 

Variation of Load. If 


In the next chapter; and the second is evident from i 
of curves of steam-consumption as given by Fig. 5 
and Figs* 57 and 58, 352-253. 

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 horse-power per hour. If the increa; 

to 10 per cent of the economy, that is, to it; 

horse-power per hour, the horse-power 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 



cylinder is fixed, is likely to have a 
indicator-diagram 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 steam-pressure, or by a combinal 
But a compound engine sometimes g: 
very low power (even when attention 
the low-pressure 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 cut-off. Usually the 


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 throttle-valve 
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 

Automatic engines, tike tlu* (\rliss engines, ha\e 
two for admission and two lor rxhaiist of ^team. Hi*, 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 

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 


from the steam to the exhaust side 
of similar construction. 

Every steam-engine should have 
of its normal power; and again it 
that a single-cylinder engine shoi 
through the greater part of its stro" 
lions, together with the fact that it i 
a plain slide-valve engine to give ar 
use of a long cut-off for engines con 
The tests on the Corliss engine a 
XXII, pp. 250 and 251) show clea 
a long cut-off for simple engines. 
out that a non-condensing engine 
about one-third stroke. With cut-< 
pounds steam-pressure the engine 
and used 24.2 pounds of steam pe: 
running without steam in the jack 
If the steam-pressure 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 


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 cut-off. Considerin 
steam-consumption per horse-power 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 cut-off 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 




"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 single-ac 
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 


lottenburg give some insight into the possibilities of 
The engine is of moderate si/e, developing about 15' 
as a steam-engine, and about .oo horse- power as a 1 
using steam at about 160 pounds by the gauge 
superheating. The engine is a. three-cylinder 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 connecting-rod. 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 than 
of the total Meuni supplied to the engine, The pc 
the engine is given in Table XXVIII in terms < 



By Professor E. JOSSE, Royal 

Re volutions per minute i39- 


Pressure at inlet, h.p. cylinder 

by gauge pounds 136.5 

Vacuum, inches of mercury . . . 23-0 
Superheating, degrees Fahrenheit 175 

Horse-power, indicated 132.1 

Steam per h .p. per hour, pounds . 12.5 
Thermal units per h.p. per minute 244 
Sulphur-Dioxide Engine : 

Pressure by gauge pounds: . . . 

In vaporizer 132 

In condenser 3 1 

Temperature Fahr. at inlet to cyl- 
inder 132-0 

Temperature Fahr. at outlet from 

condenser 66.2 

of circulating water inlet ... 49 . 6 

outlet. . . SO-9 

Horse-power, indicated ..... 45.3 

per cent of steam-engine power 34. 4 
Combined Engine: 

Horse-power, indicated . . ... . 177 -4 

Steam per h.p. per hour, pounds . 9-7 
Thermal units per h.p. per minute 183 
Mechanical efficiency 85.5 


about 35 pounds in the sulphur-dioxide cylinder a 
ture of about 65 F. ? the efficiency would be 

T 57S+46o ' 

n -"55 -^ 

and ^ - s2 = o.oo. 


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 
steam-pressure, superheating and vacuum, and n< 
vapor- pressures in the sulphur-dioxide 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 
horse-power 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 horse-power p 



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. 



efficiency and economy of steam-engines i 
cxl on the indicated horse-power, 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 friction-brake 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 engine-friction may depend largely on 
nsmitting power from the engine, especially v 
>es are used for that purpose. 

M ' 



cent of the indicated horse-po^ 
condition of the engine. The ; 
pump (when connected to the i 
the friction of the engine. It is 
cent of the indicated power of 
air-pump. Independent air-pui 
best speed consume much less 
States naval vessels used only o: 
of the main engines. But as in< 
direct-acting steam-pumps, 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 

The following table gives tl 
number of engines, determined 1 



pumping- engines, by measuring the work done i 

Initial Friction and Load Friction. A part of th< 
an engine, such as the friction of the piston-rings 
stuffing-boxes of piston-rods and valve-rods, may 
to remain constant for all powers. The friction a 
head guides and crank-pins 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 brake-tests 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 rope-driving, between the a 
piston-rod of each piston extended through the c) 
and was carried by a cross-head on guides, and the ai 
worked from the high-pressure piston-rod. The cy 
had four plain slide-valves, two for admission and two 
the exhaust- valves had a fixed motion, but the adm 
were moved by a cam so that the cut-off was detern 

The main dimensions of the engine were : 


Diameter: small piston 
larere Diston 






Hortr I*owrra 

with l 
air pump, j 

-Ml 7 




Sf, | 

?i 7 
ft^ *, 


brake (numbers g, 18, it), 28, and 2oJ were irregular 


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 
necting-rod 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* and the friction h< 
for Omitting tests with small power* (for 
brake ran unsteadily), it appears that each series of t 



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 


The compound ctntdeii! 

sented by Kitf. 60 devc-loju 1 
power to the brake, so tl 
friction. Thr diagram si 


but at half load (125 horse-power) the indicated hors 
I.H.P. = 0.07 X 250 + 1.07 X 125 = 151, 
and the efficiency is 

125. -f- 151 = 0.83. 


By F. DELAFOND, Annales des Mines, 1884. 

Condensing with air-pump, tests 133. 
Non-condensing without air-pump, tests 34-46- 

Horse-Power Cheva 

Cut-off Frac- 

Pressure at 


tion of 

Cut-off, Kilos 
per Sq. Cm. 

per Minute. 




























6. 20 

















o. 100 












o. too 


















o. 142 






























o. 167 









no. 8 










































in. 7 






















































125.0 " 


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 



friction than the other tests. The tests on this 
clearly that both initial ami load friction are aff 
cut-off and the steam pressure, and thai friction 

be made at the eut otf which the rngine is expeeU 


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 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 






in friction, when developi 
sation it had 20; conseque] 


of the indicated power, 
to the high vacuum maint 
Thurston's Experiments. 
tests on non-condensing e 
with his advice, Professo 
for engines of that type 
load, and that it can, in 
ing the engine without a 



No. of 

























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 

*!$'* . 


ffl^rt * 4 '. 
i '% * r*i 

: ll'^/l v : ', 





Parts of Engine. 

\O rt 


Main Bearings 
Piston and Rod 

Crank Pin 

Cross Head and Wrist Pin 

Valve and Rod 
Eccentric Strap 






Link and Eccentric 
Air-Pump .... 




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 piston-rod 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< 
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. 


INTKKN'Al. <' 

RECENT advances in the | 
been found in the develop!) 
and of steam-turbines; 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, #as-rn#inr: 

'1C f t*/V\ 


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 hot-air 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 non-conducting material, and working 
freely in an inner cylinder. Between this 
cylinder and an outer one from A to C is 



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 

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 Kii-t- ! 
quit k!v 


strokr; \ 
litllr tlu 
Ilir air ; 
of thr ili 
ratt*r, fr* 


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 



as Stirling's hot-air 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 horse-power per hour; but the fi 
large, so that the consumption per brat 
pounds. This engine, like the original S 


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 



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. 

Gas-Engines. 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 


engine itself; the second type of engines, 
engine is an example, is the only successful 
time; the other type has some advantages wt 

Gas-Engine with Separate Compressor. - 
a compressor, a reservoir, and a working q 
as a gas-engine 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 

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. 

'^ ! 


^00 1NTKKNAI, 

U*mpiTatuiv> I'onvspondin 
hrat added from A ti / !- 

and flu* ht-at withdrawn t'n 

f i- 
M that thi* ftl'u it-iu'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 u|if'r,jli'i! 
cllit'inu y, Ifu^v tar tht 4 i j 
flit' rohuMf .tdi.mUn'r , n 

above the atmosphere the eiliciency is 


/ 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 eiTicieni-y 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 


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 






Gas-Engines with Compi 
ful gas-engines of the prese 
in the working cylinder. 
end of the cylinder only, 
the cycle, so that there is o 
working at full power. S 
four-cycle engines. Some 
of the cylinder accomplish 
as two-cycle engines; they 
tion when single-acting. '. 
have been made double-ac 
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 

The most perfect ideal 


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 

*)" . 


1 'lA^l 

J< ' 



provided that the temperatui 


= 104-7 


== (2500+ 460) 


1 ~ i -4os : 

If th 
shows * 
as in ] 
heat as 
by wit; 
to can 

F:G. 70. G > anc 


represented by GC. The he 

and the efficiency is 


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 



_ T I53 6 - 6 5 + 1-405 ( 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 


times the volume at D, and 'that the volume at B is 


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; 




and the expression for elTki 


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 


of ;20tothi'inrh, ami iih * 
pisttm; tlu- upl*'*' pan i 
appear In tlu' m^n-. 'H^ 
pounds, and liuMvdtMiHiin 


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 
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 


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 non-cakinj 
c-oal,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* water-gas 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 


Hydrogen, li ....... 45. > 


Methane, C*H 4 i 34, <) | <xj,8 j 104.7, 


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 non-caking bitur 
larger proportion of hyc 

In a paper on the use < 
gives the composition ol 
Scotland, and Germany, 
following table were de< 



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 

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 gas-engines 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'Stfo-y 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 


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 gas-engine 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 

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 



time. The actual e: 
for gas, and for lar 
represented by the 


but a part of this ; 
carbon monoxide* an< 
may reduce the expc 

Water- Jackets. 
engines have the h 
water-jackets; 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 


and oil-engines 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 steam-consumption, so that it should he employ 
the calorific capacity of the fuel cannot he d 

Since the heat-equivalent 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 horse-power 
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< 

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 non-conducting cylinder. The ratio 


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 horse-power. 

In the discussion of efficiency we 
heat-consumption per indicated ] 
because the fluid efficiency (or the 
working substance) should for thi 
confusion with -the friction and 
engine. For the same reason, an< 
steam-engine can be determined 



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 


w : 

1)5 rll } ' > 

time considerable import 
out spent gas, but it atte 

In indicating a gas-en^ 
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 

Two-cycle engines co 
which supplies the mixtur 
ten pounds above the atm 
pression must be determi 
measurement of the indie; 

Valve-Gear. The suj 
combustion engine are ; 
least two valves (or the 


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 valve-gear for 
tion engine resembles that for a four- valve 
daily that type of steam-engine valve-geai 
lift- valves. The solution which is most evi< 
monly chosen is some .form of cam-gear; 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 bevel-gears; 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 '' 



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 dead-point, o 
ward. The disengag 
and there is great dan 

When electric or ot 
hand-power, 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 


for controlling the power of an internal-combustic 
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 oil-pi 
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 

But for gas-engines 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 


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 horse-power. 

This discussion of tt 
varying the mixture of j 
for many purposes that j 
a gas-engine. 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 


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 uftlu-Ka* niittn*\ a 
now iriuLs t> iwvomr univ 

1 M * ! Thr hot tubr tnjl; 

krpt rrd hot lv a Hun 1-1 

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 



same way. Premature explosion in a small e 
started may be an inconvenience, but in a larj. 
lead to an accident. 

Gas-Producers. - 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 
gas-producer 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 
by-products, 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 


N : 


j' I 






tin* prvst'iH time tin- Hirl. 
caking hituminou-, ial. . 
tion, at St, l.oui*. in tu-^t, a 
raking bituminous i'o;il and, 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 


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 down-draught. It is probable that diff 
fuel will need different treatments. 

Blast-furnace 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 horse-power, it is evident th 
to develop power from that source must be 01 

The gas from a blast-furnace 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 coke-ovens is a rich : 
producer-gas 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*; 



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 


ThtTt* an- thtvt' tyjt*^ t* 

thcisr that t|r| 'it'Ilt S Mit a- 1 ^ 
clt'jit'iiflin^ on asf-tif.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< 

llir Ilitift* rrtrnt i arht 
supply lit'ing drawn fwJ 
lint* i.s stippliril itit! IIMH 
ninrr or I-H^ in riiurti 


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 


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 


appears to be no reason why there should bo troul 
of some form of carburetor like those used for gas 

The Four-cycle Engine. - - Fig, ;H gives a verticil 
Westinghouse four-cycle 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 
steam-engines 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 

cross-head Is needed; 

a common arrangement for all except massive 
The cylinder barrel and head are wulerjurket 


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 t-n^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-\ 
lm\rr than | thr , 
atlvanta^f |*i'utini the 
nihi-r uay. The iir^i / 
\\UN that ly Inii^ili! <*! 


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 cylinder-head. Then 



engines have been introducec 
Two German engineering fir 
especially for burning blast-i 
as 1500 horse-power 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 
engine-cylinder, and arrang< 
driven by one crank (which 
one for compressing air, ai 
of the two pumps are des 

The air-pump compresses 
phere and delivers air to the ; 
cams at the time when the ] 
controls a bypass-valve TA 
pump in communication i 
stroke of that pump, whid 
the first place the compressi 


plungers In a long open-ended cylinder; these 
connected to cranks at 180 so that they appro? 
from the middle of the cylinder simultaneously, 
has a cross-head at each end of the cylinder to it 
thrust of the connecting-rod, so that the engine 
great length on a, horizontal foundation. Towai 
end of the cylinder there is a ring of exhaust-ports 
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 gas-ports may be controlled by annular valve, 
by hand when the engine uses blast-furnace gas. 
conditions the engine is regulated by a governor, M 
the pumps that supply air and gas. These pum 
driven from the outer cross-head, 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 L'v 


i H 




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 


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 one-seventh 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: 


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< 
water-jacket, 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 


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, 

t' r 

but since the compression be 5s also adiabalic, 

and consequently 


mK'ratutv /'? I ' lr * 

prrssuiv at tu- '* * 

ill !' : 

jlr l 



ZnjirtrtL llut i>, lv rrilu 
liy it writ's uf i.tlruLiffM 
Tliis JN a MTV impnt'Lini 
will hau' in prat tin- litiU 


[I is 11 pnM* *l !ha*. 

i rill i*' .t J *a'* f? ' 



.ii thai ill*- Iraian* 

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 


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 two-cycle 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 valve-gear 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. 

Two-cycle engines would not require much co 

xvhulr .,>su-m. 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 





(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 
ating-gas 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 4-59 

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 horse-power, and be 
by dividing 42.42 (the equivalent of one horse-pow< 
units per minute) by the thermal units per indicated 
per minute. But if the brake horse-power 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 

(JAS-KNiUNl- 1 WITH t! I 
ta\i a i- '" ' 

1*1? if I- ;;* a* M t *?' U >'fr j- 

4 -J 

4 >-' 

4 ^ 

4 ( * ! ' 


eight to one will give the minimum per brake horse-power, 
remainder of the table is less conclusive, but it appears 
that a ratio of eight volumes of illuminating-gas to one v 
of air is proper, and that for power-gas the ratio should be 
what larger than unity. 

(3) A committee of the Institution of Civil Engineers * 
three gas-engines 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 horse-power 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 horse-power per minute. This 
trates an inconvenience of using the brake horse-power 




ivrt R% 

l'rotV-Mr \tt \ i in i 

thr infill* m ! tin- tifttf 

llit'iinal unii - }*i in*!! 

tMtt'il h(J l <* }tV*rl ,n l 


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* 


development of power by the combination of a Taylo] 
ducer with necessary adjuncts, and a three-cylinder Wes 
gas-engine; a detailed report of the tests is given b; 
Parker, Holmes, and Campbell,* the committee in ch< 

The gas-producer had a diameter of 7 feet inside 
lining, and at the bottom was a revolving ash table 
diameter; the blast was furnished by a steam-blower 
from a battery of boilers used for other purposes; t 
made to determine the probable amount of steam tak 
blower, but the variation of steam-pressure 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 boiler-tests made with the sa 

The gas from the producer passed through a coke 
and then through a centrifugal tar-extractor 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 engine-cylinders were 19 inches in diameter ai 
inches stroke. At 200 revolutions the engine was rat 
brake horse-power. The engine was belted to a dire 
generator, and the energy was absorbed by a water-rhe 

The results of a test on a bituminous coal from Wes 



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 horse-power . 
Mechanical efficiency, e 
Brake horse-power . . 
Gas per horse-power pe 
Thermal units per horse 
Thermal efficiency of bi 
Coal per brake horse-pc 
Combined thermal effici 

It is interesting to co 
plant with the tests ; 
from which the results 


Duration hours, . . . 
Coal required by plant, 
Thermal value of Georj 
Heat abstracted from 01 
Efficiency of boiler . . 


correspond to one pound per brake horse-power pi 
of a pound per indicated horse- power; the makei 
power-plants are now ready to guarantee a eo 
one pound of anthracite per brake horse-power 

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 


ffi I 

IIP;' 1 - 




quently 0.32. At an 
power, the oil-consui 
(34.4 horse-power) 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 heat-engi 
retical cycles, which 
major part of the hea 

The following tabl 

of Engine. 

6.75 X 13-7 

9.5 X 18.0 

26 X 36 ? 


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 

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. 

Waste-heat Engines. *( )n page 180 attentioi 
the fact that the exhaust-steam from a steam-e 
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 steam-engines. ', 
from a gas-engine 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 

1; W i I' 1 ' 
I ii ( [*:. 


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, 


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. 

Fan-blowers 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 
delivery-main 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 fan-bl 
ventilating-fans have their axes parallel to the di 
air-current, 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 


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 

When water is sprayed into the cylinder of 

of operations rrpivsriHt 
tlu* air is rompivssrd, 



s|ll*i 1 

' I 



cif tin 4 otmprt-ssor vvl 

that tlir !'iiiii|nvs>itiri i 
nrntial i iirvr haunt; il 


rk {' * ujj 

Thr \vtrk ff 

%rlL ' 



in which the subscripts refer to the normal proper 
freezing-point 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 horse-power 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 piston-compressors. 

Effect of Clearance. The indicator-diagram 
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; 


anil thi . t i 
without t 


f.n tor l*> 

aiur 11111% 

Tfinpemture at the I 
tin- t omprr*> r yliiiitt-i 
Ijtouf hi in willi tt it w.i 
vupur Ci>lli*\v,s ihr li w o 


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 steam-engine, < 
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 


If thr 
will to- 

the rlraramr 

rxprrssrtl in uli ^ 


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 


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 

n_ 1 

M ( //> 


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, 

Three-stage Compress* 
iTfftiifvtl, as \\hnr air * 
to UM- ;t t 

whit h flu- aii' ' pa-^ 
vva\ frtni uiu* 

an* /, ami /, 


Thr \vurk of iomjrr 

it**, ftil'il tt-iil'i iif ii 

and l "._! 

Equations (206) ami (207) k*ad to 

from which by elimination we hav 


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 three-stage 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< 



Piston speed, 
feet per 
minute . 

1 60 

This table does not 
nor is the clearance fc 


would be 


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 valve-action. 

Professor Riedler * obtained indicator-diagram 
cylinders of a number of air-compressors 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 : 



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 air-hu 
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 


\ufti tin 

itM.tiii i 


lilt- mri|,ii! *4 tft jr ?s 
liy tilt" f ftf tip. fit Mil J'.itfr 

irtil it i- 1 * t u*<ft** ?*+ : 


Seaton * states that the efficiency of a vert: 
air-pump varies from 0.4 to 0.6, and that of 
horizontal air-pump from 0.3 to 0.5, dependii 
and condition; that is, the volume of air an 
discharged will bear such ratios to the disp 

He also gives the following table of ratios o 
pump cylinders to the volume of the engine cyli 
discharging steam into the condenser : 


Description of Pump. 

Description of Engine. 


acting vertical 

Double-acting horizontal . 

Jet-condensing, expansion 
Surface- " " 

Surface- " 

" compound 

Jet-condensing, expansion 
Surface- " 
Surface- " " 

" " compound 

Dry-air Pump. In the recent development < 
ing, especially for steam-turbines, great emp] 
obtaining a high vacuum. For this purpose tt 
pump which withdraws air and water from t 
been replaced by a feed-pump which takes wa 
condenser, and a dry-air pump which removes 
is necessarily saturated with moisture at th 
the condenser, and allowance must be made fc 


If ih< 
an 1 

tn i* 

;,! / I ,, 

|!U t tli^ * 
i iti Ml ,!, n 

t ulltlrliNlHi* 



85. J Lj.8s 

X 7 7;-- 2080 e 
51.9 0.878 

Assuming the air pump to be single-acting 
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 


If thr 

if thr r\|rnl "< *'*' 

the uir in ihr tlr-if^ 1 
whivh ihr lUlfirira^n- 


t \t H:) trVfilll!i' % 
Will tir 

thr i Mini*!"*"-'^ 1 *'* & 

tit > ii.: 


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 14-7 = 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 piston-rod, which will b 
pass entirely through the cylinder, will give for th 
the low-pressure cylinder 31! inches. 

Since the pressure p f is a mean proportional be 
p 2 , the clearance factor for the high-pressure cyl 
the same as that for the low-pressure 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 ili-j*-nl >u tin* i 
mvivr niiu It uHmtiMn a- 
Tin* | **! iT{uirnl I 
frtn rjualitli i t*^ * t' r 
ills- .ipl'atvnt * a|a !!^ * 
a}]ai**tit * aja iH' alrra 


{"fir !r!Sl]*f!4f?4l'r 4! ft' 

will !* i'^r ;>" I 4 '. a!ui**, 


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 


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 0-00393 

0.980 0.00351 

with ;- ! 

? - ,,,,,,, s . 


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 Compressed-air 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 steam-engine. 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 
Air-Consumption. The air consumed by a given 
air engine may be calculated from the volume, pi 
temperature at cut-off or release, and the volume, t 
and pressure at compression, in the same way that t 
consumption of a steam-engine 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 supply-pipe, only on account of the chilling a 
wn.ll*; of tht* rvlindrr rhirim*" jiHminKion. which ;rrfm 

jtvs>urt' in> .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 


the walls of the cylinder of a compressed-air engine 2 
working therein are of the same sort as those taking pla 
the steam and the walls of the cylinder of a steam-ei 
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 
pressed-air engine than in a steam-engine. 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 

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 exhaust-valves, 
cultv mav be overcome in Dart bv making the valves ar 


automatic valve-gear 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 horse-power: 
33000 F ' 

and conversely to develop 100 horse-power 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 piston-rod 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 


of the putton displacement, If the lompresMim omirred ufl 
dently early t raise the prt-HMire 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- MnalU-r um! lltr ni/r uf thr cylinder would t 
1'hr air-rtnsuipton 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 ton f*r the um of con 
pn?)Wi i d air for tran<*tiiilfiic jmH-rr, 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 pt|e tii .,!*4- ^in* there i^a f pressui 

In (IciwinK tltrtif|it thr piji- at *siaitt smii^rjitwrr^ there 
a nrrr-%|iiiti$ri|.f tnrrrai-tr t! volume . : that the pijic delivei 

tuhir frrl ftrr minute, Our takttkfit*ii for the air-cc 
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-= pi|n.*, und tMmpre:**.rd *isr engine should deliver 

X jJ^.ft * i*#j f htre j*ower. 

If the frictitm of the compre-vMrd 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 %ifii|lr rm|irfr wi 
fount! to l*r hurie-jHwer; it .fi%w|tirniiy ? 

of the .ir*m-pMWrr i 

fr doing wos 

compound compressor is used, then the indicated steam-power 
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 steam-engine, and that the transmission system 
should properly include only the compressor-cylinder, the pipe, 
and the compressed-air engine, then our basis of comparison will 
be the indicated power of the compressor-cylinder. For the 
simple compressor we found the horse-power 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 air-consumption. 
It may then be assumed that with complete compression our 
engine could deliver 200 horse-power to the main shaft. In 
that case the efficiency of transmission when a compound com- 
pressor is used may be 0.53. 

Efficiency of Compressed-air 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 steam-power may be 
realized on the main shaft of the compressed-air engine. On 
the other hand, when compressed air is used in small motors, 
and especially in rock-drills and other mining-machinery, 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 


madr by Mr. Daniel at lards gave an Hl'tni-sicy varying from 
0.355 to 0.455, W M | ( r*^wes wrung from ,-,75 atmospheres 
.$ atrt!ttt|lirfr>, An r\|H-riwent 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- n-ttwrns why it i< ^H-iully de \able, as in mining and 
tunnt'lHng. It i^ now >i to a on*ileiable extent for driving 
haml-loul*. smli a* drill*, t Unifying c hm-t, ami talking-tools, 
in mat him* and Uiler ^Si|*". itml in hbtpyards. It is also used 
for o|HTalin# 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 he-re bytiratdu j*tiwer i* liable to give 
trouble from fmvjrig. 

Ci.ii|i*i*oi air ha? trrii ii^nl to a MTV i nii-iilrrii bit? extent 
fur tratisfttlititti? JHWT in IVix Ilir '-.vsinii aji|H*An to be 
v,x|K*nMvr and It* i.- tr%rt| mainly i*n aft*utnt of tt ctinvtjinicncc 
for {U*livi*rin|t !*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 |i|r wltitli i% hrttitl rxtrtmlly byi 
rlwrrtiiil firr, I*rfr%M$f I'mvm ^timatrH tlutt tin t-ikirncy 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,rh|jctl by Mrlariki WK 
air nl 'i)o to HP |itifii|s |MT *jUitfc- intii in rr^trrvtiim having 2 
rafittify tl *^ fubir frt-l, Utr tar al?* iiff1ra a of ho 

water at a tem|HTaturr 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 street-cars 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 reducing-valve 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 reducing-valve 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 air-compressors. 

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 

W - 3 X 464-7 X 144 X 75 
20520000 foot-pounds. 



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 * -|*4-r : 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 rwYirm-y of 'Coring ami rritoring rnrrgy by 

usr f rctfii|irrwrtl 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 |i|v mill bccott 
its triii|it*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 *ir|rmtiftg MB flic RfliJCtio 
of thr Urm|w-riitllfr 111 l|if!i|i|*, 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 fhm-ing 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 three-stage air-compressor 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 boiling-point of its 
liquid and then liquefied. Linde's liquefying apparatus consists 
essentially of an air-compressor, a throttling-orifice, and a heat 
interchange apparatus. 

The air-compressor should be a good three-stage 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 throttle-orifice 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. 


.K-Vri.\i;-M. \rlUNI-s. 

ftr producing k 

e ir ^|nrr. It ni 
>i lw lrnijHrature 

A Ri?rw<u:*ATtxis-.\c*itWK N ;i 

tm|H*ruturfH or for tliii|t '*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 tt-rtiiifi 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^ t|r|*riiil n the raj; 
jttr|ilori nf miir uttafiir li|wiI, fr r\st|i{r, t| ummtmia 
walrri If tin* mathinr ! i* wrk iiiti*'K ilu-tv rmt?t litsoi 
lirriiriicrmrtit fr rrtitsistling il- li|tii! 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 i-mli-f r on*Im'trf. "Iliii's Uu-y lakr hrat from 
t'tilt! utliiiit'r, ! w<rk am! ii*il Iir4i, sinl itnaity n-JiTt then 
of the in ami ittr h*4i r|ui\iili*ni of tbr work dot 

Thrsr ri*wr'*t tirni rtii|tr-% 4 lsi*-rvrf , urr wry far from btfi 
r**vrr%llilr tnitinrH, not Jy * ai mim f ii|H-rfn ilwns imi Iw 
but litT4li* they * si irvrf.'sillr ryrir, 

f r-ft liifir-! art- in t-mnmon ., i 

sulphur <lto%ii|* ur snmr oih-r 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! 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 expansion-cyimaer & 01 smaller 
size, and a cooler C. It is commonly used to keep the atmos- 
phere in a Cold-storage room at a low temperature, and has 
certain advantages for this purpose, especially on shipboard. 
The air from the storage-room 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- 
face-condenser, 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 expansion-cylinder 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 inlet-valves a, a and the delivery-valves b, b of 
the compressor are moved by the air itself; the admission-valves 
, c and the exhaust-valves d, d of the expansion-cylinder are 
like those of a steam-engine 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 expansion-cylinder, 
together with the friction work of the whole machine, must be 
supplied by a steam-engine or other motor. 

It is customary to provide the compression-cylinder with a 
water-jacket 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, 


is replaced ly .m HwtftUiin* ,i Meant engine jet-con- 
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 u-wly removed U-fure 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 jiitMit-d >IK-|I a ilruir, Thr lU-H C'tilrmiin Company UM 
u jrl i-tHlrr with prnvitiun fr ti4!rjiin^ and withdrawing water 
and ihrn |ii s * ilir uir ihrounh JMJH-S in ihr citld-rtKim on th 
way tn ilir rx|ansun 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 |i|H i a anc 
drains bat'k intt* ttir tmtrr. 

an air rrffiiirwliiig nun Iitnr i- 

tit ilw rM rim i- m-ti-n*fily 
and the skr f iln- tna* hint- i- Utrnr '* 
ftrmam't'. Hi*' itTfrm,nur ituv U- 
fhr nuu him- n i t, Itrn-il 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 
imrt-iiMtl hy runnto) 
jrc"-urt"s; lr example 

i* n u*t! 4 |ij* in a iion-freeanj 
r >$ir <ti*'tir<ni'* liriti through thi 

Mri | ilir t ti|fi|f*"%.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!nit|iheric 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&M-d 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 
cut-off in the expanding-cylinder 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 valve-gear 
and large, short pipes communicating with the cold-chamber 
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 cold-chamber, and 3 may be taken to 
be the temperature of the air leaving the cooler. With a good 
cut-off 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 expanding-cylinder shall be complete. 
The compression may be made complete by setting the exhaust- 
valve so that the compression shall raise the pressure in the 
clearance-space to the admission-pressure p s at the instant 
when the admission-valve opens. The expansion can be made 
complete only by giving correct proportions to the expanding- 
and compression-cylinders. 

The expansion in the expanding-cylinder may be assumed 
to be adiabatic, so that 


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 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. * 

it* || ^ ? f 

t t I* a '** I " 

* i 


"r I 

ir ii *. 
, * f .* . , , < 

s I \,f 
I Ihr 


fi sni-i * 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* ri|ti4iiititi fijj) or fi t * 

l t ^ trt i ( />, f , .a*l f, by Ij ft; to tA 

it; ~ 


H -- 1 t 


me auierence between the works of compression and expan- 
sion is the net work required for producing refrigeration; conse- 

or, replacing M by its value from equation (232), 
W = 2i *i + ^ Ji ~" V 

/ t / 4 



The net horse-power 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 
expanding-cylinder, and U is the temperature of the cold air 
leaving the expanding-cylindcr. The gross horse-power devel- 
oped in the steam-engine which drives the refrigerating- machine 
is likely to be half again as much as the net horse-power or even 
larger. The relation of the gross and the net horse-powers for 
any air refrigerating-machine may readily be obtained by indi- 
cating the steam- and air-cylinders, 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) 


^1 ~ ^4 


If the initial and final temperatures of the cooling water are 



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 compressor-cylinder 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 -=-M-7^ (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 expanding-cylinder, its apparent piston displacement will be 


If p v the pressure of the air entering the compression-cylinder 
is equal to p^ that of the air leaving the expanding-cylinder (as 
may be nearly true with large and direct pipes for carrying the 
air to and from the cold-room), equation (246), will reduce to 

D. = D c p- ....... (24?) 

* i 

Both the compressor- and the expanding-cylinder will have 
a clearance, that of the expanding-cylinder 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 
indicator-diagram; but a large drop at the release of the expand- 
ing-cylindcr 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 cut-oil of the expanding-cylindcr. If 
the cut-off 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 expanding-cylinder, 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 expanding-cylinder will not be quite complete. 

Calculation for an Air-refrigerating 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 cold-chamber be 14.7 pounds per 
square inch and the temperature 32 F. Let the pressure of 
the air delivered by the compressor-cylinder 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 expanding-cylinder. 
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 



of thr air rowing i'mm ih- uiit|rrs^t*r ami 
tlimU-r will l- 

/, - 

7*4 - Ufo * 

Tltt- rortt Stif* 

. U 


gitl from tfc 

.', /,a54l 

i i " 


}n-r minuir; ruH'-*rt|iiriitSy 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 a|i|sfrfii |ii.%in 
tvill lr 

j,,yeii ft. 


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 

tiw|4*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 


J v r % f 

2.33 * -979 ~ 2 -3 8 cubic feet. 

If, further, the clearance of the expander-cylinder is 0.05 of 
its piston displacement, the factor for clearance becomes 


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 compressor-cylinder 
15^ inches, and diameter of the cxpanding-cylinder 14 inches. 

Compression Refrigerating-Machine. 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 is-t-*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 t^hn-, !**! \.iIvr.H, ;ml vjilvt*s ii 
jn-Hltm. SmstU nui-hiw% tr-'twlly h.ivr ! il*ui4riiclirig 
jm-HMir tylttuSrr, L.uifr m.i-hif-. Iwi-r vrrtinii 
which may S" sinjjlr iutiiiK nr i|i*ul>U- iicimi;. 

Tin- i u U* whiih It.i". Sw't-fi 'Siiitnl fur llir 
rrfri^rritifiig iiwt hM- ! im*m|I*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 h-irrt 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!li|ilii rtliO" iIl iliilu *iUtr-, 

Proportion* f Etfrigtrtting-Michlttw, - 

IpjttttS *nlrfrr*S in llir *ih l ihi- * im!rn-j'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 


Irwttt llir ctf;ilft|f *il by it 

|i s _ j| >//,.- ^ (S ...... 

Ttti* u*tnirrw*r ivlintlrr t--* .aSm-ai"* ti|ri| hy a Wittrr-ji 

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 


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 

c f (t, - t,} + H, - H v 

and an approximate calculation of the horse-power of the com- 
pressor may be made by the equation 

P = 778M \c v (t, - Q + H, - HJ 

or, substituting for M from equation (249), 

7780 \c (t t } -{- H H \ 



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 steam-engine 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 vaporizing-coils and the 
heat-equivalent of the work of the compressor. The heat that 



must be carried away by the cooling water per minute is co: 

<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: 

The vapors used in compression-machines 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 Refrigerating-Machine. I 
it be required to find the dimensions and power for an ammoi 
refrigerating-machine 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 

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 freezing-cans, 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 horse-power of the compressor is 

p _ 77301 \c 9 (t s - Q + H, - H 

33000 (H a - ft) 

^ 778 X loooo {0.50836 (208-85) + 556 - 5351 =4I> 

33 (535 ~ 58) 

If we allow 10 per cent for imperfections, the compressor will 
require 45 horse-power. If, further, 15 per cent is allowed for 
friction, the steam-engine must develop 53 horse-power. 

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 


X 80 




If 10 prr rt-nt i- 
action* tin* piton li.--.plarrmrt wilt } M - mic 
elutmrfcr may t* nuulr t-^| im h-i irul ihr * 

Pluidt Af Thr ihiuh ituti tuvr t> 

won frfri|H'ralifi||-iiiiii'titftrs iirr rilu-r, -tjl|hi 
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, ,ii|ii *il**t* jjir pfrvtiifr *f ll 

rarlwn fiii%iilr, *tfr unrn in stir I 

imperfect vaJ 

ir fmit, and t 

n eomptf 
!.* known 


t ti 


MHi I 74; 

Klttcf it'irtt ill ihr raflv Mmjrr-v>t*tt fitl!tnri, but It I 

ill llsr frfri|rr-4l? I hi* 
ihr fifw-filn %-4tiftir larifc, si ituf I tic 

fttf ttrfr rilfirf f bully, Mtt 

OVrf, alf !. Jfiil, IIM lllr itiiii liiitr rtf|i| 

4it*'.t|r liii* 

fully, bill if ltii;i llir tii'*atfvaftitgr ift^l 'Hsl|4!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 |r|iicti!i--* MIiili?i i! t-n Iwliir l Ci 

A-* n *5lw in- Itsr fil4i% I^lrt's 1 

ill |iw Icf|t|w-fa!iifr til?rftitrli*iir turlwrrn 

of Jiiitl iimntunk. am! ihr 

hr It li,r* l-r tunl by till* 


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 non-freezing 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 steam-pipe, 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 ,ii-r 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'ilt-r * 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 rti||ifir 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" ri|ian,itijj-eyj|fl| 
littVr (Iblfililiitiill -ilir Viihr-j, wilh tntlrftrftitrnl tlfl=ff V|l\ 

Tlir ilimrm *' ,trr j*iii-n in ih- fi*i 

itr 4 


III ilir tiT%!b, $l 
i'f'iiiiiirf's, il 

! flit ff*ft 


it i' by 


Uf-j rfr nH4* lir-4 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 %iii|rn *h<w for lite ci 

llt?lft .! |*fr-fjiifr *|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. 



Number of test 

Duration in hours 

Revolutions per minute 

Temperatures of air, degrees Centigrade : 

At entrance to compression-cylinder 

At exit from compression-cylinder 

At entrance to expansion-cylinder 

At exit from expansion-cylinder 

Mean effective pressure, kgs. per sq. cm.: 

Steam-cylinder: head end 

crank end 

Compression-cylinder: head end 

crank end 

Expansion- cylinder: head end 

crank end 

Indicated horse-power : 



Expansion- cylinder . 

Mean pressure during expulsion from compression-cylinder, kgs. 
Mean pressure during admission to expansion-cylinder, kgs. . . 

Difference _ . 

Calculation from compression diagram : 

Absolute pressure at end of stroke, kgs 

Absolute pressure at opening of admission-valve, kg.: 


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 

65- os 







60. 10 






1. 20 








i.6 3 










1. 14 
1. 19 




















, 0.56" 







20. 6 








System of the machine. 

Dimensions of the steam 

Dimensions of the 
compression cylinder. 






Diameter of 
piston, mm. 

Diameter of 




Diameter of 
piston, mm. 

Diameter of 








55 -S 
















7 ' .. 






Revolutions per minute 

Indicated horse-power 
of steam cylinder. 

Indicated horse-power 
of compressor. 

Absolute pressures of vapor, 
kilos, per sq. centimeter. 

temperature. 8_ 



In compressor 

In condenser. 

In compressor 

In vaporizer. 










4.8 3 J 

i. 06 

ii. ip 

It. 2 
II. 2 
II. I 


10 15 

10 I 

10 15 
10 3 

3 * 


59. i 







26, i 





S- ii 


8. ....... 

IO ......... 



Ice formed. 

Temperature of 
water or brine 




Temperature oi 
water supplied, 
degrees C. 

Per compressor 
horse- power, 
per hour, 
gross, kilos. 

Per compressor 
per hour, 
net, kilos. 

At entrance. 

At exit. 

-a , 




li. ip 

II. 2 

II. 2 
II. I 




6. 05 




=^ 3 




6 .... ... . . 

7 . . ... 



ii. 3 
ii. 3 

20. 6 


I8. S 




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 horse-power 57.1 

Power expended on compressor 19.5 

" " " centrifugal pump 9.8 

" " " water-pump 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 water-pump supplied cooling water to the condenser 
and for other purposes. 

4 it* 

nNti MAt'IttXKS 

A similar fr-4 <n tltr l*i u-i nut him- 
rr of 

r iinm- ...... ....... 7.9 H, 

am! inirnnrtjiitu* . . . . . 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*u-u-i rrfriRcratinii ittarhtm*, in a aped 
building provide! by tm* l.imlr C*u|any whit'h had eve 

ronvrriiriiiT ami fiitiltiy (r r\ai **rk. Tlu- following tab 
gives llir |riiiti|il iSIntc'fi-5.ii'* *f ilir 

A,\! Mf'TKT 

.i illt.i.ff, \ll\, M It 


if, i 

y 8 MI 



Thr Limit* u.w*l 4ml *4' alltiwrtl to rlra 

at nil^Iitrr wf liquid v;t|r 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 rfti|fi"*.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 ftr-at Wiin withdrawn by t 

r Sit rtil, Tlif rnif.ifl* r irftifiw'ffitttfr'i 

By Professor M. SCHKOTER, Vergleichende Versuche an Kallemaschinen. 

Piclet machine. 

One vaporizer. 






Steam-engine : 

21. 8r 




6. 1 1 
3 os 

19 72 


+ 0.6 







2. 02 
4 .08 




+ 0.6 




3 84 











21. OO 
21. OO 













+ 8.9 


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 cooling-water, entrance 
Mean temperature of cooling-water from 

Mean temperature of cooling-water from 

Initial temperature of comlensing-water, 

Initial temperature of condensing-water, exit 
Final temperature of conclenning-water, 

Final temperature of condensing-water, exit 

'Refrigeratlve effect, calories per horse-powe 

Linde machine. 





a 89 
5 9 





3. 95 





9. 54 











20 . 83 
17. 96 


9 -5$ 







+ l 


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 cooling-water, entrance 
Mean temperature of cooling-water, 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 horse-powe 


hi- Ci-tV ;"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*m|ili|t \valrr ;tl alUt J5*> C. 

Tltr firrswiiirr in ihr tontjrr-%or drjtrmlrd, of runrse, on tl 
trm|H*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 
ttrrrs|Mmling ii ihr highrr trinjK-raturr in llir (ontlrnn^r. Tl 
mi fit in ttft i jrr*>urr f ihr tv(*rkiri ailiitm r of tnirj*r diminbhe 
ihr lirilir Iffii|rr*itiifr frll. 

Thr hrat yirldrt) jrr httr lo thr ammonia in ihr vaporis 
ritli'MlalfiJ by iiiiiiij|4%ift|i, ii*i*cfltrr ihr amount f hrine use 
in an hour, ihr *jirriik hrai of ihr btmr, and iu increase c 
iriti|irr*tiiifr, Ilitt ihr initial *ftd fifirfl i.'fii|t*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 tnvolvr-4 akit the jacte 
water 4 nd its of trntjirraiurr. A trrllon is ipplfg 
fur ihr vArkiiuni of intital *ind itnil trtti|irriiuir of ti 
ttwlifig-Wiiirr, 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* rt|tiiii to ihr jibitratlrd by ihr riwiling-wtte 

Till* Jrf Wit f ijiifrfriii r ln-lWrrti 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..% ii|i 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 heat-engine; for a 
heat-engine will have a higher efficiency and will use less heat 
per horse-power when the range of temperatures is increased, 
and per contra, a refrigcrating-machine will be able to transfer 
less heat per horse-power as the range of temperatures is 


By Professor J. 1C. DKNTON, Trans. Am. .S'c. Mcch. Kngr., vol. xii, p. 326. 





Preatuira above ntnionplmrn, poiuiibi por Hqunro lunh : 




ay ,H7 

Temperature, dugrucm Fnlirnnholt : 



a .ao 


,|,| .6^ 


S4 ,OO 

outlui ...,,,,.. ,.,,,,...... 

8? ,ftft 


Hi ^6 


Jack^t-wtvtart Inlaid, ,..,.,,,., ,..,,..,..... 

,\,\ ,6 j 


S*t J 

t .0 

^y .a 




a 60 

ttnterl UK tutndonBttr .,,.... 



Brino, paumlN per inhiuCw, . , . 


tua H 

Specific ntutt.. ,....,.,..,...,,,.,..,,.....,........, 


a. To 






from <H>fii]>rti;ie>r clinplm'iHmwi, , 

Heat aooount, H.T.W, per minute ; 














Total t.ako.n from tumiHwin., 

jH*> (a 


108 s^i 


3. c 

Power, ota. : 




7' 7 

7t .d 

8 .6 

OB. 7 

54 7 

<i*O, A 

Tr t a 





Kefrigerativo lfot: 




74. "j6 

B.T.U. abBtraatfed from brine pnr nriKjwr minute . 


34 . I 

14. x 


aj , ^7 

Table XXXIX gives the data and results of tests made by 
Professor Denton on an ammonia refrigeratmg-machine. The 

only iu-ms mjuirmi; rxplaiuiimi an- ihr rrfrigrnttivo effet 

am) thf i,tl liiilnl U-mi<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 Jarkt-t 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 f -<jii} t t!>Mf} u.ji/l |iigr r |o* r |^ 

rrfrii|rr*illv- ritVii W4-S *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- jMtt-r in ,r hnurs Wits 

!iV I1Illlli|>Hili|* llir fr|fiirl',diu* rSln | tft thtTftMl 

tiiJnwir by llir nuinU-r *f iiitjiwir-, i 4 f,iv ami itn-n 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-||||*|J|if| of {{jf{ 

f n*iil |-r ls*si''M' j'nttrr frr hf, ami Wj-* ntk'iiltle 
ty i!!l!i|hiti|* llir ii.i.r', j-r hr->*- jnvn-r |*t niinutt 4 by 6 

ami tttuslJfif* In j, > 144, 

Thr main f|i-'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 i$ittifii4 fr<fi'|Jrfdliti|l 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 mnfirj-ii^ti *ASI|I !hi-- ir-*-,! thr *|*rcif 

ihr ilfilll'. Will* li 'rf-f%ri| ;i-i ji s;tsri r<| ffi*fll llir I'Cllf 
ttl ihr MRintuttU. W-ii'J ilrlrfltiillrrf |.% slifn I r%|*rlllt"fit, 


fGenerator I S-77 

Average pressures! 

above atmosphere^ Cooler [ 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 

Heater-l 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 >^33-7 

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 4-1 

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 



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|>iin-m4i'hine it Ita.^rrl cm the ussmmptloa 
that a jHrtjnil f ctwl can evajnr4te irn ]tmmh nf wntrr; but an 
automatic cm|ening engine **f the uti-rti |itrr tlinki be able 
tti run on *to or a j f irmi jn-r twir^r-jitiwirr fcr hour, 



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 


4-4 ri."v <*' M 

ami in thr othrr tw-o u|H-MitMit% thru- was lurrfttl insulatii 
from hrat. Ninr *f ihr u|irraiu>ns an- i-atrntrojm ; forinstaiu 

ihr rntro|y of slraiu M|||liri| 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 i-uu-r 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 Miti|ttt*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. S|tj*i.-;r llwf a fhtti) i> flawing fn 

I hr hir^rr jt|H- ,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; 
fr--irii!-* ih- im of kl 

thr k%l trrm in ihr | 

t*l it br l!u! lltrfr i-4 4 If it iiiiir |ittin In a 

,, ..jttrr ; tltr in ,1 rtrri* lltr ^rv-mwv 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, i-iitli ftttttmi 

H tU*r-H 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 


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 



ft us 

which w lh* iMi 
small orituc. 

Flow of 


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' llirf-t'ltifr li-j *tnr-i 

' rf -I'v jv s 5 - 

J|f * S 

thin plut* if is i % }. -** i!n- '*jif,ili 

for llw* rt*ffiitiift if llir rt|ii'i!issfi j;Ai jif-ii a% though We 
lin with *in aitittMiu r%|*ifi^is*n i 4 ftun-funilutling d 

Xi* ihr f*4i ! tliaf lh- |-s-ftrf|.*si : Itflr Jtnti the 
ittrrnifll line itfr |*fsiiiji,sll% iilmiii ?i| <JM^- ftj! *how$ tli 
jurrfrtl UAH tia** m ii%ifr|,f,ilin rn*f|f% it mi ttin^rtjiiriilty fc 

all ill*- *hini?r in ifiifiii-sti' r-nrrgy I* 
fur (itiisiiir mlii* It in ilii- r4.w i<s. i||ilii to iaerei 

thp til lllr if,!-*, inirat| til 1C 

of i n$f moi<ir. If iliii ti ill 

JWfiiifi C^5*l' 


i* * 

'?' I "" JV > | , | * *' 9 

- "*u v-vjwu.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. 


and the work of exhaust is 

so that the effective work is 


* 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 


If the area of the orifice is a, then the volume discharged per 

second is 


and the weight discharged per second is 


w = 

when v 2 is the specific volume at the lower pressure and is equal 

H.oW !' H 

I* from npuiiMit I^,H ani i', from 



" " j;, v 1 1. 

Thr rqualitms tlrtltitrti for iltr tlmv nf air apply la the flov 
from a largr i-ylimlrr 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 tr|rr that tht? to 
shall mil U* inu* It ullninl In fri. iitn ii|f,.iiti-4 ihr s?i of thi 
Hib- it *hmthl In- *h*rt mi mir llt.nt mt r r iv\ii r tUtHametet 
Thr flow cU-t Mii .t||-,if ! U- ;iln tr*I 1> iiwkiiig the tub 
vwy shrl, ami sSir ili-rn- of mutitUtiK i- mi imixtrtnnt; th 
i*c|Uti(rbi fr Ihr lUw f iilj ir anl -iram nwy b* appliet 
with it fair ttt'tcrrr tf Ap|n>\imitit*n ! ntiiitr.-. in lliin filtto am 
It* irrri*iii;ir uriiwt*. 

i*rIr-i-Mr Flw-gfii-r * mat|* 4 I*iri* numU-r *f rs 
Iliw f uir from n rr--fv**ir into ih- iiiMit'|itirfr, with 
in Ilir rr*rrvoir vdiytnu ttnm J4-*M IMW. f m-r 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 prr-viun- 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 iilltlxii|lirrr, 

tf lltr r.ii i ** i' rrjU-r*l by I he nutnU-r a.^fij ami if * 

rr|tkr| by tin Vitlur t,,|O| in rt|uali<>n ,*h|| we ttiull have ft 

ttlf riiiitiH lii lltr of i$ |!4'i 



pressure .less than twice the atmospheric pressure Fliegner found 
the empirical equation 

iv = 0.96440; 



- A.) 


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). 


In thr Knj?U*h ny-trm /, and fa ar- pound* JHT square inch, 
and <t Is. thr arra of tttr orit'ur in M|turc inrhr*, while w is the 
flow of air through thr uriiiir in (Huinth JHT .Hivond. If dcsircdj 
thr arra may !; gtvm in %i|ii*trr ft-rt ami ilu pn-ssurfit in pounds 
cm ihr .st{urr ft, t i- i hi- i-utiimnn umvi-nimn in thermo. 

In thr Frrfifli system *<' i >s tiw lUuv in kilogmmH prr st*cond, 
Thr jin-KMiivH nwy U- i*svrii in kiliigraiiit, JHT Mjuure metre 
and the ami ti in stjnitri- im-ifr-*; r lltr arru tniiy Iw given In 
ht|tiiir' 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 


* %-pi, 

r lir 

it- In wttltli llir vrlmitv i* 


!' v 

p + Apu r; 

- /> 2 ). (268) 

The last term of the right-hand member is small, and fre- 
quently can be omitted, in which case the right-hand member is 
the same as the expression for the work done per pound of steam 
in a non-conducting 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 


I'JU 4. 



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 right-hand member of equation (268) may be 
found in the temperature-entropy 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 



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 i-tin>:> f iiuiim will U? turned 
into ;til will MijK-rhr.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 

Raoktae'ft Equations, Afn-r ;n invrMtKution of the expert- 
nu-nts mail*' by Mr, R, I). X.t|is-r 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 M-iin*l may U- ritlnilatwl by 
the folbwitifl rm|iriitl ni 


thr* atnimftftrfr, Instil in {Htutuit *n lh* '^juarr im It, aritf ii i 
arra in wjiiarr im hr-t. 

Thr rffr if ihrir ri|iiiliiiri' 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 i-ttitatil i-% l*iiflt| fsir Ihal rilHr. 


tif tlit* external of bark prr-,?*urr (** 
IttriiHlla ftir thr *It"'hariCr f Mr-iiftl 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 si|Uire 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 %c|Wfi* inch* 

I hi* fiifftftiisi i 1 * wrlf wfifiril by Itis 



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. 









o-S 1 






















He further gives a curve for the discharge from a sharp-edged 
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 


= 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 


pressure. ami the letter. r, and r f and I 1 , ami <i, represent the 
t:orres|Kmling heal* 4 x'apuii.-.aiion ami entropies if the Ijqm^ 

lictlh equation* Jtpply oitlv if ittr Meant Un-omrs rnolsi at the 
lower pressure, whit It is the usual ta*.r. Tttry tnuy obviously 
IK- modified to apply to Mi-am that remain^ superheated, but 
.stu'h <i form *!** iii npju-ar i havr pr;t(tua) apftlication. 

Thr iiirtliiii if rnliu linn of tin* inlritrab In ft|uation (369) 
iiml (jyol IN pvrii un |MK' ti i; ailrrttttui i- rulfnl to the fact 
ttmt tht- lrm|H-ralurr nil ropy i^lU- allfnriK rratly solution of 
rt|tiiiti<n ? jfHj f ai^ of ihr vt-!mi!y U*w liurtn^ which tht* 
remain* sujw-rhraleit. 

Flow to TwtMW tnd l ! ,tt*, 
(lowing through a Iu1- *r w 
i> very high, rraihinj; #!<*.* fn-s 

Hi*- velmity tf air or steam 
h a|*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 *u|ttare 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 *et-tin ntay w-ell tr a siraiglil linr Joloeci t< 
the wi-tilisfi ly a i urvr f ratlins. Thr taper 



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 



it bring understood ikti of the available head A, a certain portic 
A* ij. UM'd | in tivi-u 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 .stt-am turbines t 

Thi* fitrllstnl ha** Urn tr-tl |.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 Iisil-ifir, 

Tltt-fr Is tnr tlilfrrrmi* U-twt-rn thr )H-haviur <f water an 
an rbslir Iliiiil lilt* air r ^!t'*ii that fiiimi J- clearly undmtooc 
iiiifl krjit in miml. t''ruiu<nal IT ".1-441111- and oihrr resistance 
lt ilir flow tf wait-r, transform rni-rj?> inn* hmi anil that ha 
i l*st *r if il in kr|i lv thr water s-> mil available afterward 
fur prtttlm in;; %! tiy; tn llw ih-r )tand the rurrgv whic 
i\ t"X|K-mlrtl In ovrri uming fruittitutt ir ilirr resistances c 
like nature by straw r air. i-* nhan^rd into Ju-at arsci rematnn I 
llir llwitl, nwy I*- a%itiUit*le fnr ii& i rnSing tijrrnllcift*. 

en Flow of Thrrr r* fivr c 

ftc|rrimrntinK n ii>* <K*w f Mriim through uriturn ami 
thai Itii'i' litvn ii|i|ilil 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 U-yint| the exit, aa 

IMI in* Hint willi an i.tsf^r, 



(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 

Formerly the weight of steam discharged was considered of 
the greatest importance, as in the design of safety-valves, or in 
the determination of the amount of steam used by auxiliary 
machines during an engine-test. 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 side-orifices 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- t|uotrti have the fo 

VH Tt'.vtU* I\ UK WfHNt-K. M.t.ltlMK.NSinNS IN 

8 'I* 

I V 1 * 


All thr rttu'u'tr* It4l ; 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 t|i'.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 iii--r 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 
t|rfimmfrr r-iiiitwlr-s ilir t*rrot c 

hr <Mfu|rfiH-r ;i! lw firr rrttl, wh 

ff*f In | 4llfilrtif*t| hi an of I 



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 

Du. KAKI, BifcriNKR. 


Prewmre IKIU 

ids ulwolulc. 

itUio of 
hrtmt to 


of actual 
in com- 

it thrtmt 

at exit. 

>f actual 
to com- 












a 5. 3 








9 j . 4 





jf {S 













a ggo 


4-2 a 

131 .3 

75' ' 









6*7 . 6 










ga. t 


14. t 


o . 0494 














37 _ 3 a 




13. 8 



*&3 *& 




3 8-3a 







d d 



















IS -4 




2 1 go 


43 -5 b 







ao w 
58 o S 

1 SS 



43 -5 b 







&> S o 




44-5 b 

fil .0 
































SS 7 


14. H 



* w 


M 53 






o , 63^ 


S 3 8 





50 -a 






W 1. 




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 



ferrf,,-* ' > 

'I } 

! > I 




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 intrri-stiitjt fraiuri- of ihr fr-.i-, i-, ihr ratio tf t 
vi'ltnity ill r*il, lotnjnitri:! ly ihr im-ilunl rviVrml UmlKtvtr, frc 
llir |iT'*Hiirr at Ilir **Sir tritiiT IHMr thr s:\if lnnt llir m/./U\ Tl 
tlws ntl Ii||*r4r ti <|r|i'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 
rrft-rrw} ! in tntir ts*n with tiriiiltMif'-* furmuU. Ttu*y dl 

llir strain %v,i' MH|rH'>rt| i> a ^truIU of i oil! Wit 
ftirmril a ji-t 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 Iiiltt-f vt^ tlrtrritmiril In !l.w ing it through irj orifii 

fllilttllff ff ft~*-ifh i% t* l;lff*" t* i|tlt!r Ifffr, l! Ilial* I*' t'flOUgK 

hay that lit', iliajtram^ -ifp^v a u-rv 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 


* -*^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,vl--i rrr |t-rforming tl 

iltirliwfi in at! itifrt !*-*r .at$l wlwfi i|jw Itrtrpflg frrt'ly !i 
thr iifi't|iiirfr, 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'lif||r S't ffrt- or into thr < tsllililfiifig ttlJn* wf all 

jZfit.t*,**} :*-fl> 3''. 

lit* 4* .,'.' In* ls( 

*}*,*. ,,-, it it 



For a well-rounded nozzle- such as is used for an injector having 
a taper of one to six, he found the following results: 

Absolute Prt-jwurf. 
Initial. Throat. 







o . 606 


Calculated Veloc- 

ity at Throat. 




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 searching-tube 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- i-rrvurr wa, * ontrolled 
U'' liui ihn.- w.i* -, t iur numtUR 

under similar ,-unliii"n- 
a ihrottlf-vaUr. It - I't 


Ihc -.IMHI 



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. 


,,,,.,.,...;' fur flu* Ir-K 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 \4|gr rain. I ilrgrrr. 

Ha>W OF s1T..\M TtlltMli.ll ^IIMKI 1 rtlilA Wll'H Rr HANDED 


|* Iwgf, 

J > -1 3 *- 

i 5 li ! 

* " l! 'H i > w 


14 ., n ) 

I , t* * < 

I fat ">'* 

8s I *, , t ! * ''"' 

1 * i . * * 

;**' *' 

i ii. . .- 

$ j ' i . * 

s , * . * 

t ' 

* ''-t% 

is* f" 1 





4 * 



? M 


% , 















a- . 





s i * 


.' H -; *.! 

WS ; l*, 

in i *J 


150 I*V 

Till* tiii'tittft! of *ft i 
irnt lo J al 

ii-4 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 



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 

+ 337-7 - 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 

The iJiami-tm art-, 


of a pound JHT stronci; r0nsr|wntly ihr an-as at the throat am 
the rxit will IK- by n|iwitt>ii i jfuS i |KI' 4.U. in Mjimri- inches 


3500 0,827 

If ihr tiifM-r is liikrn i U- *' in n-n, thr tntttt <tl jmrt witlha\ 

a Irngth if 

tuts.PJt* c.jHo - ;.-i rn; 

ant! alUiwinn fif ih- r*m!in *ii ttw~ rniritu-f 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; 


ff friin ,o ilir 
ihr vrlmily *! r%il will lit 

Taking ihr tw 
l l*r 

The t|ittiiy 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 tlUwu-irr i* tt.4*** ' A 1 * ****' n **" 
thr 3 onr in irn, ihr It-n^ih 4 ihr onit al fri f the nox 

anil iu total am! intri ny ! 24 inch 



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 feed-water 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 steam-jet. 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 water-ejector in which 
a small stream at high velocity forces a large stream with a low 
velocity, differ essentially from the steam-injector. 

Method of Working. A very simple form of injector is shown 
by Fig. 91, consisting of three essential parts; a, the steam-nozzle, 
b, the combining-tube, and c, the delivery-tube. 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 steam-pipe must have on it a valve for starting 
and regulating the injector, and the delivery-pipe leading to the 
boiler must have on it a check-valve to prevent water from the 
boiler from flowing back through the injector when it is not 
working. The water-supply pipe commonly has a valve for 
regulating the flow of water into the injector. 

This injector, known as a non-lifting injector, has the water- 
reservoir set high enough so that water will flow into the injector 



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 
in-low thr injnlur, wlitrli will lr tU" rihnl l.ilrr. 

Tu start fltr tiijni**!' '-.StMttit li\ Fti;, ji, tin- ^iram-vajvt' is fir 
ojK'nni *y r *tilly it* bUw mil 4itv \vairr itu\ haw gather! 
lilwivr llir V.tlvr, tttfi|li 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 WiiUT-vsiivr 8 s * t*|rit-i wti\ .V* 'tnfi an wal*r ii||tt*ari at tl 
owrllow liiiwrrfi ilir tumUftuig-lubc 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*iftiitii-iiil*r ii 

IfUti llir imiirf, Wllrll ihr ittjr* |tf 11 'tfljff| | lai:||i|fH 
l IK- furtttnl at tiir 'fftiiff' lif-lWrrfi llir fniiiii||tig 
tllfe, ihr v.ilvr it! llir vrriUw * is-n 

winilti ihr Wiiirr Jisiti nil 

lltt* arlir tf ihr injriur, 

Thtory of it llir IWM fumlarstrnMt ( 

thf lltrtiry wf llir injnixif arr i|riirt| from llir of tl 




The heat energy in one pound of steam at the absolute pressure 
p 1 in the steam-pipe 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 


of heat (778 foot-pounds), 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 



Let each pound of steam draw into the injector y pounds of 
water; then, since the steam is condensed and forced through 
the delivery-tube 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 

y ~ 




Tin- trims (irfx'iuitng on iht- u-iui iiir^ IV ami r w are Rev 
Sargr ami tan tomtnonly U- fit-girt f-tf, 

Tt KI-I ,iii ilra of ihr inllwiur of ihr fortiu-r, wr may consid 
(hat th' |*rt-N^uri* foiling w.ii-r ini a nun tilling injector is 8' 
doin, f *'viT, itn-au-r ttt.itt ihr |ir-?Mirr if ihr almt>s|ht*re, a: 
ihr i'rrrr*|MmSing jjfr^iifr for a lifting injritor is always le 
Now, ihr jirt-NMin- tl ihr tmoHphrrc- I-H t-*|wivt!rnt to a head 

If - 144 * U-; ; f *'-4 - .U trii. 

A lilcriil cMimair of v nhr (Ktumin of wau-r JHT |KJ>und 
hit-am) is- lifiiTit, *riirr-ftrr, 

IV 5 

In wrcItT ihfli n injnior tlwll ilrlivrr w.iirr agiiin-ii thestea 

jtfTwtifr ill A Iilrr it"* vHo* llv IWM^I i*r gfr.ilrf thilfl Would 
** 8 iI rttt't lv ii tirjitl t-ijiiiuilrtil In ihr boil 
l*itkili|| Ihr ltlrf |.fr'i"*itrr at J|o |utimU by 
^iiigr, ur ,*fn |*fniiii'< atviolulf, llir r|UtvalrrI liratl will be 

14 , )t*'\ : -*.-| tt 
Again liflrrn fr v, Ihr valur ff ihr Irrm tlrf' fitting on 


t i %, i f i t .. 

thr s.|i||lii 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 tf|rmttnH R V, 

in inDurncr f lr%% one jrr ml ami thai lit*' trrm ciepem 

un IV 



For practical purposes we may calculate the weight of water 
delivered per pound of steam by the equation 

y = 


This equation may be applied to any injector including double 
injectors with two steam-nozzles. 

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 

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 delivery-temperature 
is 165 F., then the water pumped per pound of steam is 

867.?; f -p 

-i :.-;\ .-.<...*!.. ..... .. V 


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 combining-tube with the velocity 
Vu is yVu -* K'> and t t! momentum of i + y pounds of water 
at the smallest section of the delivery-tube 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- 

UtnnU-ly im-rr 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 
iivt-n ly Mr. Suit kl.uu! ki-*rH,* \vhi hui nuijr nmny fxjwr 
iisi-nis for William Srl!-r & t"*. Ilir | Ikal |iari tf whi 
ftilltiWH i% liiFgdv ijrawn fr<m hi-, wurk-. 
Velocity of titt Sttaw-ffl, h|Maii. i;r*i|i 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 |rfjj-ratufr''> t irr"t)K:nrling 

jtfi f | 

ami uihrr* h*ivr i throat Atnl . slm-fgmK ffiiti, tl will 

ftUimi ill Jill . a '*"* ill* Itf|jf8f.f itt)|!' itjjrn 

t*T\(mi ill*" 'lr,ii l|ss 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' i|r*-li*|-i| in llir |rtt*rd 

iiiil|i|rfj ittr |*ff"vifr aS ^rjunjij, ;il .ttii |*ifl f 4fi rx|fici 
/,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,"i|iirfilly iiii|**t **sfiff4, AIs4, <i?> W'iis rrajl 

Hrfr /', iliul 7' 

thr |irr--!rr 

i$*|llS *ii llif *w5f 




sized by Roscnhain's experiments, the steam will expand and 
gain velocity beyond the nozzle, if it escapes at a pressure higher 
than the back-pressure. For an injector this last action is 
influenced by the fact that the jet from the steam-nozzle 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, 



bX 32.2X778 (867.5-0.8775X966.3+321.1-180.3)}* 
2830 feet per second, 



whirli U nearly fwirr ttu! j-.i c.tlrui.itn) fur ihr \T|K 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 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 Ur|tnd8on 
(>ii ihr lift nr hi-iitl 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 ji|r Viilvr 1 *, ;tttt{ |nrva^r' f llir injn tur. Thr first 
lhr*r tun In" nuMsurrt! ttirrt fly fsr any ^hrti i-Hr; fr example 
whrrr a li-tl i- nunir ift .in ittjriinr. Iti *{rtrrinininu the pro- 


jrli*n> tf an injrttur ii i-> -iifr i ir'uitr ihai iltrrr in neither 
lift mr hrttd fr *i mn-H^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-> u-tttitHy 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 iii|rrl?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 f|i rprrt 

\ 4|;ll V"^ * \ji.j * j -- 4^ fret, 

If, on ihr rtitiir^iry. iltr rilrsiivr hr4l |rdi- jug vcltjciiy li as 

fcrl, Ihr 



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 combining-tube is between 20 and 40 
feet per second. 

Velocity in the Delivery-tube. The velocity of the water in 
the smallest section of the delivery-tube 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 - 


, , 
= 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 diverging-tube 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 combining-tube 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 

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 sir-am U-livrr-! l*y ihr *it\tm-mu*le can 
caU'uliiU'fl in *S1 f.r.r*, lv ihr tm-thI 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 
rcHt-rvoir t< ihr ImiSrr ; Mn^r|u-ily 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!t-r 4111! slrail in 

wlirrr .v, i* ttir t|ii4ii 
t/4tttim, ,iml <' i- tisr 
of liist 

.4 tin 

iliir to vif 
r. The volu 

unit tltr ami *f 


whrrr T i lisr %-rl** sH 

In i 

H llir iPfriftif 


r inisir-si 
t M,J | 

-' -anti I", 11 

to i 

frrl. st% fnUfid 
fmm 6* 

! tlrhvrf t JtJ 18 |tlll.r t fl 

. IX 



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 delivery-tube 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 delivery-tube. 

If Kjp is the probable velocity of the jet at the smallest section 
of the delivery-tube, and if d is the density of the fluid, then the 
area of the orifice in square feet is 



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 
delivery-lube 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 



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. 

Steam-nozzle. The entrance to the steam-nozzle 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 valve-seat will no 
interfere with the flow when the valve is open. 

It has already been pointed out that the steam-nozzle 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 steam-nozzle supplied with steam a 
120 pounds boiler-pressure: 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. 

Combining-tube. There is great diversity with differer 
injectors in the form and proportions of the combining-tub( 
It is always made in the form of a hollow converging con< 
straight or curved. The overflow is commonly connected to 
space between the combining-tube and the delivery-tube; 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 Delivery-tube. 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 delivery-lube 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 |i||fi*t| 

till*' I'* If'^s 
f llir 


r *;f 

ill llir 
1 iflC 



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 combining-tube 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 starting-lever H is then drawn as far back as it will go, 
opening the valve x and supplying steam to the steam-nozzle. 
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 lifting-injectors may be supplied with water under a 
head, and since a non-lifting 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 valve-spindle; for under steam-pressure the smaller 
will open first, and when it is open the larger will move. The 
steam-nozzle 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- ilisi-usMons f Injector 
thus far givt-ri it lu* U-m *vwwil thry w*rk at full cape 
jtv but a- 1 * an injrviur ttui-4 lr iWr t lrwK the water-lew 
in a tKiiliT tt| jtrompily tt* jr'|H-r 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 uj-niiiK * ? t ^* rtiMttt-viilw, 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 fttl||ly, 

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 


In the Sellers' injector, Fig. 92, the regulation of the steam- 
supply by a long cone thrust through the steam-nozzle is 
retained, but the supply of water is regulated by a movable 
combining-tube, which is guided at each end and is free to move 
forwards and backwards. At the rear the combining-tube 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 delivery-tube, in this injector the space is only for 
producing the regulation of the water-supply by the motion of 
the combining-tube, 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 combining-tube 
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 combining-tube 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 starting-lever 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 combining-tube 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 steam-supply is regulated at will by the engineer or boiler 
attendant, and the water is automatically adjusted by the movable 
combining-tube, 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 steam-pressure, 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 self-adjusting, since an increase of steam-pressure 
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 fort-rr. Stu h injettoi^ havr 4 \\iiU- range f action 
ami i an le toiiirolleil l\ regulating ihr i.ilvr un the steam- 

Reitirtiog lajtcton* li ihr at lion of any of ilu* injector 

thus far <ir^.Tibrl ? inierru|ie*l for any rea-.ow, ii is nei-essary 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 HUH' 'ttj 1 "* il *f' <i havr Inti 
l-\i-.t-I, Mti h at t hr Sellers 
I- lit "i i. TiiJ-^ ij'tr ha 
l^'ssf !*.<! ti*//Sr' in linr, th 


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 %irm-mt/./1v HJ 

whtt'li druWH -sirr from ihr n 

water n5iM? thnniitU iti f * ilr 

until llr r*fw|rn%*ili if ^lr 

|tr!liil varttum llwl lr*wt tij 

tu!- ami H|II^ tiff ihr f4ir u ihr M%'rri!*w; ihr tnjtrtorthe 

ftr-rn Wrtirr Ui ihr Uiih-r. If ihr inj-'ir ftl|r 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. Kneu-v* ,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 tlvlivery-iuU- f ilu- ftiftrr. iltr Win" i> *rjtMtl -of ii 




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* frai-wati 

riM-s t Slir !tli*r>' it mrrl* ihr *lrain from tttr Uflrr-noswh? ar 

is fnrwl in u thin slu-ri am! iih liigli vrhn ity tntti ilu- rumbimn 
tnl i" tf thr fMfc'rr, wlu-r*- ii mi"* in coniat t with thr ma 
sinun-jft, ami itittinlifsi? wiih ant -tml-n^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* nj-ir, 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. %%,ii-r tan rtiu-r 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* i-ml | t lu- liflrr n 
ami It ha^ 4 |4i>!rtttlifi|-! |4iii? whuh rn!rt- iSir fortiT-no%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*iti|ilv if ilw-rr ii uii|rit"*ni 
tin- tttnsm |i|t% thr '*i4fiifi|| 7houll l-r niovrtl a lit 

way to lsr*4 i|-fi 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 Wiili-r 'as|i|4% 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 ^ii||4-f| w-iih 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 hi-l w^ilrr till I hi- iBJ 



cooled by the water from the feed-supply, and will then work 
as usual. If air leaks into the suction-pipe 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- 
haust-steam from a non-condensing 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 boiler-pressure this in- 
jector has a solid cone or spindle in- 
stead of the live-steam nozzle. To 
provide a very free overflow the com- {* 
bining-tube 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 exhaust-steam 
injector shows that enough velocity 
may be imparted to the water in the 
delivery-tube to overcome a moderate 

For example, an injector supplied with steam at atmospheric 
pressure, and raising the feed-water from 65 F. to 145 F., 
"will draw from the reservoir 

FIG. 96. 


180.3 113.0 
3. J = I2 .9 

i-o - 33-i 

pounds of water per pound of steam. In this case as the~ steam- 
nozzle is tonverging we will use for computing the velocity the 

0.6 X 14.7 = 8.8 pounds. 

This will givr 


! " * ' 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 ^trtfliiirtl ly \\ t*!tllr |rrssur( 

!*'...' f4 -'^ l(5 

f4. 4 * >44 

imitndft atM*iiilr of a p-iti|*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 rt|iar}.Ifi cilhc 

in thr %lriiffi m* t*r tiryom), llir vrUn iiy may I* gflrr lha: 

rilflt|Mitri| ami *i !rl!*-r 4tliw rlHiir. 

IJalr ihr ii"l -Hlrrt til i"' ff; uil il* us* (or fcIin 



the boiler with an exhaust steam injector will result in fouling 
the boiler. 

Water-ejector. 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 

(// + *); 


Substituting In equation (375), 
"i -\- yVx -* 


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 water-ejector 


IN M'',r TURK 

to r;ti**t' i ,?ocj gallon'-. *>f vv.ttrr -in hour, // - t|fi ft,, /; .,, ta 
.v - .ifi.^ 

\ .1' N -I ...... -*; N // - ........ x !* - !-; N /I * .f - \ '*, 

The vri ilir> an* 


I -<.'# S, J4 |rr| |rr 

if* - ,tJ,t< frri |*rr 

4 - !f.*K Irr! |r ^ 

-n^j iils fn-t j-r 'irt 

itfr frrl; 


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 

Ejtctor. - Whrn flu* rj itir t% isrl fur f-iii 
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| 

vr|ii iiv, tftoit to, it"* in I hi* 

xjfititt, (irtiVrft i l.i 

4 lrv \i|Mi!\, Ki to i'islsli* 

IftiantJly l tile r%|rw **f liir %rlity, wi ll|;il >i C|ftli 

uf t*r Itflnl 4 -4 mat! torii 



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. 

Ejector-condensers. When there is a good supply of cold 
condensing water, an exhaust-steam ejector, using all the 
steam from the engine, may be arranged to take the place of 
the air-pump of a jet-condensing engine. The energy of the 
exhaust-steam flowing from the cylinder of the engine to the 
combining-tube, 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 exhaust-pipe 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 steam-nozzle can be taken as one pound absolute, the velocity 
of the steam-jet will be 1460 feet per second. If the water is 
assumed to enter with a velocity of 20 feet, the velocity of the 
water-jet in the combining-tube will be 88 feet, which can over- 
come a pressure of 50 pounds per square inch. 


Till: rrcrnl rnpul U-vrU|imrW of Htrutn turhim* may b 

ttttrtbutit) Uirgrly to llir j*rffrt ting *tf flirt bin It ill rnmtructbn 
making it |*iiti4r to t'ort'ttrtu-t Lif>*r liinrry with lltr 
rr|iiirrt| 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|?rfijf-iil, tvotiltl rrc|If'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 |r|i-ir it r* nn-f-'mti- i givr altentb; 
In thr us lifi of jr|i* f ihiiih o i,4iir\ 4fnl ! llir friirlbn of jet 
i.HHljifig jffoftt ilii%ilft| ofilt'*"' 'l|i"i 1- S 4 ilia! tillirrwiif Woul 
Ij|tt*<if ftft"t|tii l* thi* tfriiti;r, 

Tlir fnlm*i4l i|iir% 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, It-mh to In th 

l|fiiiitiifi i*f I how |ififiri||r'-, Or friilitrr 
rvttlrftf from i!irs|t'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. fifris-itwr uf t % |ii*iifti|H |*'f i i|Miifr iitcti ittlti ft VftCUUl 

til ^6 iittln-i of turf* lif-y *3 |<tiintl--4 iil*'itsi" i through a propf 

!ftll/,/,lr, t|ri:rli|*rij i lr|nil\ 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 *< 


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 twenty-five 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, steam-turbines 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 


/* f < ; 

A 1 


U im(>ortant io keep flrarly in mind that we are dealing wil 
vrlinily* flutnge f vt-tmtiy ' ,tr eh-raiinn, uml forcv, and thi 
the ftn v e i- measured iii the ii^iiiil w.ij. The use of a specl 
name fr the fun-r 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 veliK-iiy or negati 1 
at'cclf ration will IK* \\ - I* f*ei per setumt, and the force < 

inipubc will IH* 



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 


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 w-heel. 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.<ttm|tttKty 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 *ifn|ile 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 



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 semi-cylindrical 
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 


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 ). 


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 ** 



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 water-wheels 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 

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 


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. 




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 

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. 


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 com|onents rl and %% which may In- rullril the rsil velocity 
of whirl IV, ami the c-tit vcUn-tty of flow, P/. 

Tlu- kinetic rnrrgy curr^|H>mling ft* ittr abuilutr rxil wltx-ity 
F 4 w the lost or rejected riirrgy tf liir cumbinatiun of jrt and 
vane, ant! for gotnl ertutrm-y ?htuUI l" itMiir smii}), The rxit 
veltK-ity of whirl in genera) nrrvt-s mt HMM| |mr|xsc 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 tm|iuUe; 

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 re|re*entt*l by *t let |l and 7 represent Iht 
anglt-s bed ant! Ink wlikh the at the entrance exit ol 

the %"ne make with the Hoe, 

The driving tm|tuUe w in to 


and the thrust i* to 


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 ,.>.. 


delivered to the vanr | r srttintl Is 
it* *^*i* 

If ~ ;- I 1 I , *%, ...... 



and since the kinetic energy of the jet is wVf -4- zg the effi- 
ciency is 

- 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 


- 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 

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. 

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 \ 
r| f jrnvi|n| that fri 
tfut uthtT f"r"j:4iif!t"r*t 04 
i Iril. Thi** is 


in llii-% i =.'" 
t l I", 7 kl t 

w I 1 *V I'* fii.iftr lMIH.ll III ,1 iifti 

^ f * 8 < 

> rt|ful t I',, *iiwl iihu this 

* 8 -.ill *t i' fr|i|,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 lit-iim at Hit* r Iw i hi* lw : k prr^Hiirr. am) ifi'M*t|iirfill]( 
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*ni|iii-' in mu'ifi' 

If 7 is mit* )r ! /I in n|tiil$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 


If this value is carried into equations (283) and (284) the 
work and efficiency become 

W^} j K t 3 cos 2 ( 29 o) 


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 

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 two-fold; 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 


foregoing discussion to a simple impulse turbine of the de Laval 

Assume the steam-pressure 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- 

The computation on page 444 for a steam-nozzle 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 non-con- 
ducting engine, is given by equation (144) page 136 as 

x-r, 810.8 _ , 

e = ! -- a_a - i -- - - = 0.262; 

r i + ffi ~ ? 8 5 6 - + 337-6 - 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 

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 horse-power per minute. 


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 horse-power per minute correspond 

1314 X 60 -f- 1099 = r 7-2 
pounds of steam per horse-power per hour. 

The total steam per hour for 150 horse-power 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 

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 = 1750-4- (3030 1050) = 0.884 

P - 4i 3'- 

The two triangles aid and elh are equal, and 
le = id = 3030' 1050 = 1980; 

FIG. 104. 


consequently the exit velocity of whirl is 

W/ = ek = 1050 - 1980 = 930. 

Consequently the work delivered to the vane is 


PV = -[3030 - (- 930)] 1050=- 39 6 X I0 5 
S S 

, w 


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 horse-power per minute ; and the steam consumption inci 

345 X 60 -f- 1099 = 18.8 

pounds per horse-power 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 i-rV in 
The circumferential space occupied by the six jets will be i 



!..! inches out of 62.8 inches (the perimeter), or somewhat less 
than tme-lifih. The section of the nozzle is shown by 


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 one-third 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 !> 

\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?! 


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 


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:j|ifw ttrhrr!, toi 

a vrry numltrr ! M-H f *n*^ ,r., t$fif to 

ctttf hundred iind liffy. 

III fcttiit'r llir 

i in tti 

f ihr vaflr^ llir J*rf 

l I*. 



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 back-pressure. 
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 equal-angled 
.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 


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"",|ifi|f !"* 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* Wa-s iliiillr 


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 vunr-n 

A ^fir-. i% r4*i ; ,iifirj| l% 
an , r. 


ihr lriritiu-< 




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 
marine-turbine, 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 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 rcm|iiiring 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 


I ros 


; F/ F, lift cosec t , etc. 

The til thr vant and guides must be increased 

invenely iiro|Mirttonitl 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 4i4f-j*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*I-ilV l 

|f sf* 

l*|tM*t!y tlf 1% 




**i|ic's I* | ? 
,iir ilfitwil in 

tJ |||:;|||fii:f, I*, 

'4.lf |,| 1"^ ||| C 

i" 4 $> 1,1 i<i off 


r -^lltsr Imr AH 
r, Irffrfrit I*/ 

" mil-. 
f fif I^", 






and a* ihr intrinsic rnrrgy tif thr jet is 



thr Hiiiirm-y 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 kim-iir 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 Mtim-whal lar^rr ratio than would otherwise be 

A tiiriiitHl of allowing fur frirlion is to redraw the diagram of 
Fig, 107, shortming thr linrs that repn-nent the velocities to 

In unirr to firing out ihr mrtiuxi cirarly an excessive value 

will lw. ii*-' 4 igin-tl ft* ihr t tit-tlii/irru fur friction, namely, y 0,19, 
wt i ha i ill*- rt|iirtiini lor vrltH-iiy may have for its typical form 

^ ~- x J^A it >') - o.c; Vigh. 

Again ihr i-urflii-irni will \n- uHHumttl to IK,* constant for sake of 

%i fit f-t 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 |irti|H-r without frit 
lion, titf*i Salirr quantity 
hrintf i*flr-**jitli *I ihr 
initiil vrh.H-'ily of whirl, 


Starting With l\ ihr Vrlm'llV f ihr 
is tlfitwu i* Ir!rfffttt!r ittr tr 
of Vitnr*. The riil vt-l* ilv l* f I-* stuilr 

It t-xii 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 lllr-i of rnfiif! J,1 

Viiftrs it. 1 * itira.Hlifril nl! lisr iSsil|t*^ 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 i-i tifei' 

m-v> *ltl|4rir 

afttl llir vrl 

mi Ilir 

II l*!il I S| 




antl iiiiiilr-i, inti 


lit if-;i Is* 





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- 
ature-entropy 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 -4||i,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?l|r licr|% afr 

thfiJsi, all ilir tiii iii-*iii-s 

i iifltl* *!* alf 

wl lH* tf 

,, , ,Hf.,| a _ |,, 

.a *w <i,ncc 


;p a , ttifa .** - 

li b llil fif li* ii 

tyj*' nf itirliiflr !}|r 

t-ilrndril A! Itl Itiit^ 
is allatttrti l* -ir iff sti -A <*tm\ 


M| fc'ffijw'faf 



If the Ji"fi| '4j*nr! 4 ill 

|K of $s tikrly I li,r 

f if tin- -i|rn| m\}.' 

*JO, litefc ?' 

rf i lafffr f$vittl*i'f *{ 
|r no ifto frrt 

I*- if* i ft4tft!j(f% itiilc.rtsi fif 




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* veltK-ity of the vanes as stated is 260 feet per second. 

The- m-xi t|u<wtitm in the discussion of this turbine is the 
cltHirihmion cf pressure. If the coefficients for friction and 
cilhrr hisst-s arr lakt-n 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 temperature-entropy table. 
Alnii frm that table or frm Table I in the "Tables of 
Prupertir* f Su-am/' the rrresjKnding pressures can be 
tlrlrntiiiiiti, The work h arranged in the following table: 


4 * 


!*.. *Mi 

Ratiw *( prsur. 






0> 01 





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, 


To determine the si,*r> of tin- m.;4ir% or thr juv-MKr* 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 ti||fj if ilirrr t- t|]>rrt uhlr ir-ak.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 4-3.'ii|f!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 * |* 




5 i "-i 

f I IU, 
S } t \i 

1 1 ; 4 j ,|y 
i til ! j|f 

! 16? 




y i S j w,$ 
yt*i i toio 



a. 78 






8- ft 5 




at .0 

it). 8 






88. 3 



By Ihr nid of thr trm[H*rature-entropy table, the qualities 
iinil ^jit'tilir vcitumrn may lie determined directly with good 
ftpprtuiinution. It b-ing nrcessary only t fallow the line of the 
tri|it'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 rntro|iy 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 temperature-entropy 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 





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 : 















O. IO 

O. IO? 

O. II 

o. ii<; 

O. I 






O. IO 

O. IO3 

o. 106 

o. 109 

O. I 

(i-y) (i-yj 




















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( 

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 



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 
horse-power per hour. 

Assume that the turbine is to deliver 500 brake horse-power; 
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 

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- 
horse-power, 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, 




ii. |ffj*tfiifii, ills 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| 


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 s|x?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 pru|x<r length ftr the twenty-fourth 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 

ci|iylI 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 |ir|Me, then* being of course no corre- 
|ximltng 1ft fact thi* method of computing at convenient 

interval* ami Intrr|MlittIrtg 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 

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*' hk-h i jr r 

t> l<if#r, iifiti *i f*u!r Ir-v, liwn mull ^imtiSii U- a||iljril; Siyf 

thr vjtlui' tf Niirh a iwir K*r 4 I*K mfri., ;tfinut*tr |*ii4gi' ig 

nttl kmwn, uml any r-iisnuii' mirt I- ifw-dr. 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,i||r |tl) II 
iff II* iiiitiiilll ill llir Imici rfi|. '!* dllitA ft^f irtkil 

In IM." any 

lilt* l 


arr Ir*'+ fur llir 
slritlil-rngiftrs llir ratls 
rrni, Fr iiirlilfifB l ih* K;iir 
f I*iflt.itlitfi in IP r|W!fr 
itl lltr |irr ! *tirr rtitl, 

ivi*|iii!ift frni strata- 


-'S ;Sft*t 


U-lwrrn llsr 

srt til ir 

vdtH'ity i> iittlfiiy if ttwt 
entrr* nti a|* 

i"* rtff||4tii' It WUIllii fftf l 
fftilf!r r fl!i*t/,lr' arr j*ti* r|, 

funrr U aliiiiiiiil i Iin4ling ll 
whct-l .sltiitl titn-*ily iniu 

ll||lfrtitli|r 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 


*tir rt 

%d*ii>, If aiiioi 

i ft'jc*|i|ri1< r llli 

I i 

it ai 


p- ?lifrt 




**/* represent a vane which has steam entering it 
ily with the veltK-ity 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 


lll* - till 

will U- 


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 pressure-compound 

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!i|rrlir Irfmili and should preferably have a small 

tiianu'U-r IP rnliiM- Irak-tgir. Thr hurh pivvuw |urtmn 

ktVI'ii Mttallrf tluffKlrr l* frt illUti- ,iff4f1|>rnti-iif tf |*Wil-i am} 
Viinr*. SomHimr* ftirfr ifr ttlfc tit,ifllrfrf ; ff lltr -aillr |nr- 
|HM\ lint iitllr frtifa ttiHJ|litai* t4 ttiinjntuitMfi iitlrlttil 

|y filli'Sl t haJ?r f tliiimrlrr, .ill i' llrri-VHifl H Its 

ll*r |iriittfi l Iiiliiil4r llf.if }*T n!.i|r lafgrr Hi in 

the Ifti;rM" in |H-ri|hrral ?|K-r*l."'-. i*\ li.iri. .ir tt 


I ft 

i i s i 

Tttt" iitc-fittfiiiiyiii|| gi%'ra irtilfa i.4 t-%ia on st 

turtnm* by t*rft***tr Siiwluk, TM iiifi|**ifr iviih rr^utis 

*, lltr*r %liwli| ! f-|ctfc*i ii* 

, 4 MI) rifciritti l .^4 I .jo. 

Thi* ly|* t( iiiftiifir fyjt dj*|-lir4| ^mtr^ftiUy I II-?* 


Hi jifr^aiifr til a j**r is 

fr, i*r liwt Jm^I f *i*! 

1 ; 'llr fr-4-*!*!!* r i 

t-i ftiialiil|t | -i|f.;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- 



its casing, and from tests of his own, Professor Stodola gives the 
following equations for the horse-power required to drive smooth 
wheels and to drive wheels with vanes forward : 

Smooth wheels v 

H.P. =0.02295 a. D 2>s (} 7. 

Wheels with vanes 

H.P. = [0.02295 a. D 2 - 5 + 1.4346 a. I 1 - 25 ] ( 


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 velocity-compound 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 


twt or im- >r- 

. lt 'alr mtltt Ili 
cf tfifumii 
Siiur ihr jrim 
iilmnl)% will i 

Lrl u* likr fr 

Walls ill rtoifka 

tif 0.i, wti 

1*1 ihr ifitikl 

! 3* ffll'tft-i f llt 
far tf -* '30 s *. Th*' 4hwlMl 

and IHIF nlr*iMli% 

arc toy 4 !*. Ilry 

mill twvu nrarly 1 4^ nii 

nr wt 


lit*- j4i< .ui.n 

- t 


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* ' 


l$t>?'tr.j*iwrr jn-r 
Ttic rflu-irnt'y for 

L I s * t" 4 

by the 


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 horse-power 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 horse-power 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 horse-power 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 

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 
tMrt-i |-i mimiir. 

liir |r thr t 

which In llw* !rni|rr*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! 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 tsi|iitnt 
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 trm|H*ralurr 14 hit* 

.|" 4 It* I S*/" I'*. 




vutumr U 44S rilttir frrt. The 4 

iiii 114*1 ** 44 . 

II f 

I** thr 

Ttlt* f thr |u|tlt(| 


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 horse-power per hour 
and 770 horse-power 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 one-fourth 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- 
perature-entropy table at 1.56 units of entropy gives for heat 

vfKAM -Tl' 

content* tuiS, Thr umtrnti .it t,*vj fumh ())$} has 
alrraily Ut-n 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 ittsi|t c *i it* work, !'***. llirrr 
ulluwrti o.tji lr fritin in its*' im/./.i*-, iniil <,*.$ (r lu\w. In the 
llilrs lifltl Viinr-H, 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 


I till - |i t|i.M ,t.f, 

per fwiiritl. N*w r liit* lh? valur tj^j i! ^j,i I',, sitwl y it it|i 
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* 



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 
one-fourth 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 

53-4 -5- 43-5 = 1-23 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 



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 temperature-entropy 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. 



Heat contents. 


Specific volume. 











1 02 




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 t-ontinuation 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. 



A turbine developing 8000 horse-power 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. 


Duration, minutes 






Throttle pressure gauge 

146. 3 

ixc; . -i 

142 . 2 


I4Q . 7 

Throttle temperature F 





t !l2 

Barometer inches 


20 .0 




Exhaust pressure absolute pounds . . 
Load kilowatts 

161 .4 


2<< . 7 




512. o 


731 .0 

Steam per kilowatt hour, pounds . . 
Thermal units kilowatt minute . . . 



39 2 

3 6 9 



If the efficiency of the dynamo is taken at 0.9 and one kilowatt 
is rated as 1.34 horse-power, the steam and heat consumptions 
per brake horse-power are, for the best result, 

1 1. 8 pounds 239 B.T.U. 



Duration minutes 




1 80 


Boiler pressure) pounds 


IAD 6 

I <J2 I 



Vacuum inches . . 

28 * 

28 2 

28 8 

28 4 

28 1 

Load kilowatts 






Steam per kilowatt hour pounds . . 






Thermal units per kilowatt (minute) . 






* Thesis, M. T. T., 1905. 
f Thesis, M. I. T., 1906. 





the ertit-iem-y 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 


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 impulse-reaction 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 

| 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 tom|Kmmi 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 enlrant-c prtmsure, and the passages 

Thrrr h mi uttrmpt to awld axkl thrust, and therefore the 
rxil 7 from tin* vam-s* may be made small; it is commonly 

rtjtiat ui the rxit angle a from the gulden. A common value 
for lltr-ir angles is Ji**. 

llir giiitlr% ami vanw follow alternately in close succession 
leaving only the nrersHary flearancp; the kinetic energy due to 
thr ntiiliiir c-xli 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 i-nrrgv 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?h-nr-i r 

tf Iir;t! sill** mrl 4 i|*l*i!*:4 !<i *Jsr !tlsfif 


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 



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^mf-tr 
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 




the gain of velocity in the vanes is equal to the gain in the 

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 

Ttlr II! 

in prat li'r ' 
in a ja|rr ! 
mation in 


fl'ii'liwtl krfiv.iifr 

w'9&$a * ^ $.'JSMki3*' j ' $& 



Hift* *|*mt 

Intrrmwlifttr wall *ir*wrr* 
t'hAttwt 'sirawrt^ . . , 

|titttirhi|n tttl 
Smatt * f tir* 

Prf, fal . 

p stwntl. 

Ratio of 




vanw to 






















t 10-130 


o. 47-0.51 


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 

0,01 + diam. in feet. 

The t>ro|xirtmn f may be taken from the Mowing 

table ; 

" ' ~ HCHE8. 




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 i|iiti ! tt !* ilw Ir4ij|t" JM'** llu- 
fa ft fit *S in |fiitllir tic 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*-*n|fti nf l 

but alltiWiinrt* 'ltll t*c i i jfti 

i frsiilt'i i4 trsf-v. 

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 

iff |tt tir 

tl lr*U f 

tf llir f sir 

ffir l 

f*r? 14 | 

- mr*! ill 


rl ihr | lit* 

lift J*rf sci'i.ifltl, |r! iltr 



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 ^ 1-800 ,\ )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 ct|mtki for vckn-ity 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., 



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 high-pressure and the low-pressure 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 : 

High-pressure Intermediate Low-pressure. 

2.2 4-95 13-75 

If we decide to use ten low-pressures and twenty intermediate 
stages they will require 

10 X 13.75 + 20 X 4-95 = 236-5 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 high-pressure end and may have 



the number of stages assigned above. In that table is given also 
the number of the stage counting from the high-pressure 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- 



t it 

tjft 7 
t>t 8 
As 7 


1 1 JO . ? 

+ o 














Sped Ac 

J. SO 
4- SO 
6. !) 
j 6. o 



I S B 





pifHsure cylinder, 4.05 fr tmch intermediate stage and 13.75 for 
each low-irwwu; 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 4-05 " r 40-3 

%-! f 

leaving for the heat contend after that stage 1053 thermal units. 
Thr pwbable heat contt-nt* 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 



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 ptifil-i 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 ffiiili-rtfi nf csi".!lut4 ,nr *inr.firih tf 

ItlliiW for the lliit'kilr"** i thr tsiiilr-s, >ini fli-r r*"ll bt 

ring thruugh whi*'h the *tr^im 

far ttit: fratiitift In thU a j % ^* 

iH.f <w|ii,tff in* ttr-s, 

ll I* llir 

of lilt* li*r ill*' 


It* 4 

Tilt" iliiittirtrrm <i| ihr iiiirffftnliaf*- and Kw |f r-^-s 

'ill l*r 


tlir tif ii! Itir ^rvr 


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 low-pres- 
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 forty-second stage, i.e., the middle of the 
fourth barrel is 

0415 X o-41 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 low-pressure 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 high-pressure 

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 low-pressure 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 low-pressure 

cylinders. Leakage pant the dummy cylinders is checked by laby- 
rinth packing, which is variously arranged to give a succession 



- A 

f i , f !< 

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hiAVr litlt lilllr ffittiwft, Sutititury lufbillr."* 4!" h^vr 
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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 

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 _ 


J load. 

} load. 


-ull load. 

ii load. 

i load. 







4 1 ! 

Steam pressures, gauge . . . 










2?. 7 





Revolutions per minute . . 








Load kilowatts 








Steam consumption, pounds 

per kilowatt-hour .... 








per electric h.p. per hour . 








Heat consumption B.T.U. 

per kilowatt-minute 
per horse-power per minute 









A great importance is attributed by turbine builders to obtaining 
a low vacuum, in many cases special air-pumps 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 


Ttir steam i-onsumptiim in 

auxiliary roarhiw** was <i* f!l 

(VntrtfuK'il juntj fwf lir 

Ury Viif tin in jum$* .. 

I tot- well jiiifii|i ... 

|KT hour fur the 

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*um|tfon 

imhr-* vai ttttw, S<ic 
<jr tliii 


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 

Air-compressor, 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 

three-stage 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 

Bell-Coleman refrigerating ma- 
chine 413 

Binary engines 180, 280 

Blast-furnace gas-engine .... 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 



Characteristic equation 

for gases 

for superheated vapors .... 
Chestnut Hill, engine test . . . . 
Compound air-compressor . . . 





indicator diagrams 

low-pressure cut-off 

ratio of cylinders 

total expansions 

with receiver 

without receiver 



compound compressor . . . . 

effect of clearance 

friction, etc 

hydraulic compressor ... 
interchange of heat .... 

storage of power 

temperature after compression 
transmission of power . . . 
Compressed-air engine .... 

calculation . . " 



final temperature ..... 

interchange of heat 

moisture in cylinder . ' . . . 

volume of cylinder 


cooling surface 


5 2 9 











1 60 


39 2 
3 6 4 

Carburetors .... 
Creusot, tests on engine 
Critical temperature 
Cut-off and expansion 
Cycle, closed . 


reversible . 

Delafond . 


Density at high-pressure 


Designing steam-engines 

Diesel motor 

Differential coefficient dp/dt 
Dixwell's tests 


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 





application of vapors 8 

Flow in tubes and nozzles 
Biichner's experiments 

Economy, methods of improving. 



increase of size 

intermediate reheaters .... 

of steam-engines 

raising pressure 

steam-jackets 261,266 

superheating 2 7 

variation of load 2 74 

Effect of raising steam-pressure, 148, 247 

Efficiency 2 5 

mechanical 2 7 

of reversible engines 33 

of steam-engine !3> X 44 

Efficiency, maximum . . 
of superheated steam . 



Engine, Carnot's 


friction of 


internal combustion . . . 


reversible .... 






3 2 


design of a nozzle 44 


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 


initial and load 


after burning 

blast-furnace gas . . - - 
economy and efficiency . . 


starting devices . . 
temperature after explosion 


water jackets 

3 20 > 



Gas-engines Continued, 

with aimprejtHlon in cylinder . 308 

with .separate compression . . 305 

Gas-engine* four-cycle 337 

two<ycl . 338 

Gase* 54 

adiabatic equations 64 

characteristic equation .... SS 

characteristics for gas-engines . 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 

Gas-producers 33 1 >3S 3 

Gauges iH6 

Gay-Uwmc'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 

Hot-air 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 

combining-tube 45$ 

delivery-tube 459 

double 4^1 

Injector Contintted. 

efficiency of 459 

exhaust steam 467 

Ktirting 462 

lifting ........... 460 

restarting 464 

self-adjusting 462 

Seller's 460 

steam-nozzle 458 

theory 448 

velocity in delivery tube . . . 455 

velocity of steam-jet 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 

Kerosene-oil engine 335 

Kilogram S 6 

Kneass . 440-45 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 



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 hot-air engine .... agy 

Stcxiciln . . ..... .... 441 

Sulphur dioxide ,.,...,. 117 

Su{rrh?atet! vapor* ...... no 

t"haritrtrrSl!c et]untU>r) .... lai 

rnirtipy ... ..... . . 115 

s|H-i'ifk"hrt ........ u a 

hrut .......... 1(4 

ttlm*lutr wale 



35, 104, 131, J7 

.,., iud, 139 

Testing steam-engines 183 

Teats of steam-engines 237 

examples of economy .... 238 

marine engines 241, 242 

simple engines 250 

steam-pumps 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 

Triple-expansion engines .... 172 

Tumlire in 

Value of R 57 

Wwitc-hcttt engine 357 

Wdrs ipx 

Zeuner'i equations 








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Voltaic Cell .'.'.'.'.'.'.'.'.'.'.".'.'.'.'.';:.' .'.'svo.' 300 

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Handbook for Cane Sugar Manufacturers i6mo, morocco, 

Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 

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3 So . 
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Trigonometry; Analytical, Plane, and Spherical ................ izmo, r oo 


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<> 



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' Pocket-book 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 

Text-book 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 


* 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 Steel-users 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 


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 


Berry's Temperature-entropy Diagram izmo, i 25 

Carnot's Reflections on the Motive Power of Heat. (Thurston.) I2mo, i 50 

Creighton's Steam-engine and other Heat-motors 8vo, 500 

Dawson's "Engineering" and Electric Traction Pocket-book. . . .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 Steam-engine Economy tamo, 2 oo 

Button's Mechanical Engineering of Power Plants 8vo, 5 oo 

Heat and Heat-engines 8vo, 5 oo 

Kent's Steam boiler Economy 8vo, 4 oo 

Kneass's Practice and Theory of the Injector 8vo, i 50 

MacCord's Slide-valves 8vo, 2 oo 

Meyer's Modern Locomotive Construction 4to, 10 oo 

Peabody's Manual of the Steam-engine Indicator lamo, i 50 

Tables of the Properties of Saturated Steam and Other Vapors 8vo, i oo 

Thermodynamics of the Steam-engine and Other Heat-engines 8vo, 5 oo 

Valve-gears for Steam-engines 8vo, 2 50 

Peabody and Miller's Steam-boilers 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 Steam-boiler Practice 8vo, 3 oo 

Spangler's Valve-gears 8vo, 2 50 

Notes on Thermodynamics .'i2rao, i oo 

Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 oo 

Thomas's Steam-turbines , 8vo, 3 50 

Thurston's Handy Tables r 8vo, i 50 

' Manual of the Steam-engine ; 2 vols., 8vo, 10 oo 

Part I. History, Structure, and "theory. 8vo, 6 oo 

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Handbook of Engine and Boiler Trials, and the Use of the Indicator and 

the Prony Brake. 8vo, 5 oo 

Stationary Steam-engines 8vo, 2 50 

Steam-boiler Explosions in Theory and in Practice I2mo, i 50 

Manual of Steam-boilers, their Designs, Construction, and Operation. 8vo, 5 oo 

Wehrenfenning's Analysis and Softening of Boiler Feed-water (Patter'sdn) 8vo, 4 oo 

Weisbach's Heat, Steam, and Sterim-engines. (Du Bois.) .8vo, s oo 

Whitham's Steamrenglne Design. -.'. 8vo, 5 oo 

Wood's Thermodynamics, Heat Motors, and Refrigerating Machines . . .8vo, 4 oo 


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 Pattern-making. xamo, a 50 

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Spangler, Greene, and Marshall's Elements of Steam-engineering 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 <>> * 


* 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 Text-book on Physiological Chemistry. (Mandel.) 8vo, 4 oo 

Lassar-Cohn's Practical Urinary Analysis. (Lorenz.) r2iro, i oo 

* Fault's Physical Chemistry in the Service of Medicine. (Fischer.) . . . . i2mo, i 25 

* Pozzi-Escot'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 


Betts's Lead Refining by Electrolysis. (In Press.) 

Egleston's Metallurgy of Silver, Gold, and Mercury: 

Vol. I. Silver 8vo, 7 30 

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Goesel's Minerals and Metals: A Reference Book i6mo, rnor. 3 oo 

* Iles's Lead-smelting I2mo, 2 50 

Keep's Cast Iron 8vo, 2 50 

Kunhardt's Practice of Ore Dressing in Europe 8vo , i 50 

Le Chatelier's High-temperature Measurements. (Boudouard Burgess. )i2mo, 3 oo 

Metcalf's Steel. A Manual for Steel-users 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 

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Ulke's Modern Electrolytic Copper Refining 1 . 8vo, 3 oo 


Barringer's Description of Minerals of Commercial Value. Oblong, morocco, 2,50 

Boyd's Resources of Southwest Virginia. , . ...8wo, i 3 oo, 


4 o 

X 5 

Chester's Catalogue of Minerals. g v o, paper, i o 

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Dana's System of Mineralogy Large 8vo, half leather, 12 5 

First Appendix to Dana's New " System of Mineralogy." Large 8vo, i o 

Text-book 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 Rock-forming Minerals in Thin 
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* Martin's Laboratory Guide to Qualitative Analysis with the Blowpipe. lamo, 6 
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Stones for Building and Decoration gvo, 50 

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8vo, paper, 
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* Richards's Synopsis of Mineral Characters iamo. morocco, 

* Ries's Clays. Their Occurrence. Properties, and Uses gvo, 3 < 

Rosenbusch's Microscopical Physiography of the Rock-making Minerals. 

(Iddings.) gvo, 5 01 

* Tillman's Text-book of Important Minerals and Rocks .8vo, 2 01 




Beard's Mine Gases and Explosions. (In Press.) 

Boyd's Resources of Southwest Virginia 8vo, 

Map of Southwest Virginia Pocket-book 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 Coal-mines of the Western Coart of the United States i2mo, 

Ihlseng's Manual of Mining 8vo, 

* Iles's Lead-smelting 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< 

1 5< 
t 01 

2 Ol 

4 01 

3 01 

I S' 

I 51 

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Bashore's Sanitation of a Country House umo, 

* Outlines of Practical Sanitation isrno, 

Folwell's Sewerage. (Designing, Construction, and Maintenance.) 8vo> 

Water-supply Engineering .8vo, 



1 - * 

Towler's Sewage Works Analyses _ ^ i2mD, 2 oo 

JFuertes's Water and Public Health. .f .T. A . ! I2mo, r 50 

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Gerhard's Guide to Sanitary House-inspection i6mo, i oo 

Sanitation of Public Buildings I2mo, 1 50 

Hazen's Filtration of Public Water-supplies Svo, 3 oo 

Leach's The Inspection and Analysis of Food with Special Reference to State 

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.Mason's Water-supply. (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- 
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* 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 

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Richards and Woodman's Air. Water, and Food from a Sanitary Stand- 
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* 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 Water-supplies Svo, 5 oo 

Von Behring's Suppression of Tuberculosis. (Bolduan.) 12 mo, i oo 

Whipple's Microscopy of Drinking-water 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 


Association of State and National Food and Dairy Departments (Interstate 
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Tenth Annual Convention Held at Hartford, July 17-20, 1906.... Svo, 3 oo 
Eleventh Annual Convention, Held at Jamestown Tri-Centennial 

Exposition, July 16-19, 1907. (In Press.) 
Ummons's Geological Guide-book 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 Bath-houses. (In Press.) 

Haines's American Railway Management I2mo, 2 so 

Ricketts's History of Rensselaer Polytechnic Institute, 1824-1894.. 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 


Green's Elementary Hebrew Grammar I2mo, i 25 

Hebrew Chrestomathy 8vo, 2 oo 

Gesenius's Hebrew and Chaldee. Lexicon to the Old Testament Scriptures. 

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Letteris's Hebrew Bible ' .8vo, 2 25