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Full text of "THERMODYNAMICS OF THE STEAM-ENGINE AND OTHER HEAT-ENGINES"

WORKS OF PROFESSOR CECIL H. PEABODY PUBLISHED BY JOHN WILEY & SONS. Thermodynamics of the Steam-engine and other Heat-engines. 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. Steam-boilers. By Prof. Cecil H. Peabody and Prof. Edward F. Miller. Nearly 400 pages; 142 illustrations. 8vo, cloth, $4.00. Manual of the Steam-engine Indicator. 154 pages; 08 figures. 12mo, cloth, $1.50. Naval Architecture. v + 616 pages; 217 figures. 8vo, cloth, $7,50. THERMODYNAMICS OF THE STEAM-ENGINE AND OTHER HEAT-ENGINES BY CECIL H. PROFESSOR OF NAVAL ARCHITECTURE AND MARINE ENGINEERING^ MASSACHUSETTS INSTITUTE OF TECHNOLOGY FIFTH EDITION, REWRITTEN SECOND THOUSAND PROPERTY OF IHSTITJiF OF TECai,310]Y NEW YORK JOHN WILEY & SONS LONDON: CHAPMAN ft HALL, LIMITED 1908 >O I J '. ^C' COPYRIGHT 1889, 1898, 1907 BY CECIL H. PEABODY PREFACE TO FIFTH EDITION. WHEN this work was first in preparation the author had before him the problem of teaching thermodynamics so that students in engineering could use the results immediately in connection with experiments in the Engineering Laboratories of the Massachu- setts Institute of Technology. The acceptance of the book by teachers of engineering appears to justify its general plan, which will be adhered to now that the development of engineering calls for a complete revision. The author is still of the opinion that the general mathematical presentation due to Clausius and Kelvin is most satisfactory and carries with it the ability to read current thermodynamic inves- tigations by engineers and physicists. At the same time it is recognized that recent investigations of superheated steam are presented in such a way as to narrow the applications of the general method so that there is justification for those who prefer special methods for those applications. To provide for both views of this subject, the general mathematical discussion is presented in a separate chapter, which may be omitted at the first reading (or altogether), provided that the special methods, which also are given in the proper places, are taken to be sufficient. The first edition presented fundamental data not generally accepted at that time, so that it was considered necessary to justify the data by giving the derivation at length; much of this matter, which is no longer new, is removed to an appendix, to relieve the student of discussions that must appear unnecessary and tedious. The introduction of the 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 iii IV PREFACE Properties of Saturated Steam have had added to them columns of entropies of vaporization; and further there has been computed a table of the quality (or dryness factor) the heat contents and volume at constant entropy, for each degree Fahrenheit. This table will enable the computer to deter- mine directly the effect of adiabatic expansion to any pres- sure or volume, and to calculate with ease the external work in a cylinder or the velocity of flow through an orifice or nozzle including the effect of friction; and also to determine the distri- bution of work and pressure for a 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. PREFACE TO FIRST EDITION. THIS work is designed to give instruction to students It technical schools in the methods and results of the application of thermodynamics to engineering. While it has been considerec desirable to follow commonly accepted methods, some part differ from other 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 PREFACE V is that employed by the majority of writers, and was prepared with the view of presenting clearly the difficulties inherent in the subject, and of giving familiarity with the processes employed. In. the discussion of the properties of gases and vapors the original experimental data on which the working equations, whether logical or empirical, must be based are given quite fully, to afford an idea of the degree of accuracy attainable in calculations made with their aid. Rowland's determination of the mechanical equivalent of heat has been adopted, and with it his determination of the specific heat of water at low tempera- tures. The author's "Tables of the Properties of Saturated Steam and Other Vapors" were calculated to accompany this work, and may be considered to be an integral part of it. The chapters on the flow of gases and vapors and on the injector are believed to present some novel features, especially in the comparisons with experiments. The feature in which this book differs most from similar works is in the treatment of the 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 VI PREFACE 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. MASSACHUSETTS INSTITUTE or TECHNOLOGY, May, 1889. PREFACE TO FOURTH EDITION. A THOROUGH revision of this work has been made to bring it into accord with more recent practice and to include later experimental work. Advantage is taken of this opportunity to make changes in matter or in arrangement which it is believed will make it more useful as a text-book. C.H. P. MASSACHUSETTS INSTITUTE OF TECHNOLOGY July, 1898. TABLE OF CONTENTS. CHAl'THU _,I^ THERMAL CAPACITIES I / II. JFIRST LAW OF THERMODYNAMICS *3 '"Til" SECOND LAW OF THERMODYNAMICS 22 IV. GENERAL THKRMODYNAMIC METHOD 43 V. PKRFKCT CASKS 54 VI. SATURATED VAPOR 7 6 VII. SUPERHEATED, VAPORS 10 VIII, THE STEAIMCNOINK Ia8 IX, COMPOUND EMOIMKB J S 6 X. TESTING STKAM-KNOINES .....' l8 3 XL INFLUENCE OF TOR CYLINDER WALLS *99 XII. ECONOMY OF STKAM-ENOINKS 2 37 XIII. FRICTION OF KNCMNEB a8 S XIV. INTERNAL-COMBUSTION ENGINES 2 9 8 XV. COMPRISED AIR 35 8 XVI. REFRIGERATING MACHINES 39 6 XVII. FLOW OF FLUIDS 42 3 XVIIL INJECTORS - 447 XIX STBAM-TORBINES 47 vii THERMODYNAMICS OF THE STEAM-ENGINE, CHAPTER I. THERMAL CAPACITIES. THE object of thermodynamics, or the mechanical theory of heat, is the solution of problems involving the action of heat, and, for the engineer, more especially those problems presented by the 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 property. 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. 2 THERMAL CAPACITIES Characteristic Equation. An equation which gives th relations of the properties of any substance is called the charac tcristic equation for that substance. The properties appcarin in a characteristic equation are commonly pressure, volunV' and temperature, but other properties may be used if convcnierj The form of the equation must be determined from experiment cither directly or indirectly. The characteristic equation for a gas is, as already quote"' pv = RT. The characteristic equation for an imperfect gas, like supc heated steam, is likely to be more complex; for example, t! equation given by Knoblauch, Linde, and KIcbe is -3r-#(i-Mi 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. TEMl'KRATURE 3 Specific Volume. It is convenient to deal with one unit of weight of the substance under discussion, and to consider the volume occupied by one pound or one kilogram of the substance; this is called the specific volume, and is expressed i'n cubic feet or in cubic metres. The specific volume of air at 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 62.4 0.016 of a cubic foot. Temperature is commonly measured by aid of a mercurial thermometer which has for its reference- points the freezing- point and 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 THERMAL CAPACITIES 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. a In order to distinguish the absolute temperature from the temperature by the thermometer we shall designate the former by T and the latter by t, bearing in mind that T = t + 273 centigrade, T = t + 459.5 Fahrenheit. Physicists give great weight to the discussion of a scale of temperature that can be connected with the fundamental units of length and weight like the foot and the pound. Such a scalo, since it docs not depend on the properties of any substance (glass, mercury, or air), is considered to be the absolute scale of temperature. The differences between such a scale and thd scale of the 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 slated. 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 STANDARD TEMPERATURE FIG. the surface is such thai each scclion perpendicular to the axis of T is a rectangular hyperbola (Fig. i). Returning now lo the general case, it is apparent that the characteristic equation of any substance may be repre- sented by a geometrical surface referred to 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- point. thermal units (u. T. u.). A British thermal unit is tl required to raise one pound of water from 62 F. to 63' like manner a calorie is the heat required to raise one k of water from 15 C. to i6C. Specific Heat is the number of thermal units required a unit of weight of a given substance one degree of tcmp< The specific heat of water at the standard tcmpcratun course, unity. If the specific heat of a given substance is constant, tl heat required to raise one pound through a given range perature is the product of the specific heat by the incr temperature. Thus if c is the specific heat and t ^ is Ih of temperature the heat required is Q = c (t ~~ /,), and c JL-. If the specific heat varies the amount of heat must bo oi by integration that is, Q - fcdt, and conversely ffl. dt It is customary to distinguish two specific heats for gases; specific heat at constant pressure* and speqific t constant volume, which may be represented by c a = andc. the subscript attached to the parenthesis indicates the pj which is constant during the change. It is evident tr, specific heats just expressed are partial differential coefiic Latent Heat of Expansion is the amount of heat requ increase the volume of a unit of weight of the substance cubic fooi ; or one cubic metre, at consianl temperature. It may be represented by I* Thermal Capacities. The two specific heals and the latent heat of expansion are known as thermal capacities. It is cus- lomary to use three other properties suggested by (hose just named which are represented as follows; m and o The first represents the amount of heat thai must be applied to one pound of a substance (such as air) to increase the pressure by the amount of one pound per square foot at consianl tem- perature; this property is usually negative and represents the heat that must be abstracted to prevent the temperature from rising, The other two can be defined in like manner if desired, but it is not very important to stale the definitions nor to try to gain a conception (is to what they mean, as it is easy to express (hem in terms of the first three, for which the conceptions are not difficult. They have no names assigned lo them, winch is, on the whale, fortunate, tts, of the first three, two have names that have no real significance, and the third is a misnomer. General Equations of the Effects Produced by Heat. In order lo be able lo compute the amount of heat required to produce a change in a substance by aid of the characteristic equation, it Is necessary to admit that there is a functional rela- tion between the heat applied and some Iwo of the properties that enter into the characteristic equation. It will appear later in connection with the discussion of the firsl law of thermody- namics that an integral equation cannot in general be written directly, but we may write a differential equation in one of tho three following forms; -I 1 or substituting for the partial differential coefficients the letters which have been selected to represent them, dQ = c v dt + ldv dQ - c p dl + mdp dQ = ndp + odv (3) This matter may perhaps be clearer if it is presented graph- ically as in Fig. 2, where ab is intended to represent the path of a point on the characteristic surface in consequence of the addition of the heat dQ. There will in general be a change of temperature volume and pres- sure as indicated on the figure. Now the path ab, which for a small change may Plo . ,. be considered to be a straight line, will be projected on the three planes at a'b' } a"b" and o!"V". The projection on the (y.T) plane may be resolved into the components Sy and' &T', the first represents a change of volume at constant temperature requiring the heat ldv t and the second represents a change of tem- perature at constant volume requiring the heat yti. Conse- quently the heat required for the change in terms of the volume and temperature is dQ = c v dl -t- RELATIONS OF TIIK THKRMAL CAPACITIES g Relations of the Thermal Capacities. The three equations (i), (2), and (3), show the changes produced by the addition of an amount of heal <1Q to a unit of weight of a substance, the difference coming from the methods of analyzing the changes. We may conveniently find the relations of the several thermal capacities by the method of undetermined coefficients. Thus equating the 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 t,- XT , and consequently we may write Sv which substituted in equation U) gives, c v (!l -I- cjli -f (S) It will be noted that, as T differs from t only by the addition of a constant, the differential <lt may be used in till cases, whether we arc dealing with absolute temperatures, or temperatures on the ordinary thermometer. In equation (5) p and T arc independent variables, and each may have all possible values; consequently we may equate like coefficients. . Sv ,,\ ,'. c p ** c 9 -\- i -jr (0) Also, equating the remaining (7) If the characteristic equation is solved for the pressure we shall have so that ^-dv (8) which substituted in equation (4) gives Equating like coefficients, S/> + m 4, = e > = c n (9) (10) From equations (2) and (3) c p dt + mdp = fw + and from an equation (v, which latter substituted in equation (11) gives t, j ' JA i J p &V O/> Equating coefficients of dv, C = Cn R (12) RELATIONS OK THE THERMAL CAPACITIES II Finally, from equations (i) and (3), c v dt -h Itlv ='iidf -t- odv (13) Substituting for dt as above, ? 5v -I- c v fT" dp -|- Itlv <= ndp -\- odv, op l Equaling coefficients of dp, 'xr (14) For convenience the several relations of the thermal capacities may be assembled as follows: w= / They arc tlic necessary algebraic relations of the literal func- tions growing out of the first general principle, and arc inde- pendent of the scale of temperature, or of tiny other theoretical or experimental principle of thermodynamics other than the one already slated namely, llmt any two properties of a given substance, treated as independent variables, arc sufficient lo allow us to calculate any third property. Of the six thermal capacities the specific heat at constant pressure is the only one thnl is commonly known by direct experiment. For perfect gases this thermal capacity is a con- stant, and, further, the ratio of the specific heals CMS K is a constant, so that c v is readily calculated. The relation? of the thermal capacities allow us to calculate values for tho other thermal capacities, /, , , and o, provided that we first determine the several partial differential coefficients w! appear in the proper equations. But for a perfect gas characteristic equation is pit - RT t from which we have *ST ~~ p ' S/ ~ v ' 8p R' &v JR. Substituting these values in the equations for the tho capacities, we have i i (c _ c v _ w H. f c _ tf V ' ' y? (Cp ^' m R (Cp v) > v p 0= C n ', by aid of which the several thermal capacities may be calcul numerically, or, what is the usual procedure, may be represo in terms of the specific heats. CHAPTER II. FIRST LAW 01' TUKUMOIWNAMICS. Tire formal statement of the first law of thermodynamics is: Heat and mechanical energy are mutually convertible, and heal requires for its product ion and produces by its disappearance a definite number of units of work for each thermal writ, This law, winch may he considered to be (he second general principle of thermodynamics, is the statement of a 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. 'J monly quoted as 772 for the English system and 424 for the metric system. The error of these values is about one per cent. Effects of the Transfer of Heat. Let a quantity of any sub- stance of which the weight is one unit i.e., one pound or one kilogram receive a quantity of heat dQ. It will, in general, experience three changes, each requiring an expenditure of energy. They are: (i) The temperature will be raised, and, according to the theory that sensible heat is due to the vibra- tions of the particles of the body, the kinetic energy will be increased. Let dS represent this change of sensible heat or vibration work expressed in units of work. (2) The mean positions of the particles will be changed; in general the body will expand. Let dl represent the units of work required for this change of internal potential energy, or work of disgrcgation. (3) The expansion indicated in (2) is generally against an exter- nal pressure, and to overcome the same that is, for the change in external potential energy there will be required the work dW. If during the transmission no heat is lost, and if no heat is transformed into other forms of energy, such as sound, electricity, etc., then the first law of thermodynamics gives dQ = A(dS + dl (15) It is to be understood that any or all of the terms of the equa- tion may become zero or may be negative. If all the terms become negative heat is withdrawn instead of added, and dQ is negative. It is not easy to distinguish between the vibration' work and the disgrcgation work, and for many purposes It is unnecessary; consequently they are treated together under the name of intrinsic energy, and we have dQ = A(dS + dl + dW) = A(dE + dW) (16) The inner work, or intrinsic energy, depends on the state of the body, and not at all on the manner by which it arrived at cncc to a given plane consisting of kinetic energy and potential energy, depends on ihc velocity of the body and the height above ihc plane, .and not on the previous history of the body. The external work is assumed lo be done by a fluid-pres- sure; consequently rflK- pdv W (18) where u 3 and u, arc the final and initial volumes. In order lo find the value of the integral v in equation (18) it is necessary lo know the manner in which the pressure varies* with the volume. Since the pressure may vary in different ways, the external work cannot be determined from the initial and final slates of the body; consequently ihe heat required to effect a change from one slate lo another depends on the manner in which the change is effected . Assuming the law of ihc variation of the pressure and volume lo be known, we may inlcgralc thus: r" a ^ 2,. -I- / pito) */i>i / (19) In order lo determine E for any stale of a body ii would be necessary lo deprive it entirely of vibration and disgrcgntion energy, which would of course involve reducing it to a^stalc of absolute cold; consequently ihc direct determination is impossi- ble. However, in all our work the substances operated on arc changed from one slate lo another, and in each state the intrinsic energy depends on Ihc slate only; consequently the change of intrinsic energy may be determined from the initial and final states only, without knowing the manner of change from one lo ihc other. In general, equations will be arranged lo involve differences vibration and disgrcgation work avoided. Thermal Lines. The external work can be determined only when the relations of p and v arc known, or, in general, when the characteristic equation is known. It has already been shown that in such case the equation may be represented by a geometrical surface, on which 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 W fvt = p I Jo, During the change the temperature may or may not change; the diagram shows nothing concerning it. Lines of Equal Volume. The pressure in- creases at constant volume, and the tracing-point moves from a t to o a . The temperature usually increases meanwhile. Since dv is zero, SSB Q (21) Pic. Isothermal Lines, or Lines of Equal Temperature. The temperature remains constant, and a line is drawn, usually convex, toward the axis 0V. The pressure of a mixture of a jiquiu ana its vapor is consumi lor u given temperature; con- sequently the isothermal for such a mixture is a line of equal pressure, represented by Fig. 3. The iso- thermal of a perfect gas, on the other hand, is an equilateral hyperbola, as appears from the law of Boyle, which may be written laodynamlc or Isoenerglc Lines arc lines representing changes during which Ihc intrinsic energy remains constant. Conse- quently all the heat received is transformed into external work. It will be seen later that the isodynamic and isothermal lines for a gas are the same. Adiabatlc Lines. A very important problem in thermo- dynamics is to determine the behavior of a Kiihslancc when a change of condition lakes place in a 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 Q , ~f- / ' fitto) C/"l fitlv (22) (23) that is, the external work is clone wholly at the expense of Ihc intrinsic energy of the working substance, as musl be ihc case in conformily wilh the assumption of an adiabalic change, Relation of Adiabatic and Isothermal Lines. An important property of acliabatic lines can be shown to advantage at this place, namely, that such a lino is sleeper than an isothermal line on the (p, v) plane where they cross, as represented in Fig. 6. The essential feature of adiabalic expansion is that no heat is supplied and that conse- quently the external work of expansion is done at the expense of the intrinsic energy which consequently decreases. The intrinsic energy is ihc sum of PlD . 6 . Ihc vibration energy and I he disgrcgaiion energy, both of which m general decrease during an adiabalic expansion; in partic- ular the decrease of vibration energy means a loss of temperature. Conversely an adiabatic compression is accompanied by an in- crease of temperature. If an isothermal compression is rcpre- scnted by cl, then an adiabatic compression will be represented by a sleeper line like ca, crossing the constant pressure line fo to the right of 6, and thus indicating that at that pressure ihcro is a greater volume, as must be the case for a body which expands during a rise of temperature at constant pressure. It is very instructive to note the relation of these lines on the surface which represents the characteristic equation for a perfect gas. In Fig. 6, which is an isometric projection, the general form of the surface can be recognized from the following condi- tions: -a horizontal section representing constant pressure cuts the surface in a straight line which indicates that the volume increases proportionally to the absolute temperature, and this line is projected as a horizontal line on the (p, ) plane; a vertical section parallel to the (p t l) plane shows that the pressure in this case increases as the absolute temperature, and the line of intersection with the surface is projected as a vertical line on the (/j, -y) plane; finally vortical sections parallel to the (p, v] plane arc rectangular hyperbola? which arc projected in their true form on the (/>, i>) plane. If AC is an adiabalic curve on the characteristic surface, its loss of temperature is properly repre- sented by the fact that it crosses a scries of isolhcrmals in passing from A lo C; Aft is a line of constant pressure showing a decrease of temperature between the isothcrmaLs through A ami through C; finally the projection of ABC on to the (/>, v) plane shows that the adiabalic line ac is steeper than the isothermal line be. Addition .should be called to the fad lhal the first sta Lenient of this relation is the more general as it holds for all substances that expand with rise of temperature ul constant pressure what- ever may be ihe form of the characteristic 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 rP 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 /i J.. on oti IB on v ) ne m ev icl 1C* n it is a finite quantity; and in any case, if we admit an absolute xcro of temperature, it is evident that the intrinsic energy cannot be infinite. On the olhcr hand, if an isothermal curve were treated in the same way the area would be infinite, since beat would be continually added during the expansion. Now suppose the body to pass from the condition represented by A to that represented by #, by any path whatever that is, by any succession of changes whatever /or example, that represented by the irregular curve AJ). The intrinsic energy in the stale ft is represented by the area VkBfi. The change of intrinsic energy is represented by the urea ftRbfiAa t and this area does not depend on the form of the curve AJi. This graph- ical process is only another way of saying thai ihe intrinsic energy depends on the slate of the subslunce only, and that change of intrinsic energy depends on the final and initial slates only. Another way of representing change of intrinsic energy by aid of isodynamie lines avoids an infinite diagram. Suppose the change of slate to be represented by the curve AH (Kip;, g). Draw an isodynamic line AC through the point A t and an adia- balic line RC through Ji t intersecting at C; in general the Lsocnergic line is distinct, from the isothermal line; for example, the isothermal line for a saturated vapor is a line parallel to the OV nxis, and I'm g. the isocnergic line ia represented approximately by the equation c .Ortfl const. Then the atvu AJlba represents Ihe external work, and the area bJRCc reprcsciixs the change of intrinsic energy; for if the body be allowed lo expand adiabnticftlly till the intrinsic energy is reduced to jifl original amount at the condition represented by A the external work bBCc will be done at the expense of the intrinsic energy. CHAPTER HI. SECOND LAW OF THEKMODYN/UfrCS. 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! in 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 22 (Fig. TO), and let the substance expand at the constant tem- perature /, receiving heat from the source A. If the first condition of the substance be represented by A (Fig. n), then the second will be represented by B> and AB will be an isothermal. If E a and 4 are the intrinsic energies at A and B, and if W ab , represented by the area 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 cylinder, o = A (E c E b + WK) (26) where W^ is the external work represented by the area bBCc. Place the cylinder .on the refrigerator B, and compress the sub- stance tilt it passes through the change represented by CD, yielding heat to the refrigerator so that the temperature remains constant. If Ed is the intrinsic energy at D, then is the heat yielded to the refrigerator, and W ed , represented by the area cCDd, is the external work, which has a minus sign, since it is done on the substance. The point D is determined by drawing an adiabatic from A to intersect an isothermal through C. The process is completed by compressing the substance while the cylinder is on the stand C (Fig. 10) till the temperature rises to t, the change being represented by the adiabatic DA. Since there is no transfer of heat, o = A (E a -E d -W da ) (28) Adding together the several equations, member to member, Q _ Q, = A (W ail + H'fc - W c<l - Wto) . , (29) or, if W be the resulting work represented by the area ABCB t then (30) that is, the difference between the heat received and the heat delivered to the refrigerator is the heat transformed into work. A Reversible Engine is one that may run cither in the usual manner, transforming heat into work, or reversed, describing the same cycle in the opposite direction, and transforming work into heat. A Reversible Cycle is the cycle of a reversible engine. Carnot's engine is reversible, the reversed cycle being ADCBA (Fig. ii ), during which work is done by the cnglno on the working substance. The engine then draws from tho refrigerator a certain quantity of heat, it transforms a certain quantity of work into heat, and delivers the sum of both to tho source of heat. No actual 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, rm. (?* - (? - (?* W flt A dosed curve of any form may be consid- ered lo be ihc general form of a closed cycle, as that in Fig. 13. For such a cycle we have Fio.i3> I dQ *= A IdW, which is one more way of slating ihc first law of thermodynamics. Tt may make this last clearer to consider the cycle of Fig, 14 composed of the isothermals AM, CD, and HG } and the adialmtics BC t DK, and GA. The cycle may be divided by drawing ihc curve through from C lo P. ll is indifferent whether the path followed be ARCDHGA I Tl f ' T>X-f 1'\ V *f* 4 J ( Tl f~* J "*/*' t i or A]tCl'CJ)hCrA) or, ngain, ABCJ'UA -f- CDEJ'C. Again, an irregular figure may be imagined to be cut into elementary areas by Isoihcrnwls and adiabalic lines, as in Fig. 15. The summation of the areas will give the entire area, and the summation of the works represented by these will give the entire work represented by ihc entire area, The Efficiency of an engine is the ralio of ihe heat changed into work lo the entire heat applied; so that if it be represented by c, AW ~' (30 Fin. 14. Q Q for the heat Q> rejected to the refrigerator is what is left AW thermal units have been changed into work. ' Carnot's Principle. It was first point*( out by Carnol that the efficiency of ** reversible engine docs not depend tm nature of the working substance, but it depends on the temperatures of L source of heat and the refrigerator. FI. u. Let us sec what would be the qucncc if this principle wore not iruCt Suppose there arc two reversible engines R and A, each Inking Q thermal units per second from the source of heat, of whtcH A Is the more efficient, so that is larger than AW, Q Q Q - Q Q Q (33> this can happen only because Q a ' is less than Q,', for Q is assumed to be the same for each engine. Let the engine R be reversed and coupled to A, which can run it and still have left the useful work W a W r . This useful work cannot come from tho source of heat, for the engine R when reversed gives to the sourCQ Q thermal units per second, and A takes the same amount in Lhd same time. It must be assumed to come from the refrigerator! which receives Q a ' thermal units per second, and gives up Q r * thermal units per second, so that it loses Qr - Q a ' - A (W a - Wr) thermal units per second. This equation may be derived from equations (32) and (33) by subtraction. Now it cannot be proved by direct experiment that such an action as that just described is impossible. Again, the first law of thermodynamics is scrupulously regarded, and there is no contradiction or formal absurdity of statement. And yd when the consequences of lite negation of Cur not *s principles tire clearly set forth they arc naturally rejected as improbable, if not impossible. The justification of the principle is found in the fact thai theoretical deductions from it arc confirmed by experiments. Second Law of Thermodynamics. The formal statement of Carnot's principle is known us the- second Inw of thermody- namics. Various forms arc given by different investigators, none of which arc entirely satisfactory, for the conception is not simple, as is that of the first law. The folio wing nrc sonic of ihc statements of the second law; (7) AH reversible engines working between the same source of heat and refrigerator have the stnne efficiency, (2) The efficiency of a reversible engine is independent of llio working substance. (3) A 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- dynamics. So far as efficiency is concerned, lite second law of thermo- dynamics shows that it would be a umUcr of Indifference what working substance should be chosen; we might use air or sicnm in the same engine and get the same efficiency from cither; there would, however, be a great difference in the power that would be obtained. In order to obtain a diagram of convenient size and distinctness, the adia balks are made much sleeper than the isolhermals in Fig. n; as a matter of fact the diagram drawn correctly is so long and attenuated that it would be practically worthless even if it could be obtained with reasonable - mation in practice, as the work of the cycle would hard come the friction of [lie engine. The isothcrmals for a of water and steam arc horizontal, and the diagram la form shown by Fig. 16. In practice gram closely resembling Garnet's c chosen as the ideal, differing mainly steam is assumed to be supplied a hauslcd. In n particular case an working between the temperatures 36 and 158 F. had an actual thermal efficiency of o. ideal cycle had an efficiency of 0.23, and Carnot's cy an efficiency of 0.25. The ratio of 0.18 to 0.23 is abot which compares favorably with the efficiency of turbine -7 """ wheels. /? i / Carnot's Function. - Carnot's principle asserts th efficiency of a reversible engine is independent of the na the working substance; consequently the expression i efficiency will not include such properties of the workir stance as specific volume and specific pressure. But th ciplo asserts also that the efficiency depends on the tempc of the source of heat and the refrigerator, which indeed only properties of the source and refrigerator that can the -working of the engine. We may then represent the efficiency as a function of tl peralures of the source of heat and the refrigerator, or amounts to the same thing, as a function of the sup'cric pcrature and the difference of fhc temperatures, and ma; AW ' e- Q where Q is the heat received, Q' the heat rejected; and / are the temperatures of the source of heat and of the refri$ on any scale whatsoever, absolute or relative. , .If the temperature of the refrigerator approaches near t [lie source of hcuLQ Q' and / f become A<7 and A/, and at the limit dQ and <//, so that (34) It is convenient in assume thai the equation ctin he expressed in the form The function/ (0 is known as Carnot'a function, and physi- cists consider that the isolation of this function and the relation of the function in temperature are of great theoretical importance. Absolute Scale of Temperature, ft is convenient and cus- tomary to assign to Carnoi's function the form,-;, whore T is [lie temperature by the absolute scle referred to on page 3, measured from the absolute xcro of temperature. '.Phis assump- tion is justified by the facts that the theory of thermodynamics is much .simplified thereby, and (1ml the difference 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. 100 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 SECOND LAW OF T1IKUMODYNAMICS 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 It GRAIM1ICAI, KKI'KKHKNTATION OK KFKICIKNCY 33 new function, howcrcr simple [hat conception may he-; and (here is an added advantage in being able to return La a simple con- ception at will. Efficiency of Reversible Engines. Returning to equation (34) and replacing Cnrnot's function/ (1} by -?> a.s agreed, wo have for the differential equation of the efficiency of a reversible engine tlO <ll ii . i Q V or, integrating between limits, Q r T' and the efficiency for the cycle becomes T Q This result might I wive been obtained before (or without) the discussion of Kelvin's ^mphlcul method, and leads to the same conclusion, that the absolute temperature cnn In; made to depend on the efficiency of Carnol'.s cyclu, and may, llu'refort 1 , be inde- pendent of any thcrmomc'U'ic substance. As has already been nairl, this conception is more important on the physical side than on the engineering aide, uncl its 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. 34 SECOND LAW OF THICHMOIJYNAMICS 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 . . Q Q T as found by equation (35). The deduction of this integration is more simple and direct, but the uraphlcnl * * n i ^ EXPRESSION FOR KNTKOPY 35 I-' HI. 31. is interesting and may give the student additional light on (hi.s subject. 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) J and for ihc entire change may express the change of entropy by ,, L A/Q /A' * tfy asa I -** r / I f f* ' Fl. 11. 36 SKCONI) LAW OK TIIKKMOUYNAM1CS which should for any particular case either be integrated between limits or else a constant of integration should be determined. Attention should be called to the fact that the conception of the spacing of isoihermals and adiabalic.s is based fundamen- tally cm Carnol's cycle and the second law of thermodynamics, which 1ms been applied only to reversible operations. The method of calculating changes of entropy applies in like manner to reversible operations; and when entropy is employed (or calculations of operations that tiro not reversible, discretion must be used to avoid inconsistency and error. On the other hand, the entropy of a unit weight of a given substance under certain conditions IK a perfectly definite quao* tity and Ls independent of the previous history of the substance. This nwy be made evident by the consideration that nny point on the line no, Fig. icj, page 31, has n certain number of unlla of entropy* (for example, three) more (ban that of any point tin the ndiabalic (iff. Example. -- There may be an advantage in giving a calcu- lation of a change of entropy to emphasize the point that it eon be represented by a number. Let it be required to find Ihts change of entropy during an isothermal expansion of one pound air from four cubic feet to eight cubic. The heal applied may be obtained by integrating the expression <!& T Itfa T " B) 7" ille value of the latent heat having been taken from page From the characteristic equation t>v - itr the above expression may be reduced to dv APPLICATION TO A RKVKRSI11I.K CVCI.K 37 - i ' I, i \ 1 v . . t/> (p - (t jf ( v ) jojr^ (/,' t/j , ; (0.2375 o.ifiyo) lo& ~ -=0.0475. ''"' A problem for air is chosen because H can he readily worked out at Ui is place; as Ji mailer of fuel, I here arc few occasions in practice where there is reason lo refer to entropy of air. Application to a Reversible Cycle. A very important result is ohlaincd by the application of equation (37) to the calcula- tion of un l ropy during n reversible cycle. In the first place, il is clear llmt the entropy of a substance having its condition represenled ))y the point a (Kitf. 23), depends on tin- mliabalic line drawn through it; in other words, the entropy depends only on ihe condition of liic siihslunee, In this regard entropy i like intrin- sic energy and differs from cxtermd 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 /? ,g SECOND LA.W OF Til KKMODYNAMICS This is a very important conclusion from the second law thermodynamics, and is considered to represent that law. second law is frequently applied by using this equation in can* ncction with a general equation or a characteristic equation, fa a manner to be explained later. Though the discussion just given is simple and complete there is some advantage in showing that equation (38) for certain simple and complex reversible cycles. Thus for Carnot's cycle, represented by Fig. 20, the i of entropy during isothermal expansion is because the temperature is constant. In like manner decrease during isothermal compression is *-*- so that the change of entropy for the cycle is T 'J' But from the efficiency of the cycle wu have o-Q' _ T - r . Q Q r Q r T Q, T r A complex cycle like that represented by Fig. 24 may broken up into two simple cycles A and CDFE, for each of which individually the same result will be obtained thai 1^ the increase of entropy from A to B b equal to the decrease from F to 6\ afl4 the increase from C to 1) is equal lo lh decrease from tt to F, so that the MIRH mnlion of changes for the entire cycle gives xero. Fin. 94, MAXIMUM EFFICIENCY 39 Km. Fig. 25 represents the simplified ideal diagram of a 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- 40 SKCONI) LAW OK THERMODYNAMICS jcctccl at 20 C., the combined dlinumy of the diagram computed to be ^x 20 3 5 'I' 2 73 3 -0.56; 250 -I- 273 had the heal been all applied nt 500 C., the efficiency have been 500 20 *' ; fcj 0.62. 500 -I- 273 The loss in this case from applying pan, of the hcnl nt la temperature is, therefore, o.fia o.;6 ; " -" o.oo7. 0.02 " 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 ftj*prMiclj or i < Ttty, NON-HHVKUSiniJi CYCLES 41 Integrating for ihc entire cycle.-, we shall have C<1(\ ^ . CilO, Ar ' , . Jr <0 ' ' J T"~* ' ' ' Ul) where JV represents u negative quantity. The absolute value of W will, of cuur.se, depend on the efficiency of Ihc non- reversil)lc engine. If ihe efficiency is small compared with llmt of a reversible engine, then the value of W will bo large. Tf (lit: efficiency approaches (hat nf a rcvcrsihle engine 1 , then N approaches aero. Ft is scarcely necessary It) point out. that N cannot be positive, for that would infer that ihe 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 ea.se the equation representing tin- distribution of energy contains a fourth term K to represent the kinetic: energy, and equation (15) becomes i/(j - A (rf.V -I- til ! tlW -I- rftf) . . . (42) As before S represents vibration work, / represents- disgreguLion work, and W represents external work. If the vil)ratian and disgrcgation work cannot be. separated, then we may write tlQ - A (HE + d\\ r i-(//C) (,| 3 ) If a non -reversible process like that just discussed takes place in apparatus or appliances tlrnt are made of 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. SECOND I-AW Of TtfKRMonVNAMICS 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. CHAPTER TV. GENKRAT, TII1-RMODYNAMIC METHOD. IN the three preceding chapters a discussion lias been given of the three fundamental principles of thermodynamics, namely, (i) the assumption Unit the properties of any substance can be represented by an equation involving three variables; (2) the acceptance of the conservation of energy; and (3) the idea of Carnol's principle. Jn the ideal case cfich of ihcsc principles should be represented by an equation, and by the combination of the three several equations all the relations of the properties of a substance should be brought out so that unknown proper- tics may be computed from known properties, and in particular advantage may be taken of opportunities to calculate such prop- erties us cannot be readily determined by direct experiment from those which may be determined experimentally with precision. Recent experiments have so far changed the condition of affairs that there is less occasion than formerly for sucli a general treatment. Of the three classes of substances that arc interest- ing to engineers, namely, gases, saturated vapors, and super- heated vapors, the conditions appear to be as follows. For gases there arc sufficient experimental data to solve all problems without referring to the gcncml method, though the ratio of the specific heals is probably best determined by that method. For saturated steam there is one property, namely, the specific vol- ume, which is computed by aid of the general method, but there arc experimental determinations of volume which arc reliable though less extensive. The characteristic equation of super- heated steam is now well determined, and the specific heat is determined with sufficient precision for engineering purposes, so that there is no difficulty to making the customary calculations. 43 The one class of stiljslancvs for which (In- necessary pr**? 1 must be computed by aid of the general meihod, art tile fluids like ammonia and .sulphur dinxidc, w for refrigerating machines. On the whole, even with conditions as stated, it that the student should master the 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 clifTi'rrniiat. Application of the First Law. ..... - The first Kctienil principle may be lulu-n u> be rrprcsi-nli-;! by njuutiuu (i), inul ilu- fir.st 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 O/ U h cvltlcni tlmt Now equation (,|,|) Is an abbreviated way of writing Iho for continun] tllRcrvnilm'wn which may be expanded to ;/: 4 5 GENERAL TIIKRMODYNAMIC METHOD or replacing the first pnrtial clilTcrenlial coefficients by equivalents, 8 a 8* ihc subscripts being \vrillcn to avoid possible confusion oilier partial different in I coefficients to he deduced laier. From the first law of ihermodynumirs and equation ( have in like manner dQ /I (<!E + pttv) Cj,'// -I- wfty. Since the differential (/v is inconvenient, we may replace it so that 17 Making use of Ihc equation v * 8/ , givcs AITI.U'ATION ()! T1IK SKCUNIl LAW Uui llu- ithhum|ii(oti of u diimu-U-riHiii 1 . ajvmtitm c f>, Vt ami / uirrii-s willi ii ilu- usHumpliun llmL Sj in, fnnii tc|uiiluih (.0 \vi* tntiy have tl{> - A ((//; | {Hlr} - ml ft ! tnlv. cr, Appllcfliion of Iho Second Law. Tin 1 ht-itnu! inw of clynnmici inn be cxprfwii'il liy ctjuwlion (.^H), PHKC 37i T 1 '^ J ^ (.17) 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 or *.(& T\ T \8v/f ~YS ' 8 A ~ ( Sc \ i W. UvA" T (49) on ( 2 ) we haw m m, from cquation (So) First and Second Laws Combined _Th th the first and thc sccond -- To & to the Al.TKKNATtVK MKTIKW iilioriK (1)1 ('*), nnd (3) may la- oUainrd hy ctimliinin^ ilu- ei|iuuinns rmillmtf from tin- application nf llu- laws M-purtiU'ly. Thus ^illations (-15) ami (.|c)) give ' ' (5-0 And and (so) uiv t ' i tu ill .i7' (.|H) }.',\i- 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 ih.in 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 : ml*. go GENERAL THERMODYNAMIC METHOD No\v from equation (16), representing the first law of thermo- dynamics, dQ - A (dE, -I- pdv), it is evident that dQ is not an exact differential, since the equa- tion cannot be integrated directly. The fact that in certain cases p may be expressed as a function of v t and the integral for external work can be deduced, docs not affect this general statement. Suppose that there is some integrating factor, which may be represented by -, so that o may be integrated directly; we may then consider that we have a scries of thermal lines represented by making const., o ; const., etc. const., These lines with a scries of adiabatic lines represented by tf> = const., </>' = const., </>" * const., etc., allow us to draw a simple cycle of operations represented by Fig. ssa, in which AB and CD arc represented by the equations ~ - C, and ~ - C', while AD and BC arc adiabatlca. The cffi- h If tf ciency of a reversible engine receiving the (I FID. heat Q during the operation AJi t and reject- ing the heat Q' during the operation CD, will be Q AW Q (10 . But - is an exact differential, and depends on the state of o ZEUNKR'S EQUATIONS 51 the substance only, and consequently is the same at the end as at the beginning of the cycle, so that for the entire cycle 5 Now during the operations represented by the adiabaiics AD and BC no heat is transmitted, and during the operations rep- resented, by the lines AB and CD, is constant; consequently the integration of the above equation for the cycle gives 0' *= s = o, S S' .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, Now -^, + g* so that n BE o BE A~Sj' A-*7 These properties Zcuner writes 52 GENERAL TIIKRMOUYNAMIC METHOD Solving equation (54) first for o and then for w, AT+H*!. 0V = w~ s/, Sv In equation (3) dQ ndp -I- odv, we may subslltutc the above values successively giving s? t because ifc s ^ -/- "r- op Sv And also .. ^ Replacing o and by their values in terms of X and K, ZKUNKK'S EQUATIONS 53 In these equations a is the coefficient of dilatation, or - -j- / is equal to 7', uncl v r A . Y/i -. - - . A A \5/)/ii /I A \w/ p If this devivtiUon of Zcunur's equations is borne in mind, the irealnu'nl of thcrmotlynamics Ijy many Ocrmun writers may be readily recognized to be only a variant on that developed by Clausius and Kelvin. CHAPTER V. PERFECT GASES. THE characteristic equation for a perfect gas is derived from a combination of the laws of Boyle and 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. 54 CIIA.KACTKUISTIC KQUATIQN 55 Characteristic Equation. From equation (57) we muy calculate any special volume, such as v lt getting v l - v (i -|- a/). Assuming lhal /, in equation (56') is the normal pressure of [he (ionosphere // , uml Kub.slUuting the vulue jual found for v,, we have for ihe combination of Ihe laws of Boyle uml (luy- Luasac pv -f- /) ^ - (5 s ) If it he assumed that a KIW conirucls a- purl (if its volume ut 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- thermometer. 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 -* PROPERTY OF ' r 1 i.j! 'JJCT GA.SKS j- Absolute Temperature. Recent investigations of the prop- erties of hydrogen by Professor Cullender* indicate that the absolute zero is 273.! C. below 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 frccx.ing-point. Now Kcgmiult t gives far the weight of a Hire, or one cubic decimetre, of mercury 13.5959 kilograms; consequently the specific pressure of the atmosphere under normal conditions is l>v " 10,333 kilograms per square metre. Using the conversion units given above for reducing (life specific pressure to the English system of units gives /> 2116.32 pounds per square foot, which corresponds lo 14.697 pounds per square inch, or to 29. gat inches of mercury. It is customary and sufficient lo use for the pressure of the atmosphere 14.7 pounds to the square inch. * Phil. Mag,, Jan., 1903. f MSnwires do 1'Instttnl da France, vol. xxl. SI'KCIl-'lC VOLUMKS 57 Specific Volumes of Gases, --I'rom rm*m (Iclcrminiilioiw of (Icnttilit's of KIISC.X by Li-due, Mnrlcy, untl Kiili'igh il appears tlitil [he most probable values of UK- specific volume of the i-onimuna- ses ii rr VOI.UMKS JN iTHir MKTUKS Ul- ()NK ICII.tH 1KAM, AimospliL-rit air ....... .... Oxygen .... }iy<\niKvn 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; u.7i it.ar 178. a To iht'si- may In- addi'd tin- valw for uirlion tlioxitlt 1 , 0.506 culm- mi'lri: per kiltigrnm r S.io 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 expression Tlu- values for /^ rurri'siiontliiiK in ihe French nncl the Kn^lUh of unilK may lie uilrulaled HH f l-'renrh units, a 73 Knglisli unilK, A! - uL.. Vfduc of R fnr other ^itscs may bt- calc'iiliiicil in a Jikr nmiincr. s g PERFECT GASES Solution of Problems, Many problems involving the proper- tics of air or other gases may be solved by the characteristic equation J>v = RT t or by the equivalent equation T T which for general use is the more convenient. Jn the first of these two equations (he specific pressure- and volume lo be used for English measures arc pounds per square foot, and the volume in cubic feet of one pound. For example, let it be required to find the volume of 3 jwundt of air at 60 pounds 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 lh.es volume at 200 C. and at 10 atmospheres. Here i X 2 373 10 V 473 v & -47.1 X j. * Specific Heat at Constant Pressure. The specific hcnl far true gases is very nearly constant, and may be considered to be APPLICATION OF LAWS OF TIIKKMOUYNAMICS 51) .so for thermodynumic equations. Ucgniiull gives for llu: mean values for specific heal al constant pressure the following results: Atmospheric: air o-^.ns Nitrogen o.a.| % tH Oxygen 0.2175 Hydrogen .^--po Ratio of the Specific Heats. - My a 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 thermodynamics. 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, ). 6o I'KUI'KCT It is convenient at this place to make the application of the laws of thermodynamics by aid of equation (55), page 49. * ' c,, c v <=--> '1-/V s -. (63) From the equation we have pv Bt KT, Bf .'. c,, AR This equation shows conclusively that if tin- charactcmlic equation is accepted the differences of the specific heals must be considered to be constant, and if one U treated as constant so also must the other. Conversely, the assumption of conalnnt specific hcaLs lor any subsUUHT is in cflVrl the a.sHumplIon of the characteristic equation for a perfect gas. The solution of equation (64) for (he ruiio of the specific heal3 gives -- son 1 .JO/). torn X 0.77H . ''vv . t, JU.UL 426.9 X 273 X 0.2375 For those who have not read Chapter IV, the following deriva- tion of equation (64) may be interesting, In Fig. 26 let ah repre- sent the change of volume at constant pressure clue to the addition of heal ^A/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 ISOTHERMAL LINK 6l the last transformation making use of the partial derivative Bv R 5 ^ " ]>' Thermal Capacities. The values of the several thermal capacities for a perfect gas were derived on page 12 and may ho written } f lL t f c \ , ., L t, .... , \ tr } f } ) ' ' n t f /' 'i'> .. I'/' ''' ' \ UI V M t- /7 I ? *-r, the transformatioiifl in equations (66) and (67) bring made by aid of the rhorftcterlMllu equation. General Equations. To deduce the general equations for gases from equations (i), (a), and (3)1 It la only nrrcHwiry to replace the letters /, ni, n, and a by their values Jusl obtained, - - v Isothermal Lino. The eqimlinn Ui iht- iKothcrmul line for n. gas is obiainw) by nmklng T connlnni In the chnrncicrlaile efjijaUon, HO that /n- R'l\ - /), or ^' " ^1*1 - - (73) This equation will he recognised as the expression of Boyle 'a tow. It isj of course, the equation lo an equilateral hyperbola. PKUFKCT GASES To obtain the external work during an isothermal expansion ; may substitute for p in the expression we may W ". from the equation to the isothermal line just stated, using for limits the final and Initial volumes, v t and v v If the problem in any case culls for the external work of one unit of weight of a uns, then v l and v a must be the initial and final specific volumes; but in many cases the initial and final volumes arc given without any reference to a weight, and tt h then sufficient to find the external work for the given expansion from the initial to the fina! volume without considering whether or not they are specific volumes. The pressures must always he specific pressures! in ihc Englfeh system the pressures must he expressed in pounds on the square foot before using them in the equation for external work, or, for that matter, in any thcrmoclynamic equation. ' For example, the specific volume of air at 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. o ISOKNKUCilC LINK In both problems ihc pressure per stjimru inch is multiplied by i.j.i to reduce it to the square fool, In the 1'ii'sl problem tbe pressures are absolute, thul is, they are measurud from /em pressure; in ihe second problem the pressure by the gauge is 60 pounds above the pressure of llie atmosphere, which is here assumed to be 1*1.7 pounds per squart- incli, and is added to give the. absolute pressure. In eareful experimental work ihe pressure of thu ulinospheiv is measured by a barometer and is added to the 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 thus: i' V rr. 1 1 1 ' /'') l> or, .sulxslUulinK r l from equation (d,\ ^ , ( . | V (75) 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 log, to, \, 1'EKFKCT OASES This may also be seen from UK consideration thai if heat h continually applied, and all changed inio work, there will be a limitless supply of work. Adiabatic Lines. During an fidialmlic change for exam- pie, the expansion of a gas in n 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 const. ' -&6.) (77) This is the adiabatic equation for a perfect gas which is most frequently used. If adiabnllc equations involving other vnrfa~ bles, such as v, and 7',, arc desired, they may be derived from equation (76) by aid of the characterise equation, which far this purpose may be written flV *- EH) T so that and L I T.v.*- 1 * \ v [ MHABATIC LINKS Or equations (78) nnd (70) may be dalueed directly from equation (70) UK equations (76) nnd (77) were from equiuion In like manner we mny deduce from equation (71) T}>' - V,/', " (80) or we may derive it from equation (76). To find (he external work the equation W f* ptv may be used after fUihsO'iufiiiK for /> from equation (77) In Fig. 28 the nrca between the xi OT', ,. the ordimuc /', and iho ncllatmlU 1 line an ex tended without limit, becomes V, fl I'd!. 10. nnd not infinity, ns IR the. case with ihe isolhermiLl line, Here, aa with (he cnlcuiatton of external work during itso thermal expansion, specific -volumes xhould be used when the problem involves (i unit of weight; but work may be calculated for .any given initial and final volumes without considering whether they are specific volumes or not. The pressures n re- al ways pounds on Ilia square font for Ihe KnglWi system. For example, the external work uf ndlalHiUc cxpunitlon from 3 cubic feel and o"o ]ioundfl pressure by the KIUI^C tn the volume of 7 cubic feet Is W M'7._XMfl X 231140 fool-pounds, 66 PKRFKCT GASKS 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 cent. Intrinsic Energy. Since external wnrlc during n expansion is done at the expense of tin- intrinsu- oniTgy, I lie obialnable by n fnfinJie expansion ninnot IK- ^r<sttf< intrinsic energy. Jf it be ndmitted tliat sneh tin changes all of the intrinsic energy into external \vrk we 1m ve IK which gives a ready way of culcu luting practice we nlwys deal wJlh difTcri.'nn'.s r>f intrijisic- that oven If there be a residual Intrinsic energy after (in adlabatlc cxpnnslon the error of our niclluKl will be from nn equation having ilie form Sponntiat Equation. The expiinsitins aiul of ulrand other gases (n practice arc 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 ENTROPY Change of temperature during such an expansion may be calculated by the equations (85) I-H 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 68 I'KKFKCT ifASKS and, integrating between limit 1 *, <f> 3 - </), - c, lo^rf -I- (r jp - c ' i <f> 3 - </>, - 0, lutf, -.* which give ready means of ciUmhimK fhun K cs of cniroi These cqutitions give the vnirnpy dian^-s pn- pound, and fire be muliipliod by the weifilu in pounds u, K i vc the change the acliml conditions. For example, the change- of 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. COMPARISON CU' 1 T11K AIR TllKKMOMKTKU 69 Tin- most complete experiments for this purpose were made liy Jimli- and Lord Kelvin, who forml nir slowly through a porous pluf; in a lube in such u manner llitu no beui was ininsmillecl Ui r from the jtir during tin- process. Also Ihe velocity both lii'fiirt' untl beyond tlu- plutf was so small that tin- work due lo ihe elmnjtc of velocity could be disn^ardnl. AH the work Unit would be developed in free expansion from the higher Lo iho lower pressure was used in overcoming the resistance of friction in die plug* unit so itinverli'd into lieut, and as noiK- of this bent csuiped.il was relainrtl by (he air itself, the plu^ remaining at a umstHiU leniperalure. ll iherrfore uppeurrt llwl llie imrinsk: ent'ry remained tin- siime. ami thai a 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. 70 PERFECT GASES Deviation from Boyle's Law. Karly experiments on permanent gases (as they were then known) indicated lhat there were small deviations evident lo a physicist, but not af Importance to engineers-; but now that air is compressed let pressures as high as 2500 pounds per square inch, it becomes necessary to take account of such deviations in engineering practice. Perhaps the best conception of ibis subject, and of the four recognized slates of fluids, can bo hud from a considernlion &/ Andrews' * experiments, which for ilu 1 present purpose arc coo- vcjiicntly represented by his isolliermul curves, which arc* repro- duced in Fig. 20,a, together with the curves for uir. The latter arc approximate hyperbola: referred to the proper axes, that for xoro pressure being nearly the whole height of the diagram below the figure as it is drawn. At .)H.t C., the isothermal for carbonic acid shows a marked deviation from the hyperbola, a* may bo seen by comparison with the curves for air, or better from the /net that a rectangular hyperbola through J* will pug through Q. On the other hand, the isothermal for 13.! resem- bles that for steam, which is commonly known MS a ftnlu rated vapor whose pressure is constant at constant temperature; the hori/ontal part of this represents a mixture of liquid and which at the Icfl runs into the liquid and as liquid carbonic acid has considerable compressibility, this curve becomes n line with an appreciable inclination to axis of zero volume. At the right, the thermal shows a decided break and alt away as the volume becomes larger that of the saturated vapor. The isolhernml Pin. for 2i.5 shows similar the passages from one condition lo another are more gradual The dotted curve k drawn through (he [joints of saturation ind liquefaction, and its crest corresponds lo the critical temper-own?. * Phil, Trans., t%(*>. pnrt !i, p. 573 , nml ifyd, jmri II, p. ,, 3( . IWNHITV AT MKlIt I'KKSKUKK Tin- Isnihmnnl fur $i.i in iluirly alum- the critical Irmprni- lurr ami iliH-% nnt ihdiialr a liijurfiu titui. The M'vrrul Mnli^ "f a lluiit imi IK- rnumiTiiUtl us i, IJijiiit). .j. SiiuirAtrd viijHtr, iniluilinit mixture*. nf liquid und j. 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.*.\, t'M-l .' I' Air Sulphur tlin KlIltT . 7H,| Wnicr I f HI {n 4 h Fri^aure. If ihr ihtul mcilu&h (Klwn on fur llir .iiluUMii sif prntilrm* InvnlvliiK ihr proprrllei air <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,, PKKKKCT OASKS Rontgen's Experiments. J)irtvl cx|>mmeiH8 to determine K may be made as follows. Suppose thai u vessel is filled wfrh air at a pressure /> while the pressure of I he atmosphere i fa Let a communication be opened with the atmosphere suftlcfoat to suddenly equalize the pressure; ihcn let it be closed, .am) lei the pressure p. 4 be observed after the air lias again attained lllfc temperature of the atmosphere. If the first operation is suffi- ciently rapid it may be assumed to be adiabalic, nnd we use equation (77), from which .leg IJI .. ^11 The second operation is al cimsliini volume; the specific volume is the same at Iho final stale aa after '&t adiabalic expansion of the first operation, llui the Initial ODrtl final temperatures arc the same; amm|iicn(ly Ing which substituted in equation (91) jjlves "" 1() g /! Th^ same experiment may be made by rarefying th the vessel, in which case the sign of the second term Rbntgcn* employed this method, using a vessel contaJnrla 70 litres, and measuring the pressure wilh a gauge made m the same principle as the aneroid barometer. Instead of cuwtm* ing the pressure p a al the instant of closing the 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. KXAMPLKS 73 EXAMPLES. ^ 1. Find the weight of .| cubic metres of hydrogen ill 30 C., iind under the pressure of Hoo mm. of mercury. Ans. 0.3*11 kg. 2. Kind the volume of 3 pounds of nilrngim al a pressure of .15 pounds lo the square inch by ihe gauge lln( l ^ So I 1 ', Ans. i r.05. 3. Kind UK- temperature al which one kilogram of air will occupy one cubit- metre when at u pressure of 20,000 kilograms per square- metre-, Ans. ,|ioC. 1- Oxygen and hydrogen lire In he sin red in limits 10 inches in diameter iind 35 jiu'hes long. Al :i maximum lemperalnrc of noJ ; ., the pressure nuisl nol exceed 250 pounds gauge. \Vhiii weight of oxygen can he slnwl in one lank? Whal of hydrogen? Ans. Oxygen 2.21 pounds. Hydrogen 0.138 pound. 5. A balloon of 12,000 cubic feel capacity, weighing with ear, ocaipanl, i'lc., 005 pounds, is inflated with 0500 cubic feet hydrogen ul 60 I-'., the barometer reading 30 inches, Kind UK- weight of the hydrogen and ihc pull on ihe anchor rope; find also (he nmounl ihiil ihe halloon muni be Ilghlcncd to rciich u height where the Imromeler reads 20 indies, and Uic tempera- ture is 10 below x.ero Fahrenheit. Ans. Weight hydrogen 50..) pounds; pull on rope 12 pounds; balloon lightened 7.5 pounds. 6, A 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. 74 PERFECT GASES 10. Find the external work of 2 pounds of air which expand adiabatically until the volume is doubled, the initial being 100 pounds absolute and the initial temperature Ans. 36,100 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- pounds. 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 EXAMPLES 75 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. CHAPTER VI. SATURATED VAPOR. FOB engineering purposes steam is generated in a boiler which is partially filled with water, and arranged to receive heal from the fire in the furnace. The ebullition Is usually energetic, artel more or less water is mingled with (he steam; but if there is il fair allowance of steam space over the water, and if proper arrangements are provided for with drawing the steam, It will be found when tested to contain a small amount of water, usu- ally between hah" a per cent and a per cent and a half. Sleaitt which contains a considerable percentage of water is passed through a separator which removes almost all the water. Such. steam is considered to be approximately dry. If the steam is quite free from water it is said to be dry aim saturated; steam from a boiler with a large steam space and which is making steam very slowly is nearly if not quite dry. Steam which is withdrawn from the boiler may be healed Lo a higher temperature than that found in the boiler, and is then aakl to be superheated. Our knowledge of the properties of saturated steam and other vapors is due mainly to the experiments of Rcgnault,* who determined the relations of the temperature and pressure-, Ih0 total heat of vaporization, and the heat of the liquid for many volatile liquids. Since his time, Rowland's determination of the mechanical equivalent of heat, gave a more exact determi- nation of the specific heat of water at low temperatures, and recently Dr. Barnes has given a very precise determination of that property for water. Again, certain work by Knoblauch, Linde, and Klebe, has given us a good knowledge of the properties * Mimotres de FInstiiut de France, etc., tome xxv!. 76 I'KESSUKK OK SATURATKIJ VAPORS 77 of superheated slcum which can be extended to give the specific volume of saturated steam over a considerable range of temper- ature. AL llic time when llic first edition of this work was pre- pared it appeared desirable to compute tables of the properties of saturated vapor, taking advantage of Rowland's work, and eliminating some uncertainties due to the way in which Kegmuill used his empirical equations in compiUulmg tables. As all this involved changes of sufficient magnitude to influence engineering compulations, it seemed necessary to quote the original diiia at length und to give computations in detail. This hurndtK'lum to the chapter on saturated vapors was found to be somewhat confusing lo students reading it for the first time, and since the main points are now commonly accepted, this work is given only in the introduction lo the "Tables of the Properties of Saturated Steam," the reason for printing it being lhal it in not given elsewhere, as the earlier editions have passer] out of prim. Recent correction of the absolute temperature of the freezing- point of water by Callcndttr and the elder mlnnllon of the specific heat of water by Barnes make it neccssnry to recompute the "Tables of lluf Properties of Snluratecl Steam " which tire intended to uccompuny this book, and opportunity is taken to introduce further data in (hose tallies, and in addition a table has been prepared which will be found to greatly facilitate calcu- lations of adiabatic changes of steam and water, Pressure of Saturated Vapors. Regnaull expressed the results of his experiments on the temperature and pressure of saturated vapors in the form oC the following empirical equation, log p a + 6ft" H- eft" ..... (94) where p is the presftiire, M is the temperature minus the temper- ature t a of the lowest limit of the range of temperature to which the equation applies, i.e.; The constants for the above equation as applied to saturated steam have boon recomputed and reduced to the laliiudc of .15, and arc as follow; mm. of mercury, ' * Ion c log n C, For atcnm from 100 to aao C. rxprrwing the pressure In mm. of mercury, - S- log A o. ti I B L . For steam from 33 to S\A I 4 ', In |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 inch, . 7^3076 \og \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; . lop, a 6 ' Chloroform Carton l)isul|>lmlc . . f'nrlxw Itlrncliloridc . n - t>i\ n ' cfi n ll /III* fff^ a - Iit\ cfi 5- 335381)3 5.. ion (if) j ia.otj633.it 3.9531281 y. 13751 Ho 0.0668673 0.3857180 IOK-I log/! M Umlii. T.W?o8557 O.OHS^S r.WMH-1 T.rjq77fn8 T.CJtjyJilJO T.(>1W).|R5 1.006877 T.(>RG8i7(i T. 0011907 l.ycj,j97Ho / -1- ao / -f- 30 / 30 1 -[ 30 ( -1- ao -~ 20 - 20 -1- 20 - 20 - 20 1- i5oC. J- iaoC. t- 164 C. 1- 1 4 0C. 1- i8B C. Cnrlxm hiflulphldc . . Cfirbon tcirnclilorldc . Xcuncr* suites ilml there is a slight error in Rcgnault's cal- culalion of the conslnnla for tvccton, und gives instead log f> ii - Ad" -|- c/9"; ii~ 5,3085-119; loj(/i(\" -l-o. 531 376(1 0.00361,18 (j logc/J" 0.96.15333 0.0315501 /. Differential CoefAclant '-f-. (it equation (94) we have mm the general form of (95) >/ being the modulus of the common system of logarithms. Differentiating, 7?, - 7T '' lf) K " "!- TT c lo K ^ ^"! put M M or, reducing to common logarithms, ptli l-'rcnclt Units. B. For o to 100 C., mm. of mercury, log /I - 8.8512739 - 10; \ OK B <=> 6. 69305 - r ; log (v, - 9.996725828 - :o; log /3, => o. 006861 c. C. For 100 to 220 C., mm. of mercury, log /I - 8.5495r5 8 ~ T I log B - 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 fj-t by dividing a small difference oC pressure by the corresponding difference of temperature; that Is, by calculating rr^. With tt t\t table for even degrees of temperature we may calculate the value approx : matcly for a given temperature by dividing the difference of the pressures corresponding to the next higher and ihc next lower degrees by two. The following table of constants for the several vapors nnmctl were calculated by Zcuiwr from the preceding equations lot temperature and pressure of the same vapors; Ft'-KKKNTtAr. COEFFICIENT - 1 - ' f/> ,1 on 'form (,'nrlion lilt. - - . (jirlidii iclrncliliulcio If* ( W - i.nsoo.it o.ooiQHi / 1 a 0003701 0500515' . wo.oojsHso I | -j.oGfiji 3,1-0.01.3 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. SPECIFIC HEAT OF WATER. Temperature. Temperature. Temperature. 1 !.* lulllfJOH Specific Heal. Heat. Hfltl. C. C. F. C. F. O 32 I .0094 45 H3 0,99760 90 194 .007CS 5 41 1.00530 50 133 0.99800 aoA .00855 JO 5 1.00230 55 131 0.99850 100 213 .OIOIO 15 59 1.00030 60 140 0.99940 130 248 .Ol69O 20 25 3 35 68 86 95 0.99895 o . 99806 0-99759 0-99735 ?o g 149 158 I6 7 176 1.00040 1.00150 1.00275 1,00415 I4O 1 6O i So 2OO 984 320 356 39 a ,03330 ,03B5& 03-175 .04100 40 104 0-99735 " s IS 1-00557 230 428 .04760 * Physical Review, vol. xv, p. 71, 1903, HEAT OF THE LIQUID 83 Heat of the Liquid. The heat required to raise one unit of weight of any liquid from 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 IIF.AT OP TITK LIQUID. Alcohol ............. Klhcr Chloroform Carbon bisulphide Carbon UilrnchlorHlc Accton 9- o. 54754 H- -I- o. 000003306 (' q 0.5390:^ )- 0.0003959 fl 1 ~ 0.23335 ( -I- o.oooowy (J '} "" -'35 a 3 ' *l- 0.0000815 P j 0.19798 H- O.OOOOOOOP fl " o.S "43 '-I- o. 0003965 t 1 1 lit' S 1 11*1 Illl mUL IVM HIM "' !<>... ...| ..... - ...... cliff erenimviim; for exiimple, the HiteduV IUMI fr *iUuhul U c - 0.5.175.1 I- o.oojj.ufi/ \ Total Heat. --This term in defined n* tl % lwl 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 => i.jo. 5 -i- 0.36644 ( - o. 000516 f* Heat of Vaporization. If the heat of the liquid be sub- tracted from the louil heal, Ihe remainder is culled the heat of vaporization, and is represented by r, so that r II q (100) Specific Volume of Liquids. The coefficient of expansion of mosi liquids is large as compared with thai of solids, bin it is small as compared wilh thai of gases or vapors. Again, the specific volume of a vapor is large compared with that of the liquid from which il is formed. Consequently the error of neg- lecting ihc increase of volume of a liquid with ihc rise of temper- ature is small in equations relating lo the thermodynamics of a Riituralccl vapor, or of a mixture of a liquid and its vapor when a considerable pan by weight of the mixture is vapor. It is therefore customary to consider ihc specific volume of a liquid o- lo be constant. The following table gives ihc .specific gravities and specific volumes of liquids: SPECIFIC OUAVITIKS AND SPKCIl'IC VOlAJMKR ()!' LIQUIDS. Alcohol ..... Kihcr ....... Chloroform . . . . Carbon hlaulphklc , iclrnchlorldo Sulphur dioxide . Aininonift Wnlcr Specific Ornvliy Specific Volume. coniiinred with Wftlov nl < C. Cubic Meirei. Cubic Keel. 0,80631; o oat a<|O ^ o. 736 o 001350 1-5 = 7 0.000055 1.3922 o 00077,1 l .6iao 0.00613 0,81 0,0013^ i.. 1336 O.OOOf)Sl O.OIU 0.636.1 0.001571 0.0353 i o.oor 0.01603 Experiments were made by Him* to determine me volumes of liquid at high temperatures compared with I he volume at 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: SPECIFIC VOLUMES OF HOT LIQUIDS. Loja Hi Kntiit 6.0361445 - .).. 1781868 - i..l5 B 3'Hfl " Water, 100 C. 10 200 C. (Vol. at 4 = unity.) v - i -I- 0.00010867875 / -H 0.0000030073653 (' -) 0.0000000387304331' 0.0000000000066457031 /' Alcohol, 30 C. to 160 C. (Vol. at o = unity.) v i -1- 0.00073893365 t -\- o. 00001055335 /' 0.000000093480843 r 1- 0.000000000.10.113567 /' a.yfrfjoji? 0.6065370 Ether, 30 C. to 130 C. (Vol. at o = unity.) v ~ i + 0.0013480050 i o. 00000003.1.190756 J 1 1- 0.00000000033773063 (' 7- l3Q(jHl9 n 4.8164866 - 0.5385371 - Carbon Bisulphide, 30 C. to loo'C. (Vol. at o = unity.) v I + 0.0011680559 ( + 0.000001(1480598 J 7 o.ocxxxMooo8inoo6a t* 7.0671)6,16 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' - Ifl Quality or Dryness Factor. AH the properties of HaluralCtd steam, such as pressure, volume and heat ot vaporisation, dq>cod on the temperature only, and are dcicrminablc cilltcr by direct experiment or by computation, and arc commonly taken from tables calculated for the purpose. Many of the problems met in engineering deal with mixtures of liquid and vapor, such as water and steam. In such problem* it is convenient to represent the proportions of water and steam by a variable known as the quality or the dry ness factor; * Antiales tie CMmle et de Physique, 1867. factor, .-V', is defined as thai portion of a pound of the mixture which is steam; the remnant, i x, is consequently water. Specific Volume of Wet Steam. Let the specific volume of the saturated vapor bo .t and that of the liquid be <r; then the change of volume is s a- = n (m passing from the liquid to tfic vaporous slate. If a pound of a homogeneous mixture of water and steam is ;v part .slcam, then the specific volume may be represented by -|- (i .v) xu + (101) where u is Ihc increase of volume due lo vaporization. Internal and External Latent Heat. The heat of vaporiza- tion overcomes external pressure, and changes the slalc from liquid lo vapor at constant temperature and pressure. The external work is p (s - o-) _ pu t nnd Ihc corresponding amount of heal, or the external latent heal, is Ap (s <r) = Apu. The heat required to do the disgrcgation work, or the internal latent heat, is p r Apu (102) General Equation. In order to apply the general ihermo- dynamic method to a mixture of a liquid and ils vapor, it is customary lo write a differential equation involving the tern-' peraturc /, the quality x, the specific heals of water and slcam c and h, and the heat of vaporisation r\ these three last properties arc assumed lo be functions of the temperature only. The principal result of the application of the general method lo such an equation in a formula for calculating the specific volume s, as will appear later. Following the general method, a special derivation of the formula for s will be given which may be preferred by some readers. When a mixture of liquid and ils vapor receives heat there is in general " n incrLilSU in mu n-.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 Bt awl so thai the above equation reduces to (104) Application of the Second Law. - The second law ol thermo- dynamics makes 'T for a reversible process, so that the general equation (103) may be reduced to ]Jut r Si ?' First and Second Laws Combined. -The combination oJ Uons (io. ( ) and (105) gives T-AT Special Method. 1 he preceding equation may be obtained by a special method making use of the diagram abed in Fig. 30 which repre- sents Gamut's cycle for a mixture at 6 a 1 ___^ liquid and its vapor, Liu; change o[ 3 temperature A T being very small. I<cl a represent the volume of one pound of JSL- water at the temperature T, and fr (he Km. jo. volume of one pound of steiun nl I he MOM temperature and pressure. The lint* till therefore represents the vaporization of one pound of water &l constant temperature, involving the application of the hcsttl of vaporization r, and the increase of volume u M s cr where s and <r arc the specific volumes of steam ami water, the second law of thermodynamics the efficiency of this cycle be T- (r~ Ar) AT 'T "" 7' ' so that the heat changed into work will be rAT T But by the first law of thermodynamics this heat Is equivalent to the external work, which in this case Is approximately equal to the increase of volume u multiplied by the change of pressure Api consequently, or, at the limit as Ar approaches zero, Specific Volume and Density. The most important result of the application of the methods of thermodynamics to the prop- erties of saturated vapor is expressed by equation (106), which gives a method of calculating the specific volume; thus, s = AT (107) dl The numerical value of <r for water for French units is o.ooi, and for English units is ~ = 0.016, nearly. The density, or weight of a unit of volume, is of course the reciprocal of the specific volume. It is of interest lo consider the degree of accuracy that may be expected from this method of calculating the density of saturated vapor. The value of r depends on TI and 17, the total heat and the heat of the liquid ; the latter is now well known, but the total heat is probably in doubt lo the extent of sis and may be more. The absolute temperature T appears to be better known and may be subject to an error of no more than -rtfon or suW; and the mechan- ical equivalent of heat is perhaps as well determined as the absolute temperature. The least satisfactory factor in the expression is the differential coefficient -, which is derived by fit differentiating one of the empirical equations on pages 78 and 79. It is true that the resulting equations on pages 79 and 80 afford a ready means of computing values of ihc coefficient with great apparent accuracy, but some idea of the essential vagueness of the method may be obtained by comparing computations of the specific volume of saturated steam at 212 C., a point for which either equation -B t or equation C, will give the pressure as 14.6967 pounds per square inch. The specific volume by aid of equation (107), using equation -B, for determining the differential coefficient, is 26.62, while the differential coefficient from equation C l gives 26.71; the discrepancy is about nta; or if the mean 26.66 betaken as the probable value, cither computed value is subject lo an error of v^u. Experimental Determinations of Specific Volume. Hy far tho bcsl direct determinations of Uu- spi'cilk volume* I SULIU rated slcam arc those reported by 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). SPECIFIC VOLUMBS OF SATURATKD STKAM. Hv Knoblauch, fjmlf, aiul Kiel*. Volmno On. M. Tampon alum. loo Kxporl- nieittnl. Com- 1.665 i . -i i 3 1. 674 1.420 110 i, til 1.112 "5 1 20 "5 1-037 0.8933 0.7707 i.oa? o.88a6 0.7617 Tamper- alure. '30 '35 MS '50 Volimia t"n. M. [tutetl, 0.5843 0.50C>1 O..I466 0.3.170 "-S747 o . 50 j i o. ,1-105 o . 3880 iftl) 170 .I4U Nature of the Specific Heats. In the application of ilia gon* cral thermodynamic method on page 88 the term h I* Intro- duced to represent the specific heat of siUumtcd steam, and iheru is some interest in the determination of the true nature af thit property, which clearly cannot be a specific heat at rontrtaat pressure, nor a specific heat at constant volumo.aincc both prauutv and volume change with the temperature. The RpedCic heal of the liquid c properly is affected by the same consideration, but as the increase of volume is small and is neglected in ilicrmo- dynamic discussions, the importance of the consideration h much less. The specific heat h of saturated vapor in the amount of heat necessary to raise the temperature of one- pound of the vapor one degree, under the condition that the pressure increase with -the temperature, according to the law for saturated vapor. Equation (105) gives a ready way of calculating the specific heat for a vapor, for from it . dr r Now r may be readily expressed as a function of I, and then dr by differentiation - may be determined. For steam r = 11 q = 606.5 + 0.305 / ~ fo -1- G (t /,)], in which /, is the temperature at the beginning of the range, as given by the table on page So, within which I may fall. There- fore dt c. and A = 0.305 - For other vapors the equations, deduced from the empirical equations for q and H on pages 83 and 85, are somewhat more complicated, but they involve no especial difficulty. The following table gives the values of h for steam at several absolute pressures: Pressures, Ibs, per sq. in., Temperatures, t F. . . Sj>ecific heal, h SPECIFIC HEAT OF STF.AM. zoo ,1 2 76 0.82 162.3 i . 30 20.9 0,93 200 300 381.7 417.4 0.70 0.63 The negative sign shows that heat must be abstracted from saturated steam when the temperature and pressure are increased, otherwise it will become superheated. On the other hand, steam, when it suddenly expands with a loss of temperature and pressure, suffers condensation, and the heat thus liberated sup- plies that required by the uncondensed portion. riirn ^ VITIIIWI mis (.oiuiuaion i* HWIMHIM ^HIMUIH ineatn lit a cylinder with glass aides, 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 Q in which r is the heat required to vnporto one pound of liquid, and x, and .r, arc the initial and final qualities, so ilul *, -*i is the weight of liquid vaporized. The external work done during an isothermal expansion is W _ p (v t - V J M ^ H (, Vl ^ , Vl ) . , . . (109) * Bulletin do la Soclelt In,!, fa Afujfo^ c*n.W t t Compiet nndia do 1'Acatttmte ties Stfenw, U. Intrinsic Energy, Of the heal required to raise a pound of any liquid from 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 L. A -I- <?) (no) represents the intrinsic energy of one unit of weight of a mixture of a liquid and its vapor. Isoenergic or Isodynamlc Lines. If a change of fi mixture of a liquid and its vapor takes place at constant intrinsic energy, the value of /iwill be the same at the initial and final conditions, find which equation, with the formula; enable us to compute the initial and final volumes. If desired, intermediate volume corresponding to intermediate temperature can be computed in the same way, and a curve can be drawn in the usual way with pressures and volumes for the coordinates. For example^ if a mixture of iV steam and T^T water oxpfinds isocncrgically from too pounds nlm.Uiir Ihc final condition will be 15 lnimN absolute, '9395. The initial and final specific art- The converse problem requiring llir prt^urr 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 W > I Jlt&i, i For exompte t the exponent for the equation. expansion of the above problem is n . log Pi -" log fa ^ JpjLooj; log v, log Vi log 34.54 - and the external work of expansion IB s I.O.! 1.041 Since there is no change in the intrinsic energy during an isocnergic expansion, the external work is equivalent to the heat applied. Thus in the example jusl solved the heat applied is equal to IOO,OOO -T- 778 = I2(J TJ.T.U. There is litlle occasion for the use of the method just given, which is fortunate, as it is not convenient. Entropy of the Liquid. Suppose that a unit of weight of a liquid is intimately mingled with its vapor, so that its tempera- ture is always the same as that of the vapor; then if the pressure of the vapor is increased the liquid will be heated, and if the vapor expands the liquid will be cooled. So far as the unit of weight of the liquid under consideration is concerned, the pro- cesses are reversible, for it will always be at the temperature of the substance from which it receives or to which it imparts heat, i.e., it is always at the temperature of its vapor. The change of entropy of the liquid can therefore be calculated by equation (37), which may here be written _ f & _ f * J T "J T ("3) On page 83 it is suggested that the specific heat of water for temperature Centigrade may be expressed as follows: c = i 4- k where k is a small corrective term that may be positive or negative as the case may be. Using this correction, equation (113) may be written T (114) Tne nrst term ciin second term, which is small, nm be. delermined graphically, that the expression Tor entropy of water bmimes -/ (V I A- ''ft / The columns of entropy of water in Clio tables wort- determined in this manner. In iihc discussion of cncropy on page 31 it wan pointed out that there is no natural zero of entropy rnrrcHpowling Ui the nbo- lute zero of temperature. It is customary to treat llit- 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, i/S73 .52901 -|- 0,OOOS9l8 373) 0.0005918 r//); ' ^=0-0005918 (T 1 - 373) + 0.3670 .-. 0= 0.0005918 /-h 0.3670 log, 273 .... ( 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 Y ',** T This properly is given in the " Tallies for Saturated Steam," but not in general for other liquids. Entropy of a Mixture of a Liquid and its Vapor. The increase in entropy due to heating a unit of weight of a liquid from freez- ing-point to the temperature; t and then vaporizing x portion of it is 0-1-^ 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 13 'i - . - (u?) When the condition of the mixture of a liquid and its vapor is given by the pressure and value of x, then a table giving the properties at each -{wind may be conveniently used for this work. gives , When ihc initial atnlc, Oclrrminnl by *. anil /, .if /> U and the fmal temperature * or the- fin.1 urc , ihc Ami vMuo *, may be found by cquMlun (i volumes may be ciilculniwl ty lw Tablca of Ihc propcriicH of wnumlwl v ft j* i.-mmcmly give (he specific volume 5, but 1 .1 - 1 cr. The value of o for wmcr fe o.otfi, uml fr tht-r lw|iiWi will bo found on page 85. *V fl**itt^c, one pound of dry Mcnm pressure will have the values / * 337.fi K, r, - 884.0, C, - tuntK IE the final prcasurc is 15 pounds n (, - ai3.o I 1 '., r a 965.1, whence have . 788.3 o- 673,7 ,v The initial and final volumes nre , -I- Problcma Jn which the initial condlllun ami ihc final tem- perature or pressure arc given may be galval elircrlly by uifl 01 llic ])rt;ccding equations. Those giving the; final volume instead millions. An equation to an adiabalic curve in terms of p and v cannot be given, but such a curve for any particular case may be construct c'd point by point. Clatisius and Runkine independently and at about the same time deduced equations identical with equations (117) and (118), but by methods each of which differed from that given here. Rankine called the function the lltcrmodynantic function ; Clausius called it entropy. In the discussion of the specific heat // of a saturated vapor, it appeared Unit thu expansion of dry saUmiled steam in a non- conducting cylinder would be accompanied by partial conden- sation. The same fact may be brought out more clearly by the above problem. On the other hand, A is positive for ether, and partial conden- sation lakes place during compression in a non-conducting cylinder. For example, let the initial condition for ether be /, 10 C ., r 12 i - 93- I2 > and let the final conditions 'be /. <=> 120 C., ?a 72.26, 0.0191, 0.2045; tfocn and - ~ 283 72.26.V. . ' -- * -I- 393 Equation (it8) applies to all possible mixtures of a liquid and Us vapor, including the case of x t - o or the case of liquid with- out vapor, but at the pressure corresponding to the temperature according to the law of saturated vapor. When applied to hot \vatcr, this equation shows that an expansion in a non-conduct- ing cylinder is accompanied by a partial vaporization. IO2 SATURATED VAPOR There is some initial stale of the mixiuri 1 such that the of x shall be the same (it llu- bL'KinninK uml ui [lie end, though ft may vary at intermediate suites. To find Unit value make *, x l in equation (nB) and solve 1 for .v,, which The value of A', for steam to fullil ilu- conditions with the initial nnd final temperatures 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 is 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 500 error of the above calculation is nearly two per cent. For a wider range 1 of temperature [he error is less, and for a narrower range it is of course larger. This mutter should be borne in mind in considering the use of approximate methods of calcula- tions; for example, the teinpcniUt re- entropy diagram to be dis- cussed later. The adiabatic curve cannot be well represented by an expo- nenlial equation; for if an exponent be determined for such a curve passing through points representing the initial and final stales, it will be found that the exponent will vary widely with different ranges of pressure, and still more with different initial values of x\ and that, further, the intermediate points will not be well represented by such an exponential curve even though it passes through the initial and final points. This fact was first pointed out by Zcuner, who found that the most Important, clement in determining n was x lt the initial con- dition of the mixture. Tie gives the following empirical formula for determining -, which gives a fair approximation for ordinary ranges of temperature: n 1.035 "I* o.ioovv There docs not appear to be any good reason for using an exponential equation in this connection, for all problems can be solved by the method given, and the action of a lagged slcam- enginc cylinder is far from being adiabatic. An adiabalic line drawn on an 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 curve. 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 too 1 Via. ion. and the temperature-entropy diagram is* ihc equivalent of such a table. Now the entropy of a mixture con lain tng x [mrl stenm is so that the entropy of a mixture containing x purl of steam can be determined by dividing the line such d$ (which represent* the entropy of vaporization) In ihe proper rntlo. dc It is convenient to divide the several lines like ab and th Into tenths and hundred tha, and then, If an adinbnile expansion te represented by a vertical line like be, the entropy at c may be determined by inspection of the diagram. Conversely, by noting the temperature at which a given line of constant entropy crosses a line of given quality we may determine the temperature to which it is necessary to expand to attain that quality, a determina- tion which cannot be made dircclly by ihc equation. When a 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 equation and since the volume increases proportionally to the increase in x, we may readily determine the points on thai line for which the volume shall be whole units, such as 2 cubic feet, 3 cubic feet, etc. Points for which the volumes are equal may now be con- nected by fair curves, so thai for any temperature and entropy the volume may readily be estimated. Curves of equal heat contents can be constructed in a similar way. If desired, a curve of temperatures and pressures can be drawn so that many problems can be solved approximately by aid of the compound diagram. At the back of this book a 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- " TEMPKRATURE-ENTROrV TABLE 107 alurc and then find the value of x and the specific volume. The external work for udiabaiic expansion may now readily be found ' by aid of equation (120), page 102. As will appear later, the problems that arise in practice usually require ihc heal contents and not the intrinsic energy, so that property has been chosen in making up the table. For example, the nearest temperature to 100 pounds per square inch is 328 F.; the entropy column 1.59 gives for x, 0.995, which indicates half of one per cent of moisture in the steam. The corre- sponding volume is ,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 feet. Jf greater accuracy is desired we must resort to interpolation. Usually it will be sufficient to interpolate between the lines for temperature in a given column of entropy, because the quantity that must be determined accurately is usually the difference x t r t -} g l - (.v/ 2 + ft) and this difference for two given temperatures 1^ and / 3 is very nearly the same if taken out of two adjacent entropy columns. A similar result will be found for the difference if computed for values of x found in adjacent columns. Another way of looking at this matter is that one hundredth of a unit of entropy al 330 pounds corresponds to one per cent of moisture. Evidently this table can be used to solve problems in which the final volumes arc given, or, as will appear later, to determine intermediate pressures for steam- turbines. io8 HATl'RATKlt VAl'OK I. 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 - o.tj. I'tnilittriimilliinAArirr AH* aion ( ^3^ mm, Ana. 0.8,18. 7. A cubic fool nf i mislure of under the pmuurc of to jxiuiulft by ihr after It vxpnmU BdUlmilcally lil! iht* timnurv pounds by the gauge; 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*.; feel. r.o. TKMPICRATURE-ENTROI'Y TAHLE 109 io. Three pounds of water arc heated from 60 F. and evapor- ated under 135.3 pounds gauge pressure. Find the heal added, and the changes in volume, and intrinsic energy. Ans. Kent added, 3490 B.T.U.; increase in volume, 8.99 cubic feet; intrinsic energy, 2,520,000. / -* ,'* ( , ii. A pound of steam at 337.? F, and 100 pounds gauge ' pressure occupies 3 cubic feel. Find its intrinsic energy and its entropy above 32 F. Ans. Intrinsic energy, 718,000; entropy, 12. Two pipes deliver water into a third. One supplies 300 gallons per minute at 70 F.; the other, 90 gallons per minute at 200 F. What is the temperature of the water after the two streams unite? Ans. 100 F, 13. A lest of an engine with the 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- pounds. CHAPTER VII. SUPKUUKATEl) VAPORS. A CRY and saturated vapor, not in contact with the from which it is formed, may be healed to a temperature greater than that corresponding to the given pressure for the fittttie vapor when saturated; such a vapor is said lo be superheated, When far removed from the temperature of saturation, such ft vapor follows the laws of perfect gases very nearly, but near (ta temperature of saturation the departure from those laws t Ion great to allow of calculations by them for engineering purpoMfc All the characteristic equations that have been proposed, have been derived from the equation pv = RT t which is very nearly true (or -the 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 \T/ >D in it the pressure is in kilograms per square metro, v IB !n cubic metres, and T is the absolute temperature by * Mitteilungen fiber J-'orseliuttttsarbcilcn, crlc., Heft 21, R. 33, no SUPKKHEATED VAI'ORS Jri centigrade Ihcrmomclcr. The constants have ihc following values: B <= 47.10, a = 0.000002, C *= 0.031, D ~ 0.0052. In the English system of units, ihc pressures being in pounds per square fool, the volumes in cubic feel per pound, and the temperatures cm ihc Fahrmhcil scale, we have /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. 112 SUPKRHKATBU VAPORS In the English system with the pressure in pounds per square foot and the volumes in cubic feel, for ubsoluie temperatures Fahrenheit, pv 85.85 7' - 0.356 J (135) This equation has a maximum error of o.S of one per cent a$ compared with equation (121). TA1ILK I. ... . ., , 150,100,000 Vnluva of llic forlnr -- -- o.ofljj. Fnhr. Abi. Vnlub of Factor. 300 659-S 0.441 305 664-5 0.429 3IO 669.5 0.417 "5 67-1 5 0.405 679-5 0-395 335 684-5 0-35 330 680.5 0-375 a .15 604 5 0-365 340 609.5 0-3S6 245 70.L5 0-3-17 350 709-5 0-338 355 71-1-5 0-330 360 7'9-5 0.330 365 73-1-5 0.313 370 730 -5 0.301 a ?5 734-5 0.996 380 739-5 0.388 585 744-5 0.381 300 7-J9 -5 0.374 395 75-1-5 0.367 T a nip oral ura. Value Tom Fat.r. Abi. Pftcicr, Fahr. 300 75') -5 0.360 400 ,15 76-1.5 0-353 405 310 760.5 0.347 410 3 '5 774-5 0.340 415 330 335 779-5 7.!-S 0.334 0.338 4 jn 330 789-5 0.333 Lin 335 794-5 0.3 id 135 340 700-5 0.31 t 4-|0 3-IS 804.5 0.305 4-15 350 809.5 0.300 45 355 814-5 o. 105 155 360 8i9.5 O. [1)0 460 365 8 j.i. 5 0-185 465 370 820.5 o. iSo 470 375 834.5 0.175 475 3o 839.5 0.171 480 35 8.14-5 o.i 66 485 390 849,5 o. 163 395 85.1.5 0-158 195 85'). 5 Hfti/5 811,. 5 4-5 HHo.c ()0-| . 5 ()<.*) . 5 014.5 a.|.jt 95-1- Value Focior. o- 15.1 o- 1. 10 0.145 o. i.|i o. 131 o, i J7 o. i j.i Q. no a. 117 a. 1 1,1 o, no o. 107 0.1 0.| o. 101 o.ooK 0.005 O.OQ3 fl.(XJO 505 510 5'5 5)0 5)5 535 550 555 560 S6S 575 SOS Al*. OM-S 070. S 099-5 IOJ4-5 1010. s 10J.|.JJ 103-1 Specific Heat, Two investigations have been mndc of specific heat of superheated slwim nt conslnni pressure, on Professor Knoblauch* and T)r. Jakob nml the other by _ lessor Thomas and Mr. Short; f the results of the hitler's inm- tigalion have been communicated *for use in this anticipation of the publication of the completed report. * MtoollHHxen liber Punch wwarbelien t Itcfi 36. p. tot). t Thosb by Mr. Short, Cornell Unlvenliy SPECIFIC HEAT II3 Professor Knoblauch's report gives the results of the inves- tigations made under his direction in the form of a table giving specific heats at various temperatures and pressures and in a diagram, which can be found in the original memoir, and lie also gives a table of mean specific heals from the temperature of saturation to various temperatures at several pressures. This lallcr lablc is given here in both the metric syslcm and in ihc English syslcm of units. SPECIFIC HKAT OF SUPKRHKATKD STEAM. Knoblauch ami Jnkab The construction of this lal)lc is readily understood from the following example: Required the heat needed to superheat a kilogram of steam at 4 kilograms per square centimetre from saturation to 300 C. The saturation temperature (to ihe nearest degree) is 143 C.; so that the steam at 300 is superheated 157, and for this la required the heal 157 X 0,493 77,3 calorics. The experiments of Professor Knoblauch were made at 2, 4, 6, and 8 kilograms per square centimetre; the remainder of the (able was obtained from the diagram which was extended by aid of 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. 114 SUPERHEATED VAPORS The following table gives the mean specific heat of super- heated steam as measured on a facsimile of Professor Thomas's original diagram without cxtcrpolation. SPECIFIC HEAT OF SUPERHEATED STEAM Thomas and Short. 1'rewure Lb. pet S(|, In. (Absolute.) Superheat Falir. 6 15 30 00 100 200 400 20 o.53<> 0-5-17 0.558 0.571 o-SO.1 o.6ai o. 6.19 5 0.533 0-533 0-5-13 o-SSS 0-575 0.600 0.631 100 0.503 0.<;i3 0.534 -S37 0-557 o.ijSi 0-599 150 0.486 0.406 0.508 0.533 0-5-M 0.567 0.585 200 0.471 0.480 0.404 0.500 '5M o-55 f > o-SM 250 0.456 o.-i66 0.481 0.406 0.533 0.5,16 0.564 30 0.442 Q.-153 0.468 0.484 0.511 0-537 o-SS-i Here again the arrangement of the table can be made evident by an example: Required the heat needed to superheat steam 100 degrees at 200 pounds per square inch absolute. The mean specific heat from saturation is 0,581, so that the heat required is 58.1 thermal units. Total Heat. In the solution of problems that arise in engi- neering it is convenient to use the total amount of heat required to raise one pound of water from freezing- point to the tempera- ture of saturated steam at the given pressure and to vaporixo it and to superheat it at that pressure to the given temperature. This total heat may be represented by the expression I + r + c, where t is the superheated temperature of the superheated steam, /, is the temperature of saturated steam at ihc given pressure p, and q and r arc the corresponding heat of the liquid and heat of vaporization. The mean specific heat Cj, may usually be selected from one of the given tables without inter- ENTROPY 115 polation, as a small variation does not have a very large effect. The total heat or heat .contents of superheated steam in the 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: / J cpdl T, T in which T is the absolute temperature of the superheated steam, and T t is the temperature of the saturated steam at the given f pressure; and may be taken from the " Tables of Saturated * i Steam." The last term was obtained for the temperature- entropy table by graphical integration of curves plotted with values of -^ derived from the curves of specific heats at various temperatures just described under the previous section. If the temperature- entropy table is not at hand, the last lerm of the above expression may be obtained approximately by divid- ing the heal of superheating, by the mean absolute temperature of superheating. This may be expressed as follows: c (/ - -O . 1 (' + O + 459-5 n <5 SUPERHEATED VAPORS where t is the temperature of the superheated steam, /, is the temperature of saturated steam at the given pressure, and c is the mean specific heat of superheated steam. If this method is considered to be too crude, the computation can be broken into two or more parts. Thus if / ( is an inter- mediate temperature, the increase of entropy due to superheat- ing may be computed as follows: (' ~ O F I' (I ! U Ci + t) H- <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- turbine. Problems involving adiabatic expansion of steam which is initially superheated can be solved by an extension of the method for saturated steam, and this method applies with equal facility to problems in which the steam becomes moist during the expan- sion. The mast ready method of solution is by aid of the tempera- 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 PROPKRTIKS UK SULPHUR DIOXIDK 3l? )owing the nearest degree of superheating. Following clown ic column for entropy to the final pressure, the properties for ic final condition will be found; these will be the heat con- nls, specific volume, and either llu: temperature of superheated cam or the quality .v, depending tm whether the steam remains ipcrhcalcd during the exptm.Nion or btronu'H moist. If the external work of adinhalic expansion of steam initially ipcrhcalcd is desired, it can be had by Diking the difference of e intrinsic energies, The Jinil rquivnlwil of imrinsiV energy moist steam is x (r I- q xr I- q Apxu t id of this expression the qiwnlity AT -I- q may be lulu-n from c (cmpcmturc-enlropy inhle, nnd tlic quimiity Aji.vu ran : determined by did of the nU'iim Kibk-. .hi like innnner tbe :at contents of superheated slenm r/ -I r -I- ilch is computed nnd set down in the 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. n g SUPKRHEATED VAPOUS For example, Rcgnault made experiments on the pressures of saturated sulphur dioxide and ammonia, but did not de- termine the heal of the liquid nor the total heal. He did, however, determine some of the properties of these substances in the gaseous or superheated condition, from which it is pos- sible to! construct the characteristic equations for the super- heated vapors. These equations can then be used to make approximate calculations of the saturated vapors, for .such equa- tions arc assumed to be applicable down to the saturated con- dition. Of course such calculations arc subject, to a considerable unknown error, since the experimental data are barely sufficient to establish the equations for the superheated vapors. The specific heat of gaseous sulphur dioxide is given by Rcgnaull* as 0.15438, and the coefficient of dilatation as 0.0039028. The theoretical specific gravity compared with air, calculated from the chemical composition, is given by Lundoll and Bdrnsicin f as 2.21295. Gmclin t gives (he following experimental determinations: by Thomson, 2.222; by Bcrxclius, 2.24.7. The figure 2.23 will be assumed in this work, which gives for the specific volume at frecx.ing-poinl and at atmospheric pressure v = '333* ^ a ^,7 cu bi c metres, The corresponding pressure and temperature arc 10,333 n&d 273 C. At this stage it is necessary to assign a probable form for the characteristic equation, and for that purpose the form 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 (jafi) * M&moires tie I'lnst'tlttt da France, tonic xxl, t PliysHtalische-clieinlsclie Tabellan. f Wall'a irnnstnifan, p. a8o. PROPERTIES OF SULPHUR DIOXIDE The value of the arbitrary constant a may be determined from the coefficient of dilatation as follows. The coefficient of dilatation is the ratio of the increase of volume at constant pressure, for one degree increase of temperature, to the original volume; so that the preceding equation applied at o C. and at i C. gives r A i>i ^o = c p a ^ If A PnVn The value of a obtained by substituting known values in the above equation is 0.212. Now as a appears in both the first and the last terms of the 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. 120 SUPERHEATED VAPORS Reducing the given pressures to kilograms on the square metre, and the temperature lo the absolute scale, and applying to equation (127), we obtain 1.016 instead of the experimental value for the above ratio, Rcgnaull gives for the pressure of saturated sulphur dioxide in mm. of mercury, the equation log/) w a /in" cfP\ a - 5,6663700; log 6 0.4793425; logc * 9,1659563 10; Jopr 9.9972989 10; Jog /? * 0.98720002 10; w - < -H 28 C, Applying equation (95), page 76, (o this case, log R - 9.9972989; log jfl M 9.98729002; log A 8,63521.16; logJ3' 7.9945332; H / -I- 28 C. The specific volume of saturated sulphur dioxide may be calculated by inserting in equation (137) for the superheated vapor the pressures calculated by aid of the above equation. The results at several temperatures are as follows: o -H 30 C. 30 0,8293 0.2256 0.0825 AmlrdcfT * gives for the specific gravity of fluid sulphur dioxide 3,4336; consequently the specific volume of the liquid is ff eon O.OOO7' * Ann. Chain, i'ltarnt., 1859. PROPERTIES OF SULPHUR DIOX1OK The value of r, the heat of vnporiailion, may now be rn lated at the given temperatures by equation (106), W 80, I V<lP r Aul -t-i 131 -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 n- factor a, so that it may read -r The expression for Ihc entropy of n liquid find ils vapor is -t- fa// L *i if the vapor is dry. When differentiated this yields ~ H- or I If it be assumed that equations (130) and (131) may both be applied al saturation we have / Frf\ , , dr r . . . ( I [ . n . *-- EJU .1- ~ ~* . IT10) JJ ( p till dl T ' (1 V> If it be admitted further that the differential coefficient -f- can / be computed by the equation on page 120, the above equation affords a means of estimating the specific heat of the liquid. At o C., this method gives for the specific heat c 0.4. In English units we have for superheated sulphur dioxide pv- 26.4 T - 184 p*** (133) the pressures being in pounds on the square foot, the volumes in cubic feet, and the temperatures in Fahrenheit degrees absolute. For pressures in pounds on the square inch at temperatures on the Fahrenheit scale, log p - a 6a" c$ n \ a 3.9527847; log b - 0,4792425; log c - 9.1659562 10; log a 9.9984994 to; log (3 9.99293890 10; n = t + i8.4F. For the heat of vaporization r =i?(>- 0,27 (/- 32) and for the specific heat of the (134) c 0.4. In applying these equations to the calculation of a table of the properties of saturated sulphur dioxide the pressures corre- sponding to the temperatures are calculated as usual. Then the heat of the liquid is calculated by aid of the constant specific heat. The heat of vaporization is calculated by aid of equation (134). Next the specific volume is calculated by inserting the given temperature and the corresponding pressure for the sat- urated vapor in the characteristic equation (133). Having the specific volume of the vapor and that of the liquid, the heat equivalent (Apu} of the external work is readily found. Finally, the entropy of the liquid is calculated by the equation 0= clog,--- ....... (135) * If the reader should object that this method is tortuous and full of doubtful approximations and assumptions, he must bear in mind that any method that can give approximations is better than none, and that all the computations for rcfrigerating- machines, that use volatile fluids, depend on results so obtained. And further, much of the waste and disappointment of earlier refrigcra 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 10333 so that the equation becomes pv - 54.3 T * 54-3> '* 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 i fc2i.-i.ox88, PPt while equation (136) gives under the same conditions 1.0200. For saturated ammonia Rcgnault gives the equation log a bct n c{F\ a - 11.504333; lOg b 0.8721769; log c 9.9777087 10; log a 9.9996014 10; log /? 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, EXAMPLES. 1. What is the weight of one cubic foot of superheated steam at 500 K, and at 60 pounds pressure absolute? Knoblauch's equation. Ans. 0,106 pounds. 2. Superheated steam at 50 pounds absolute has half the density of saturated steam at the same pressure. What is the temperature? Tumlini'a equation. Ans. 930 F. 3. What is the volume of 5 pounds of steam at 129.3 pounds gauge pressure and at 359.$ F.? Ans. 15.8. 4. At 129.3 pounds gauge pressure a pounds of steam occupy 7 cubic feet. Find its temperature. Assume value of T for entering Table I, page 112, and solve by trial. Ans. 424 F. 5. A cubic foot of steam at 140 pounds absolute weighs 0.30 pounds. What is its temperature? Ans. 374?. 6. Two pounds of steam and water at 129,3 pounds pressure above the atmosphere occupy 6 cubic feet. Heat is added and (he pressure kept constant till the volume Is 8.5 cubic feet. Find the final condition, and the external work done in expanding. Ans. Temperature 68iF.; work 51800. 7. Saturated steam at 150 pounds gauge, containing 2 per cent of water, passes through a superheater on its way to an engine. Its final temperature is 400 F. Find the increase in volume and the heat added per pound. 8. Let the initial temperature of superheated steam be 380 F. at the pressure of 150 pounds absolute. Find the condition after an adiabatic expansion to 20 pounds absolute. Determine also the inilial and final volumes. Ans. (i) 0.895; (2) 3.09 cubic feet; (3) 17.8 cubic feet. y. In examples, page 109, suppose that the steam at 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. CHAPTER VIII. THE STEAM-KNOINE. 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. 128 In the condition represented by the point a 'the cylinder con- tains a mixture of water and steam at the temperature /, and the pressure ,. If connection is made with a. source of heat at the temperature t lt and heat is added, some of the water will be vaporised and the volume will increase at constant pressure as represented by ab. If thermal communication is now inter- rupted, adiabatic expansion may take place as represented by be till the temperature is reduced to / 2 , the temperature of the refrigerator, with which thermal communication may now be established. If the piston is forced toward the closed end of the cylinder some of the steam in it will be condensed, and the volume will be reduced at constant pressure as represented by cd. The cycle is completed by an. adiabatic compression rep- resented by da. If the absolute temperature of the source of heat is 7\, and if that of the refrigerator is T^ then the efficiency is whatever may be the working fluid. For example^ if the pressure of the steam during isothermal expansion is 100 pounds above the atmosphere, and if the pressure during isothermal compression is equal to that of the atmos- phere, then the temperatures of the source of heat and of the refrigerator arc 33?.6 F, and 212 F., or 797.1 and 671.5 abso- lute, so that the efficiency is .797.1 - 671.5 ^ 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: THE STEAM-ENGINE EFFICIENCY OF CARNOT'S CYCLE FOR STEAM-ENGINES. Initial Pressure by the Gauge, above the Atmosphere. Almcuplieric PreiBUre. i-S bounds ALaohilo. 15 0.053 o. i8t) .10 60 IOO 15 o.o8,| 0.12.1 0.157 0./H6 0.3-10 0.278 0.303 200 O.307 0.320 300 0.33 0-.3-I7 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 engines. It is interesting to consider the condition of the fluid in the cylinder at the different points of the diagram for Garnet's cycle. Thus if the fluid at the condition represented by b in Fig. 31 is made up of x b part steam and i x fc part water, ihcn from equation (118) the condition at the point c is given by $ (137) In like manner the condition of the mixture at the point d is .... (138) It is interesting to note that if x b is larger than 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 EFFICIENCY OF CAUNOT'S CYCLE I'M nag ylinder at o; but there is no necessity for such assumptions, nd they in no way alTcct the efficiency. The 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) THE STEAM-ENGINE 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 0.277, The properties of steam and of chloroform at these tempera- lures arc Pressure, mm. mercury Volume, cubic moircn . Hcdt of vnporlxiuioii, r Entropy of liquid, . . Sioom. Chloroform. 10 C. 160 C. no' C. i(5o s C. . 5.1. yi -1651..! 369.36 873-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 . EFFICIENCY OF CAKNOT'S CYCLIC = 137 calorics, '33 - 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 * - 0>79S and for chloroform 63.13 \ 100 -I- 273 The specific volumes nflcr mllaluilic cxpunmon nru, qucntly, for steam v e - Jf,tf, -I- <r 0,795 (19.74 o.ooj) -I- o.ooi 15.7, and for chloroform v, = ;v e , + o- 0,969 (0.1(449 "- 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. 134 THE STEAM-ENGINE Even if we consider that the difference of pressure lor chloro. form, 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 0.318, instead of 0.277. On the whole, steam Is the more desirable fluid, even if we do not consider the inflammable and poisonous nature of chloroform. Similar calculations will show that on the whole steam is at least as well adapted for use in 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, Fie. oled by cold water. The cylinder is commonly made of cast m, and is always some kind of metal; there is consequently nsiderablc interference due to the conductivity of the walls of e cylinder, and the expansion and compression are never liabutic. There is an advantage, however, in discussing first L engine with a cylinder made of some non-conducting material, though no such material proper for making cylinders is now town. 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 136 THE 8TKAM-KNGINE 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 0, (H4) If values are assigned to fa and p 9 and the proper numerical calculations arc made, il will appear that the efficiency for a 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, (- fat J for a volatile liquid. From ihc Inner . we have all therefore From this last equation it la evident lhal the lien I of Ihr liquid 91 for water represented by ihc poinl a in Mg. 3.1, ii nimurnl by i 3 8 THE HTEAM-ENGINE 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 (us) for (he heat changed into work by Rankinc's cycle. This approximation depends on treating <ib us a straight line, ami this assumption is more correct as the difference of temper- ature is less; that is for those cases in which equation (143) deals with the difference of quantities of about the. same magni- tude, and may consequently be affected by a large relative error. 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 STKAM-KNGINE 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 T The work clone by the piston on the steam during cxl Pi (AY", -I- <r). The total work of the cycle is obtained by adding t> during admission and expansion and subtracting th during exhaust, giving The last term is small, and may be neglected. Adcll subtracting Ap&u, and multiplying by A, .we get for It equivalent of the work of the cycle - Q, q l which is equal to the difference hclwccn the heal supplied tint! the hctit rejected as indicated, The hcul supplied is as was deduced for the complete cycle; the cost of making the steam remains the .same, whether or not H i.i uncd t-lVicirnlly. Finally, the efficiency of the cycle is = r _ I 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 HE STEAM-ENGINE 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 * (M9) where Q.-Q, 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- jackcting. 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 vaporix.es. 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 iypcrbola. 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. 144 THE STEAM-KNGINB 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 6o 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. 146 THE STEAM-ENGINE 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 ~ 617.2 821.7 0.248. 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 0.227 -' ( 1004,1 \82i.y 0,2282 ) * 0.821. / During the lest in question Ihe terminal pressure at luccntl of ihe cxjMinslon in Vhc 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 - 0.222. The real criterion of ihe perfection of the nclion of an engine is the ratio of ils actual efficiency to that of a perfect engine. It for the perfect engine we choose Carnot'a cycle the ratio is 0.736. 0,2485 In EFFICIENCY OF THE ACTUAL ENGINE But jf we take for our standard an engine with a cylinder of non conducting material the ratio for complete expansion is e_ a" 0.183 0.227 For incomplete expansion the ratio is e 0,18 = 0.807. 0.222 = 0.824. To complete the comparison it is interesting to calculate the 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 148 THK STKAM-ENUINK 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: KPFKCT OK KAIHINO STKAM-PRKRslmK. I'roliHhla l'erlorinnce, Itolltr- lireiiura hy Kffl clenoy, Cut not 'i Cjtlt, H.'l'.U. [> KPIclency. II. P. per Ml mils. 150 0.302 0,37'J 156 300 0.330 0.388 M7 JOO 0-347 0.306 US ll.T.U.par If. P. PM MlnuU. 160 Slm |r H.P.pif hour. io.S g.fi In the calculations for this table the steam la supposed to be dry as it enters the cylinder of the engine, and the back- pressure is supposed to be 1.5 pounds absolute, while the expansion for the non-conducting engine is assumed to be complete, The CONUKNSKKS '-(9 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 150 THE STEAM-ENGINE 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 '7-3 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 AIR-PUMP I5t have a different temperature from the cooling water when it [caves the condenser. If its temperature is *,, then we have instead of equation (15) c J. n n C 1 ' ' 7 '/i / \ * ~ J JJ usu '/* - '/( for the cooling water per pouiul of steam. The difference is really immaterial, as it makes little difference in the actual value 3f G for any disc. Cooling Surface. Kxpcrimenls on the quaintly of cooling surface required by n 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'. 30 1C 134 10 1.50 i tii 8 I . 77 6 r . 10 For ships stationed hi the tropics, allow 20 per cent more; or ships which occasionally visit the tropics, ullow 10 per cent (lore; for ships constantly in a cold climate, 10 per cent less fiay be allowed. 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 J52 THE STEAM-ENGINE 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 DESIGNING ENGINES 153 ime OV and OP (Fig. 35a). The former is laid off parallel to he atmospheric line and at a distance to represent the pressure if the atmosphere, using the scale for measuring pressure on the liagram. The latter is drawn vertical and at a distance from aj vhich shall bear the same ratio to the length of the diagram as he clearance space of the cylinder has to the 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. 154 THE STEAM-ENGINE 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. I.Q.S The work during exhaust done by the piston in expelling the steam is r X 144 X (r - 0.15), and the work during compression is r X 144 X 0.15 0.05 The mean effective pressure in pounds per square inch is obtained by adding the first two works and subtracting the last two and then dividing by 144, so that M.E.P. = 94.7 Xo.25 + 94-7 Xo.35 log, V *J - i X 0.85 - i X 0.15 log, - 59.1 0-05 The probable mean effective pressure may be taken as of this computed pressure, or 53.2 pounds per square inch, DESIGNING ENGINES 155 Given the diameter and stroke of an engine together with the mean effective pressure, and revolutions, we may find the horse- power by the formula I.H.P. - where p is the mc;tn effective pressure, 1 is the stroke in feet, a is the area of the circle for the given diameter in square inches, and ti is the number of revolutions per minute. For our case we may assume that the .stroke is twice the diameter, whence 2(t 2OO = 2 X 53-2 X X X loo 12 4 33000 .'. d = 16.8 inches, $ 33.6 inches. In practice the diamc-tcr would probably be made i6| inches and the stroke 33^ inches. CHAPTER IX. COMPOUND ENGINES. A. COMPOUND engine has commonly two cylinders, one of which is three or four times as large as the other. Steam from a boiler is admitted to the small cylinder, and after doing work in that cylinder it is transferred to the large cylinder, from which it is exhausted, after doing work again, into a condenser or against the pressure of the atmosphere. If we assume that the steam from the small cylinder is exhausted into a large receiver, the 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 156 COMPOUND ENGINES 157 cylinder without an intermediate receiver. In such engines the pistons must begin and end their strokes together. They may both acC on the beam of a beam engine, or they may act on one crank or on two cranks opposite each other. For such an engine, ABCD, Fig. 37, is the diagram for the 'small cylinder. The steam line and expansion line AB and BC are like those of a simple engine. When the piston of the small cylinder begins the return stroke, communication is opened with the large cylinder, and the steam passes from one to the other, and expands to the amount of the difference of the volume, it being assumed that the communication remains open to the end of the stroke. The 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 158 COMPOUND ENGINES two cylinders, commonly used in marine work, has the cranks i 90 to give handincss and certainly of aclion. Large marh engines have been made whh one small cylinder and two larj or 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< made. Nearly all compound engines have a receiver, or a spa between the cylinders corresponding to one, and in no case the receiver of sufficient size to entirely prevent fluctuations pressure. In the later marine work the receiver has been ma< small, and frequently the 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. COMPOUND ENGINE WITH RECEIVER 159 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. COMPOUND ENGINES of such fluctuations can be best obtained by constructing ideal diagrams for special cases, as explained on page 164. Triple and Quadruple Expansion- Engines. The same influences which introduced Ihc compound engines, when the common steam- pressure changed from forty to eighty pounds to the square inch, have brought in the succes- sive expansion through three cylinders (the 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 LOW-PRESSURE CUT-OFF 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 and - = R e 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 COMPOUND KNGINKS 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 cylinder. Ratio of Cylinders. In designing compound engines, more especially for marine work, it is deemed important for the smooth aclion ol the engine that the total work ahull be evenly distributed upon the several cranks of the engines, and that ihe maximum pressure on each of the cranks shall be the .same, and shall not be excessive. In ease two or more pistons art on one crank, the total work and the resultant pressure on those pistons are to be considered; but more commonly each piston acts on a separate crank, and then the work and pressure on the several pistons arc to be considered. In practice both the ratio of the cylinders and the total expan- sions are assumed, and then the distribution of work and the maximum loads on the 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 DIRECT-EXPANSION ENGINE 163 lines are rectangular hyperbola;, and in general that any change of volume will cause the pressure to change inversely as the volume. Further, it will be assumed that when communication is opened between two volumes where the pressures are different, the resultant pressure may be calculated by adding together the products of each volume by its pressure, and dividing by the sum of the volumes. Thus if the pressure in a cylinder having the volume v c is p et and if the pressure is p r in a receiver where the volume is v r , then after the valve opens communication from the cylinder to the receiver the pressure will be The same method will be used when three volumes are put into communication. It will be assumed that there arc no losses of pressure due to throttling or 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 COMPOUND ENGINES hyperbola referred to the axes OV and OP, from which a, l t c are laid off to represent absolute pressures and volumes, incl ing clearance. At the end of the stroke release from the 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 IMRKCT-EXl'ANSION KNC.1NK In Fig. 42 (he two clifigrums urc drawn widi the .111 me* wli' for volume and pressure, and are placed so us to show to Uie eye (he relations of the diugrum.s to wicli other. DiiiKrums taken from such an engine resemble I host 1 of I''ig. ,w. which have (lie same length, and different vertical 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 con.se(|Uenily n I)iK)rr prr^urr n\ / when the receiver In closed. Representing the pressure and volume at ihe wvrrnl pnlnln by p and v willi ftppropriittc .subHc-ri|rt lettcnt, nnd reprrseiU ing the volume of the receiver by i' f , we liavr ilu* following equations; p a m, j) b initial pressure; PI ** pm** V f \ n f v n Pa - p k - ( P, - A A/ h t/, v ) 4- . Vr ); v , The pressures p. and A, can l.c calculated direc ily. Then ilir equations for p* /> U nd fy farm a set of three .imulu equations with three unknown quantities, whlrli 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 3-3 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. DIRECT-EXPANSION ENGINK I6 7 As the pressures and volumes are now known the diagrams of Fig. 42 may be drawn to scale. Or, if preferred, diagrams like Fig. 39 may be drawn, making them of the same length and using convenient vertical scales of pressure. If the engine runs slowly and has abundant valves and passages the diagrams thus obtained will be very nearly like those taken from the engine by indicators. If losses of pressure in valves and passages are allowed for, a closer approximation can be made. The mean effective pressures of the diagrams may be readily obtained by the aid of a phmimcter, and may be used for esti- mating the power of the engine. For this purpose we should cither use the modified diagrams allowing for losses of pressure, or we should affect the mean effective pressures by a multiplier obtained by comparison of the approximate with the actual dia- grams from engines of the same type. For a 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 =0.6+1.8-1-0.5- so that the mean pressure miring uiu 4120 -HI X 144 " 28 - 6 P pounds per square inch, which acts on bolh the high- and the 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 Xo.fi 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- CROSS-COMPOUND ENGINE 169 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 CKOSS-COMl'OUNJ) KNOINK 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 A (n 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 equation 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- pressure. With the cranks in the order, high-pressure, low-pressure, and Fl ' KNGINES '73 intermediate, as shown by Fig. 45, the diagrams arc like those given by Fig. 46. The admission and expansion for the high- pressure cylinder arc represented by ale. When the high- pressure piston is at release, ita crank is at fJT t Fig. 45, and the intermediate crank is at /, so that the intermediate piston is near half-stroke. IE the cut-olT for that cylinder is later than 100 HMfn AIA1IM 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 TRJrLE ENGINES JIL p, f> ' /* = J#(v u + f fl) 4- t>if>Ji\ -*- (f, + ui + V B) p=* P* (* + Vi) + v n ) -s- (v w 4- *> + I'D); Pt =* pf *= 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, A ** J* In the actual computation the several volumes and the proper sums of volumes arc to be first determined; consequently the factors following p d will be numerical factors which may be con- veniently reduced to the lowest terms before introduction in the equation. This system of substitution will give almost immedi- ately four equations with four unknown quantities which may readily be solved; after which the determination of individual pressures will be easy. In handling these equations the letters representing smaller pressures should be eliminated first, thus giving values of higher pressure like p d to tenths of a pound; afterward the lower pressure can be determined to a like degree of accuracy. A skilled computer may make a complete solu- tion of such a problem in two or three hours, which is not exces- sive for an engineering method. If the 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 engine. For example, the engines of the U. S. S. Mnehias have the following dimensions and proportions: Ultth- Inter* Djiurieicr of platan, Inches Piston displacement, cubic feet Clearance, por com 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 ....... aaj S-S3 M 66 03 18 3.33 6,30* 1 80 I.Ow prMture. 35 7 66 M 18 4.94 If the volume of the high-pressure piston displacement is taken to be unity, then the volumes required in the equations for .K KNOINES 177 It" y. i B V, 0-79 7J rf w I .06 1.1O ** I 1 3 OQ BB I/A "" O.OO =" 0.31 , n. V fl rt 0.13 Vm ^ -9^ V "^ ^fl ^ y_ 1 .63 W| ' 3sa *'^ l i V M V B v w * 0.63 .39 ^ i.aG 3.18 1.85 'fa ^ ^H IHI1 ^'35 V, ^ 2.O3 t/ y M 3.6O ij(. isa T/ ( ** 4'0't 4 . JJl V.3OU1 <-il m *- A = A = 150 A = 165 A - A = 25.6 A = 112 A = 60.0 A - 52-3 A = A - 76.5 # ff = 5-5 /> = 22.1 A = p p = 67-5 A = p f = 28.3 P& - I8. 5 A = 67.5 A = Py = 25.3 P, = Pf = 5 A = 76.9 A = 25.1 Ptl J?' , A = A = 73-5 A = 29.0 A - # = 69.3 A , = p y = 28.2 ' Diagrams with the volumes and pressures corresponding lo this example are plotted in Fig. 46 with convenient vertical scales. Actual 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 OKSICiNINCV COMPOUND KNGINKS 1 79 diagrams as a basis and faking n comparison of the approximate and actual diagrams from the engine already built, as a guide. It is convenient to prepare and use a table -showing the ratios of actual mean effective pressures and approximate mean effective pressures. Such a Uilile enables the designer to assign mean effective pressures to a cylinder of the new engine and to infer very closely what its 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 engine. A rough approximation of Ihc power of nn engine may be made by calculating the power tin though (ho total or equivalent expansion took place in (lie 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: MUI/ni'UKRS FOR. FIN I) WO I'LUHIMH.K M.K.I'. COMPOUND AND TKIl'U-: MARINK KNCUNKS. l)e*;rl|>iloii of Knn!n<i. jackaiad. Un)oklil. 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 ,1 7T3O 4 X 40.06 X 3 X 4 X 60 -t- 33000 * 412 H.P, If the factor to be used in tin's case is 0.75, then the actual 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 approximately 350 -h 460 0.19, If, however, by the use of a more volatile fluid the result at lower temperature could be reduced to 65 F., the efficiency could be increased to 350 - 6$ 250 + 460 0.26. At the present time when higher steam -pressures arc common, the comparison is less favorable. Thus the temperature of steam at 150 pounds by the gauge is 365 F., so that with r.$ *Mintiul du Conducted ties Machines & Vaporous combinfes au Martinet JJhialres, nlao Kanhine Steam Engtnv, p. 44,). BINARY ENGINES iflc pounds absohilc for 115 l r O for Carnot's cycle is l)ack- pressure the ., 0.30, 365 -I- 4o and for a resultant temperature of 65 F., the efficiency would be *(>< 6s , i* M * t O.7O. 365 -|- 400 If a like gain of economy could be obtained in prnclirr, it would represent a saving of 17 percent, which would lie well worth while. Further discussion of this mutter of rwnoiny will be given in Chapter Xf, in connection with 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 conditions. CriAI'TKR X. TKSTINU STKAM-KNtiWKS. 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 TESTING STEAM-ENGINES jgt are commonly built under contract to give a certain economy, and the fulfilment of the terms of a contract is determined by a test of the engine or of the whole plant. The test of the entire plant has the advantage that it gives, as one result, the cost of power directly in coal ; but as the engine is often watched with more care during a test than in regular service, and as auxiliary duties, such as heating and banking fires, arc frequently omitted from such an economy test, the actual cost of power can be more justly obtained from a record of the engine in regular service, extending for weeks or months. The tests of engine and boilers, though made at the same time, need not start and stop at the same time, though there is a satisfaction in making them strictly simultaneous. This requires that the tests shall be long enough to avoid drawing the fires at beginning and end of the boiler test. ' In anticipation of a test on an engine it must be run for some time under the conditions of the test, to eliminate the effects of starting or of changes. Thus engines with 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 INDICATORS nust be freely lubricated with oil. An iron wheel running in a furnished with blocks of wood requires lialu or 110 lubn- :alion. To avoid the increase of friction on the 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 Ictcrmincd. 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. INDICATOKS 189 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 TH ROTTLI NG-C A, LO RIMETER 1OT 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 - <" ser {\J ISO! Example, The following arc the data of a lest made with calorimeter; Pressure of the atmosphere . . . Steam- pressure by gauge . . . Pressure In the calorimeter, gauge Temperature in the calorimeter . 14.8 pounds; 69.8 " 12.0 " a F. Specific lieat of superheated steam for the condition of the -st 0.48. x = 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. LIMITS OF THE THROTTMNG-CALORtMETER. Pressure. Priming. Abioltile. Cauga. 300 =85-3 0.077 250 2OO '85! 3 0.070 0.061 175 160.3 0.058 150 '2$ '35-3 no. 3 0.053 0.046 IOO 75 60.3 0.040 0.032 5 . 35-3 0.033 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 ni.se 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 ihroltling-calarimcler. The Thomas Electric Calorimeter. The essential feature of this instrument (Fig. 50) is the drying and superheating of the steam by a measured amount of electric energy. Steam is admitted at # and passes through numerous holes in a block of soapstonc which occupies the middle of the instrument; these holes arc partially filled with coils of German silver wire which are healed by an electric current that enters and leaves at the binding- screws. The steam emerges dry or superheated at the upper part of the chamber and passes clown through wire gauze, which surrounds the central escape pipe; this central pipe surrounds * Trans. Am. Sac, Meek, Rugs., vol. xvli, p. 608. FIG. 49. o * the thermometer cup, and leads to the exit at the top, which has two orifices, either of which may be piped to a condenser or elsewhere. To use the instrument it j s properly connected by a sampling. lube to the space from which steam is drawn, and valves arc adjusted lo supply a convenient amount of steam which is assumed lo be uniform for steady pressure- this last is a mailer of some im- portance. The current of electricity is llum adjusted lo dry the steam; this may be determined by noting the lemperfilure by the thermom- eter in (he mural thermometer cup, because that thermomclcr will show a slight rise corres- ponding lo a very small degree of superheating which is sufficient lo indicate the disappearance of moisture, but not enough to affect the determination of quality by the instrument. The wire gauze surrounding the thermometer is an essential feature of this opcralion, as it insures the homogeneity of the steam, which, without the gauiic, would be likely lo be a mixture of super- heated steam and moist steam. Readings arc lakcn of the proper electrical Inslrumcnls from which ihc clcclrical energy imparted can be determined in watts; let this energy required to dry Ihc steam be denoted by JS r Now let Ihc electric current be increased till the steam is superheated 30, and let , be the increase of electric input which Is required lo superheat ihe sleam. If W is ihc weight of steam flowing per hour through the PlO. JO. THE THOMAS ELECTRIC CALORIMETER 197 instrument under the first conditions, the weight when super- heated will be CW t where C is a factor less than unity which has been determined by exhaustive tests on the instrument. The amount of electric energy required to superheat one pound of steam 30 from saturation at various pressures has also been determined and may be represented by S; this constant has been so determined as to include an allowance for radiation, and is more convenient than the specific heat of superheated steam, in this place. Making use of the factors C and 5, we may write which affords n means of eliminating the weight of steam used; this is an important feature in the use of the instrument. Returning now to the first condition of the instrument when steam is dried by the application of B, watts of electric energy, we have for the equivalent heat 3.42 ,; and dividing by the expression for the weight of steam flowing per hour, we have for the heat required to dry one pound of steam 3.42 E. E. W = 3-42 CS x)r, where r is the heat of vaporization and i x is the amount of water in one pound of moist steam. Solving the above equation for .v, we have 3.42 CS E^ X ~ l ~ r V Jf desired, the constant factors may be united into one term, and the equation may be written K E. With each instrument is furnished a diagram giving values of K for all pressures, so that the use of the instrument involves only two readings of a wattmeter and the application of the above simple cqwilion. For example, suppose that the use of the instrument in a particular case gave the values E l - 240, and /, = 93,0 for the absolute pressure 100 pounds per square inch. The value of K from the diagram is 54.2, and r from the steam-tables is 884, consequently 2dO 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 radiation. CHAPTER XI. INFLUENCE OF THE CYLINDER WALLS. 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- provements. As soon as the investigations by Clausius and Rankine and the experiments by Ilcgnault made a precise theory of the steam engine possible, it became evident that engines used from quarter to half again as much steam as the ad ia ha tic theory indicated, and in particular that expansion down to the back- pressure was inadvisable. An early and a satis- factory exposition of these points was made by Ishcrwood after his tests on the U. S. S. Michigan, which arc given in Table III. 199 INKUJUNCK OK THK CYUNUKK WALLS TAIM.K III. TKSTS ON THK KNfilNK OK TUK U. S. S. MICHIGAN. OVUNIWK PUMKrKW, ,*d INfllKHJ HTHtlKK, K VWf. Ily Chlct-KnKlncrr IHIIKUWWW, Resetircliat !n llxl>erlir>itai Stenm Duntllnn, hiiu Cut-tiff Revolution* |HT iiilnutr Holler prrawuir, |KT 1 1 U mi i IP lc r, Inrhen of nifnury ..... Vnrtiuni, Inclita uf mrn ury ...... Strum |KT Itnnw (niwrr jtrr Imur, iiuiU I'cr rent of wnlcr In rvUmlrr t n-lcnw . 1. 71 1 t/u JO.fl 11. 7/m Jfi.l .1.1- '5-.1 4/u '7--1, .13-7 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 U.O.H MICHIGAN 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 atmosphere, Tin-manner of the vfirliiiionoflhcatcam 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. Ot Km. ii. INFLUENCE QK THE CYLINDER WALLS 2OI To make the diagram clear and compact, the axis of abscissa: is taken at 30 pounds of steam per 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 INKM/KNCK OK THK CVUNDRK WALLS of Ihc steam limn condensed remtuns in the form of water and docs little if anything lowiird producing work. This may De scon by inspection of the mhlc. of results of Dixwcll's tests on page 370. With jmliiralcd Hlctun ami with 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. ,*. GRAPHICAL REPRESENTATION 203 a line ae is drawn at a convenient pressure, and on it is laid off the volume of W -I- W pounds of dry steam as determined from the 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 ae 304 INFLUENCE OF THE CYLINDER WALLS MO .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 KIRN'S ANALYSIS 305 sion. The mixture, moreover, is not homogeneous, because the moisture on the cylinder walls is likely to be colder limn the steam, though naturally it cannot be warmer. Finally, the 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 DwelslwuvcTS-Dcry.f 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, Pia. exhaust, and compression. The numbers will be unccl .. .. scripts lo designate the properties of thu working fluid under the conditions represented by the points indicated, nncl the letters will be used in connection with the operations! inking place during the several parts of the cycle. Thus at 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, 206 INFLUENCE OF THE CYLINDER WALLS pressure is p t , and the temperature, heat of the liquid, heat of vaporization, quality, etc., arc represented by / q lt r v x lt etc. The external work from 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] 053) 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 HIRN'S ANALYSIS 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 G -|- A W c , in which % is the heat of the liquid of the condensed steam, and G is the weight of cooling water per stroke which has on entering the heat of the liquid </ and on leaving the heal of the liquid q t . During compression the external work W, t is done by the engine on the fluid in the cylinder, and at the end of compression, i.e., at admission, the heat-equivalent of the intrinsic energy is / . Hence It should be noted (Fig. 54) that the work W n is represented 20 g INKI.URNCK OK TtlK CYI.1NDKR WALLS by the area which i* hounded by the slnim line, the ordinatcs through o ami i and by the \mw lint-. And in like manner the works W h W et and II',, are 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'.' - (iS9) (160) /UK, . (161) (162) 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). TURN'S ANALYSIS 30<; 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- quently 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 thermometer. Let the heat lost by radiation, conduction, etc., be Q e ; this is commonly called the radiation. Let the heat supplied by the jacket be Q f . Of the heat supplied to the cylinder per stroke, a portion is changed into work, a part is carried away by the condensed steam and the cooling or condensing water, and the remainder is lost by radiation; therefore (171) The heat Qj supplied by a 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 small. 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 engine. It is apparent llml the heal Q c , thrown out from the walls of the cylinder during exhaust, passes without compensation lo the condenser, and is a direct loss. Frequently it is the largest source of loss, and for this reason Him proposed to make H a test of the performance and perfection of the engine; but such a use of this quantity is not justifiable, and is likely to lead to confusion. The heat Q t that is restored during expansion is supplied at a varying and lower temperature than that of the source of heat, namely, the boiler, and, though not: absolutely wasted, is used iit a disadvantage. It has been suggested that an early com- pression, as found in engines with high rotative speed, warms up the cylinder and so checks initial condensation, thereby reducing Q a and finally (? also. Such a storing of heat during compression and restoring during expansion is considered to act like the regenerator of a 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- F. * AnSOLUTB PRRSSURKS, FUONt INniCATOR-DIAORAMS, AND PROPRRTIRS OF SATURATED STEAM. ttmi. HAII Bun. f> Cut-off . . Comnrcaslon . Admission . 83.6 M!? aR.i . a 317. a iBr.i 901.3 864.8 803. a 877.., 3.190 13-934 ao.,|u.| iR-3'l-l 39. B 333. aicj.o 813.3 93^ 863. 9 . 11.804 a 6. -164 13.664 * Thou vnliios nro tnkon from tho Jlrat edition of the Tables of I'rojwnlos ol Snturatfid Stonm. APPLICATION" 2I 5 MEAN PRESSURES, AND HEAT-EQUIVALENTS OF EXTERNAL WORKS. CRANK END. HBAD Eun. Man Prtsmrts. Equivalents of Work. Mean Pressure). Equivalent! of Work. Admission .... Kxpansion .... 87.7 44-5 14-8 78.3 3-369 3.877 1.836 0.0295 89-3 4?.i 14.8 21.3 3-7II 4-159 1.847 o. 1104 Compression . . . VOLUMES, CUBIC FKET. CRANK END. HEAD HNO. 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 M 2 X 3692 , = 0.0742 pound. '^ ' The steam caught in the clearance space at compression, on the assumption that the steam is then dry and saturated, is obtained by multiplying the mean volume at that point by the weight of one cubic foot of steam at the pressure at compression, which is 0.03781 of a pound. ,, 0.034-1 + * = 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 G 14568 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. -v. 1 0.0761 X 4 (5-190 4 5.307) 63.4 X 4(5-19 -1-5-207) - 0.6336. V. 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)] 63.311, .'. 7| - 0.0019 (181.1 + 893.2) - 3.041 Q a = 86.243 + 2.054 - 60.238 - 4 (3.369 +3.711 ) = 24.519, Q b = 60.238 - 63.311 - } (3.877 + 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 548 16.35 = 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 boiler. H(U)I .Bill Until in j|i[ M'K'W'trj/II vjtunod 'aini 'MiwMjd'^ liiunott inn|in *O "t >-. in 6 ro 1/1 i~ 1^ Q O M K I-. (^O M OQ sn in i-wj in ci (i o> i- O 4 w 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 MW aw O M "O fi M Q. I w -g Superheated steam may yield a considerable amount of heat before it begins to condense; consequently where superheated steam is used in an engine a portion of the heat absorbed by the walls during admission is supplied by the superheat of the steam and less condensation of steam occurs. This is very evident in Dixwcll's tests given by Table XXV, on page 271, where the water in the cylinder at 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. 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- sequently Q' - Q + QJ ~ AW - Q* + Qr - Qr. . - In a like manner we may find the heat Q" supplied to the next cylinder; for example, to the 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. 334 INFLUENCE OF THK CYLINDER WALLS It will be noted lhal the steam in the cylinders becomes drier in Us course 1 through the engine, under the influence of thorough 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. APPLICATION OF IIIRN'S ANALYSIS TABLE Vf. 225 APPLICATION OF IIIRN'S ANALYSIS TO THE EXPERIMENTAL ENGINE IN Til!'- EMIGRATORY QV THIS MASSACHUSETTS INSTITUTE OF TKCIINOLOCJY. TRIFLE-EXPANSION; CYUNOKH UMUCTKRS, Q, ift, ANII a-i tttctiKa ; STROKE, 30 KRS, Q, ift, INCHKS. Traas- AM, .Sto. ^/<fc//. Kitgrs,, vol. xtl, p. 740. Durnltott of (cat, tnitititea . Total number of revolutions Revolutions per minulu . . . . . 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 . . Total 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, luio Vacuum in condenser, liu cury 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 I. ir. nr. IV. . . , , 60 s*w SK.I flo 5^ 8-j i 60 5 'H a 60 5M cat, Ibis,: Cl ... 1*03 57 61 He "57 5<> 64 I33.f ao ( } 05.0 r.3S J 73 L . . . . ij 50 S3 iS 51 87 Kl8 i.iSn )H. ... aa8.(7 33T86 aoa^,j 20353 . . . . .11.9 43.1 96 6 43 J0 5-3 43.8 is, 1>y ihc 111. ftllSO- M.8 M-fl 14.7 1.1.7 } o( nier- *S77 a 3-9 o-3S 1 . . . . 0.05 0.05 O.O4 O.Oi) 1 . . . . 0.03 0.03 O^O^ 0.03 0.18 0.18 INFMJKNCK OF THK CYUNDKR WALLS TAUUK VI Continued. lisiiluir hrr^urr* in lli<- yllmlr-r, IK nl in IN |nT B'|- III.! Hiltli-iirrsuturr i yUrnU-r 11. IS" ?v .17 -^ XS-.1 M- ao> JJ.K i j.d t J..| I-S 5-7 A. j 10.7 I 1,0. 8.i; .( Q.( 7-. 7- 0- q- 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 HA-' <M-5 7.S-.1 '!t-4 JO.-t i J. i 5' 4 4..1 S-7 ft. ft la.ft to.K 7-7 8.0 U.-1 o.( 7.5 ? 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 ij.i; rj.3 __ . APPLICATION OF HIRN'S ANALYSIS TABLE VI Continued. 227 I. II. III. tv. Intermediate cylinder During exhaust, 10,18 During compression, 0.78 0.84 Low-pressure cylinder During admission, A\V t ", crank end 8-33 8.QJ 8. 19 8.66 During expansion, 6.81 6.86 6.87 7.87 During exhaust, 5.08 c.ofi "!.o8 5.16 4.81 During compression, Quality of the steam in the cylinder. At admission and nt compression the steam was assumed to be dry and saturated: High-pressure cylinder 0.848 0.875 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 . . . () . . 132.93 = 3-5-1 -18.69 - 8.36 o.4S 4-S& 1.50 4.93 0.58 130-77 23- 43 -19. 28 - 7.22 o. 5 i 4-08 1.52 5.20 0.58 141. t i 17.49 -iS-33 - 3-5 0-19 2-39 i.$4 5-6? -59 149-84 14-93 14-03. - 2.38 0.52 2.50 t-54 5-95 0.50 * Superheated. 238 1NKLUKNCK UK T11K UYUNUER WALLS TAJH.K VJ -Continual, I. 11. 111. IV. Jnlrrmnlitiir i ylimlrr ^ HmviRlH In by siriitn . y - . i.lt. KJ UiJ.dt >37-7 1.16.64 1 1. 11 UuriK cxtmiialon . . . (_'' . in.ftj i U u . 1 ii . n.l oj -'30.10 jji (Hiring rximuti . . . . (V O. Jj '57 31.88 Uurlitft (tirti|"rcftilnn . . ^'/ . Su|i|illr(( liy jiukrl . . (>/ . o.-l-l O.Kj n-5' 7-50 0.6l 7-07 si 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 1.3? 1.33 1.W IXIH- |"MHifr r yllwlrr 1 Hrmiglii In liy Pimm . t>" During nclml&sliin . . . (.V '';;*! i .10 . 50 S-.-i? H7-JJ I Hiring cxintiialoii . . . ^'*" ij.S< 7- (") n . fi< - 10 M f hiring oxniuiit .... (J," J..S.I 'M - 1.-14 O.I I Ihirinu umi|irra't|ttii . . ^'j" O.l.l o.ot 0.00 0.00 Su|'|iHnl liy jmkrt . . ('/' y.riH ft. jo 7. -II 7-M Ijitnt t>y mill ui lii ii . t't 1 .1-1 1 -i o .1 . je Tuinl li^t tty rn'lUil'in if Hy (frrUfiilnary ir^ii . 3C(' 1 f,ti7 10. JO IO.JI (0 ,- liy ntimllini (170 . . . U.ftK 10. M) -75 8.0) I'covrr ftnn mummy; 1 Hrwl ri|itlvAlcnu n( wurk \<rt M.l'. .yllti'li-r . . . . A\\' . ,,,, .,VI u. 17 fittrrtn. i vllmlrr. . . . AW 7.U f'.ijs 7-77 8.41 1.. 1'. lyllmtvr /Ml"" y.f I 1 o . of i 10. B 7 Tulnh . .... tf,. JH J5..V1 3?. Hi ""^H" TotJt) h*fll fiirnlshnl ly jai \tet9 . . J? ^ J?,fU J7-7' * Uimriliullnn n( wtirb Il'fifi (ift*iiirf f vldtrlrr . , . i t .ceo t.(*o 1.00 f.CO Init<rme<Unip tyUndrr O.HI a. Bj 0.85 o.SS i.i i 1. Ji l.IQ 1.14 Ilnrw-(tiiWrr ItM.iJ to^.i "3-1 190.3 Siritm iwr H P. |*r Iwuf ... 1 4 . 65 i -I - A ' 13-00 '3-M iri'.r. j^r If I'. |-r mtmiir . , M7 Ml 336 h will IK- nutitl ilmi fiir tri IV i.|g.8.| n.r.u. per stroke are, bmuf{Ul in liy tlu- htcum Mipplictl to ilu- 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 QUALITY OF STEAM AT COMPRESSION 229 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. 23 INFLUENCE OF THE CYLINDER WALLS test of steam drawn from the cylinder during compression showed little or no moisture. Nevertheless, there would still remain some doubt whether the assumption of dry steam at compression is really justified, were we not so fortunate as to have direct experimental knowledge of the fluctuations of tem- perature in the cylinder walls. Dr. Hall's Investigations, For the purpose of studying the temperatures of the cylinder walls Dr. E. H. Hall used a 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 To 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 CALLENDAR AND NICOLSON'S INVESTIGATIONS 2 3 I they gave the means of investigating the heat absorbed during compression and admission of steam, and the heat given up during expansion and exhaust. Three different disks were used: the first one half a millimetre thick, the second one millimetre thick, and a third two milli- metres thick. From the fluctuations of temperature at these distances from the inside surface of the wall some idea could be obtained concerning the variations of temperature at the inner surface of the cylinder, and also how far the heating and cooling of the walls extended. The account given here is intended only to show the general idea of the method, and does not adequately indicate the labor difficulties of the investigation which involved many secondary investigations, such as the determination of the conductivity of nickel. Having shown conclusively that there is an energetic action of the walls of the cylinder, Dr. Hall was unable to continue his investigations. Callendar and Nkolson's Investigations. A very rcfmcd and complete investigation of the temperature of the cylinder walls and also of the steam in the cylinder was made by Callendar and Nicolson * in 1895 at the McGill University, by the 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. 1NK1.UKNCK OK T1IK I'VUNllKR WALLS 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, VII. iNM.i'1'.N'ft- TW-. Ml. ] rni-: CVLJNDKR. if t'iv. IV. tit r.^u (wl j^di tnittuir ilD't lc4<ft l t ll(4 ftl*-B1 IP! psw ij ittld ' 4) J I 1" 4 IK 4 , W ' " 14 t ' Mf , " ^ i " ^ ' ,-i f> n t ,& t i 4U j old . <,| I >-\ ( " '*i/ | & *! . f t ,, 41 ' (HI 1, ' U|ftS t , t ta ,, . -. .*. i 4 "1 41 r>f| '."*. * - '-*'' " ;;i ' Cl FlOlft 71 4 gi o o 10)4 o o$j6 o.oioo 0.040! i O.tj) 0.04)4 !(* 0.0090 ' O.Ml 0.0066 1 a.Hj I 0,0041 |0t4. 0.0ll6 0.09 '7.11 M jft-0 ' I) I CALLENDAK AND NICOLSON'S INVKSTIGATION.H '33 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 CYCLICAL FIKAT-AnsC}f<l''I'fON KO14 C'UCAKANC'K NKKFACKK POII loin of surface consMnreil. Ara of inirlact, aqiiftrg fail. Mean itmitemlutt, V, *"Vtl. Cover face, 10.5 Inchw (Hnmetcr . . I'iston fnto, 10.5 fnchci diameter. . . "05 MU s The heat absorbed by the aide of the cylinder wall unnivmtl by the piston up to 0.25 of the stroke was estimated let lir 5$ B.T.U. per minute, which added to the above sum given 585 II.T.II.; from which it appears that 90 per cent of the comU'nwUinn '"> chargeable to the clearance aurfaccH, which were (.'xrcplioimlly large for this type of engine. Further InHpccllon 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 steam-engine. 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 re.st showed that the valve and piston were tight. The valvo was further tested by running it by an electric motor when the piston was blocked, the stroke of the valve being regulated so that it did not quite open the port, whereupon it appeared thai there was a perceptible but not an important leak past the valve into the cylinder. There was also found to be a small leakage past the piston from the head to the crank end. But the most unexpected result was the large amount of leakage past the valve from the 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 LEAKAGE OF VALVES weight of steam passing through the cylinder. Under the most favorable condition (for the seventh test) the leakage wa,s 0.0494 of a pound per stroke, and since there were 97 stroke? per minute, it amounted to 0.0494 X 97 X 60 = 287.5 pounds per hour, or 32.6 pounds per 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 fr.om 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 = t where I is the lap and e is tbc perimeter of the valve, both in inches, and p is the pressure in pounds in the 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. CHAPTER XII. ECONOMY OF STKAM-KNGINRS. 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 much. All the examples in the table arc taken from reliable tests; a few of these tests arc stated at length in the chapter on the influ- ence of (he cylinder walls; others arc taken from various series of tests which will be quoted in connection with the discussion of the effects of such conditions as steam- jacketing and com- pounding; the remaining tests \vill be given here, together with some description of the engines on which the tests were made. These tables of details arc to be consulted in case fuller informa- tion concerning particular tests is desired. The first engine named in the table is at the Chestnut Hilt 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 9.6 237 TADI.K X. EXAMPLES UK STKAM-KNUINK Kl'ONOMY. 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 Mnrinr mtlwrUealcd Rrtlllfrtlccl Mnrlur vrififnr Rush . . . Mnrinr cnjtlnr }>uti Vnmn SInt|itr 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 5" 7^ tX.r, 7' fK) .W CM hi fu *i|0 *ca '17 H5 1.17 'HJ fit fts yf 77 7ft fi-i.l 37i 'IS n.a n.. i 13 13- '5. n!l 31. Ifi.. II). tfJ It. J.|. '5 3-13 30,| 548 j'.S 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. TABLE XI. TRIPLE-EXPANSION LEAVITT PUMPING-ENGINE AT THE CHESTNUT HILT, STATION, BOSTON, MASSACHUSETTS. CYL1NDEK DIAMETERS T3-7, 24. ,175, AND 39 l^CHKS; STROKE 6 PERT. By Professor K. F. MILLKB, Technology Quarterly, vol. ix, p. 72. Duration, Jiours ...................... 34 Totnl expansion ........................ si Revolutions per minute ..................... 50.6 .Si earn -pressure abort atmosphere, pounds per square inch ...... 175. 7 Barometer, pounds per square inch ......... ...... '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, TAIII.K XU. THll'l.l-: KXI'ANSKIN MdKIWlNTM. MU.1,-KNfJINR. K iMAUKri^WS j.ij. ,\.\.$, AND TWf) OK 51/1 INfllKH; BTKOKK 78.7 INi'ltKH. Hulli l,y SutJkK "( Wlnirrlltur, Mlvhrl/t tin Vt-rfins Deulsclier Iiigtniei ire vul, \l, ji. 5j.j, Urviillllliinn |r inlniUr ..... Slmm'|irrruuiir, |niini'li |wr wjltnrr Im It Vrttuuni, Imln-u <i( tnrrdiry . , . . ?r hnrBF-iKiwcr |KT Imu Mcnn fr fniir tcotn .... CVial |njr Imrw jwiWf r |KT limir, \rean lir four (eaia .... Sirnm fwr IKJII nil nf fnl . n..|A jHiitrn t,,io 1 II III IV *$,.,> ' 5 ft - ' H 56.18 S6.l8 i '1 5 ' * 1-17 .0 i,|8.,| T-10-0 inJI' 4 " 1 37.30 37.30 1850 1$ t() i ' 5.1 ii ..|() ll. .19 "33 ' .17 -..1" 1-3Q 1.19 H. 7 H R..IO R...7 0.6] The lest fin (he cxpcrimrninl engine ul the Massucluisclts Institute of Trcluuitti^y is fjuoled here because its efficiency nncl t'concimy nro chosen for clUruftaiun in Chapter Vtll. Taking Sis [terformunce as a basin, il appears on page i.|8 that with 150 pounds holler- pressure and 1.5 pounds absolute 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. TABLF, XIII. MARINE-ENGINE TRIALS. By Professor ALEXANDKR S. \V. KENNEDY, Proc. hist. Mech. Engrs., 1889-1892; summary by Professor H. T. BF.ARK, 1894, p. 33. 1 u. $ "3 u C. 30 ViUe de | Douvres. j Meteor. 3 o C. C. 50. t 72 9 105.8 4-72 6.0 2977 30.8 367 8 '.97 T. 4-1 70.1 48 !0.6 = 73 3-3 1994 15.0 2.OI 7.46 139 T. 21 .t) 57 30 i ft 19.0 <5r.r o. 70 1.8 13-4 250 1.46 9-iS 70 r S-3 33 M rt i 57 36 10.9 6.1 S6 80.5 3-51 3-4 IO22 56-8 2.J? 3-8 S (com -pressure above nimosphcrc, pounds per square Pressure in condenser, absolute, pounds per srjuare Ii nek -pressure, absolute, pounds per scjuarc inch . . . 380 2.66 7.9(1 603 398 2.9 7-40 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. ECONOMY OF J TABL; TESTS ON THE ENGINE CYLINDER DIAMETERS 23, $5, AN By F. T. MILLER and R, G. II Duration, hours Revolutions per minute ....,., Steam-pressure, pounds per square inch mmphere Vacuum, Inches of mercury . . . , . Horse-power 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 engine, TABL COMPOUND LEAVITT PUMP] KEN! CYUNDftR 37.2 AMD By F. W, BEAM, TVww. Am. $ AUTOMATIC XVII. ENGINES OF THE V. S. RKVKNUK i Inttif 4 l)iamrtt*rf ryiii Stroke t inche* .,...* Duration, hour* , , , Revolutions |er ttilmilf Stram-|t*JUH* lit ftt Vaeuumy itidtru*f mm wty Total * ... 4 am! ^7 55 71 <*>, i jei.s 6. a Steam frr The details of tin* tt*sts on tlu* V* S. Revenue 4 Hit awl GuUatin nrr Riven in Table XVII, as made ab a iKMtrcl of mivitl engineers to determine the advantti pounding and uteam jat'ket^t. Thrtv <ther e tested at the time, but they were of older tyj>es interesting. A of teg to by M, F. are XXX aid XXXI, are in 'I ami i in the 244 ECONOMY OF The details of the tests on t cinnati, together with tests on 1 Table XVIII. TABU DUPLEX DIRECT-ACTINO FIRE- INSTITUTE OK TWO STKAII-CYUNDRttS 1 6 INCH: par minute. of fttrokii. West* length 01 utrokt* KMC. Httam- IMrtssure by f*u. W u . 40 10, IO ^8., 114 tt.70 11.07 55, ei IK) 1 1 . 49 11.07 Si-4 135 ic. fio II . IO 5J,li 156 lo.go ic.aft 47- J 193 lO.Ot) 10.31 45.6 175 11.77 u . 70 4^,6 ' 11.74 u . 66 4ft. S JWIWI ft.; u,, u. 41. TABt: TKSTH OF AUXILIARY KTKA^ By P. A, Engineer W. W, WHITK, OF IMPROVING ECONOMY * The two on the 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 devices; i. 2. 3. 4, 5. Compounding. 6. 7* 246 ECONOMY 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 OF RAISING STEAM-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 the.it 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 adva.nl 248 ECONOMY C: If f is taken to be 100 F 300 ? and 400, the values of t But the influence of the cy Improvement unless we resort studying Delafonci *s tests Figs. 57 and 58 on 25 sumption is plotted as ordin* 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 TESTS m the could be determined* The engine with and without in the jacket, both condensing condensing, and at various from 35 to i< above the of the atmosphere. The effect and the friction of the also obtained b; 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 250 ECONOMY i 58 represents tests with ste densation, at 50 pounds be curves are the per cents oj steam-consumptions in poui HORIZONTAL COR] CYLINDER DIAMETER 21.65 INC BARREL ( BY F. DELAFON] Number of test. Duration, minutes. Revolu- tions per minute. Cut-off in per cent o stroke. i a 60 105 60.0 58.6 6 3 7 ! 59-4 9 4 36 5 H 12.5 5 73 58.8 5-5 6 7 II 61.5 59-9 6.7 8 39 58.1 12.5 9 120 59-8 7-5 10 IOO 59-3 8-3 ii 90 59.8 10.5 12 ss-s 58.0 14 13 50 59-1 18 14 94 59-6 5 15 102 59.6 5-5 16 40 59.4 it. 5 17 40 60 14 18 91 58.3 5-9 19 90 59.5 9 20 75 59-0 15-5 DKLA POND'S TESTS results for individual arc represented by dots. which or near which the curves are drawn. As there a few in any a fair curve representing the be drawn through all the points In most The < HORIZONTAL CORLISS KNU1NK AT CRBU8OT JIC*$ 4 j,jt INCIIVS ONIVJ NttNKtWttPNXfttt*. II? R im^AWNi*, lift Aft***, iKK$. Number <-* Dumffoi tut* mlnuiM I 7 3 SS 3 1 IJ 4 So i 60 I 30 M 9 60 10 60 II 30 12 70 13 |0 14 |0 3 71 i**'? lit. 4 61,1 ff ,4 6t.t i-r i rtnf til 17 jo si U tf> iH aj | .17 i j toi.o IJ]M 71-7 76,7 77*5 77,0 7, 7*1,0 it, i 1,5 1.7 ii 47-S 181.5 217 til 30Q X 204 toi radically from the at so early a cut-off is u probable error of CONDENSATION on Fig. $8. It not appear worth while to try t< curve to reprencnt teats. The complement of raising the steam m m ECONOM of either pair of results v 25 per cent, which would of brake tests for this engi ical efficiency when runn: it was only 0.82 when ] brake 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 _ 26.9 The gain from condens and the conditions of ser to twenty per cent. Cle vacuum than with a poor feature which should be < pressure; when the condit effective pressure is large advantage of maintaining when the mean effective be best illusfrafeH wifh OF pressure for a 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 256 ECONOMY In this case the larger cngin capacity of the smaller one, the absolute size of the is little if any advantage In limits of practice* But the from as will be apparent front tl in Table X are for c standards. ' and of the use of from or s and such are pos engines* Bipuaslofiu - There are can be is by the o by the of 0' which can be mcnts; compound and tri the tin employed. The \ a triple, or COMPOUNDING The total for a compound or triple engi; obtained In two ways: we may use a large ratio of cylinder to the small cylinder, or we may use a short the cylinder. The two methods may be by the two Lcavitt mentioned In Table X; tl the to the cylinder of the compound Louisville, Is a km than four, and the 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 ^ 258 ECONOMY OF STEA1 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 COMPOUNDING 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 engines. 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 . Slmpit il III ao 11,8 2 6p ECONOMY OF STEAM-E 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. 22 Gain from using triple engine instead o I EXPERIMENTAL ENGINE Properly the comparison for finding the gain from cc ing should be cm thermal units per horse- power pe but the data for such a comparison are not given fc engines, and as all the engines have 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 262 ECONOMY OF the piping being so arranged 360 840 830 800 280 280 \ \ \ \ S\ V \ s \ \j ^ V N X \ 4 "S, \ EXPERIMENTAL ENGINE 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 264 ECON01V 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 ordinates. The most important this engine is of the adi steam in the jackets. 1 purpose: (i) with steal receivers, (2) with steai heads and barrels, (3) w the cylinders only, and (< The most economical steam in all the jackets the receiver- jackets, as i There is a small but dis the receiver- jackets also EXI'KKIMKNTAh ENGINE TABLE XXIIL TRIPU>KXPANSION KXI'KKIMKNTAt. KMCUMK AT rHUSKTTS INSTITUTE Of TKCHNOUx TVtf'ff. .-l Aw. . ' ! '4vittt ttwrtl 1ft pt i n* I 1 |ti trill 1 1 J ^ ** I *;ii t & f i 1 i * 1 j * s ^ ' 1 , 4 ! j ^ j g 1 ! * ^ r i ir , } ** * i 1 4 f l Ii h/'r^ :(:,!* Ctrl I i 1 o a ti i iS , <* d* v -, J; } A f j a I i f i Hi l * 4*^ 1 t f# 4 * * ft < i 1 1 j B mi i* f ii | 4 M 4 ; -. i a A ** i 1 1 i ft *j| 1 11 1 1' 1 ii 41 >.* ft , ' H ^ ? i 1 i 4 || tt %i / *' 14* l * i it i , I * ft 4 * I , iff uj (y % ^j M" W 1 * I- .- 4 | IH 4 , if ft; i * *| 4 ll t ' ' f li*<, l 1 * , II 1st r & || M f 4 14^ i <* -* ,<, i j t a ; W ft' rf | ' / i t * t 4 5 II f 1 f 1^ M 7 KT ',1 4 ij *i* i fc * it < 'MI; * i?;;,, 4 III ii ij iif J ! * * i it |i -** Mj << l s i - 4 * 1 tr* t i " M *j : ij t lt ii* - ttt A*\ it* ll lf <^ M , ' f f, , 4 / f ^, , i 41 lj III *' M *| I4| *,**. ,y | ^ ., |, j| f , , 4 1 MI( to ii in i * i l<f . - ; ^ /i f . j It 4 f | *4 Hi ii' 4? 4, i4^ 1 14 / <>. f I * 4 r 4 *l | j i t** 1 I? B WiJ #*<ljif^% l* f * |4| *j-|* ! **'j - 1 1 iii IMWWM* ^ I? *l |* M< *' ** 1 H / * ft f. 2 i ( j * ^ f B| 1 ,' i f ,i 4 w! o i |f ^ fc ! |, v t 4 / i* - ^4 i*t' M *ii <4I 1 * 4 , M i * ' , * W ^' *H ill *i ii; ** /' !- 1 M *' ' n * i * i ? r J l! *! 1 | i| *< . ** , , ,!" <,' ^ M4 i|j 14 j* *** rt*,i *i | 14 1 | ! i^ 4 ?i| t | | , , t |j I Ii t| $**! *!_ 1 ,' I *j 4I| 2 % (* S Ij *,,* 4 * # * v ' 1 4$ * i % to! i,* i til I III I , M fv , , 1 U IK* 266 ECONOMY Table XXIV givtxs tests In the jackets ami stea the results of these wil TA TRIPLK-KXPANSIt >N KXI'fcK nilTSKTTS INS firm-. RFHKATI.RS. ! n 10 it i* i GAIN FROM STEAM-JACKETS 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 268 ECONOMY 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 only -174 The corre8[K>ndence Callemlar and Nicolson ci has already From the to MIV INTERMEDIATE REHEATERS 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 270 ECONOM which is scarcely more tl the jackets. These tests they are too few and refei Superheating. The in the interference of the c] engine economy is by tl 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 DIXWELL'S TESTS TABLE XXV. DIXWELL'S TESTS ON SUPERHEATED STE CYLINDER DIAMETER 8 INCHES; STROKE 2 FEET. Proceedings of the Society of Arts, Mass. Inst, Tech., i8 Sati irated Stez un. Supe I II Ill IV 127 83 63 180 Cut-ofi 0.217 0.443 0.689 0.218 Revolutions per minute Boiler-pressure above atmosphere, pounds per souajre inch. 61.5 50.4 60.4 5O. 2 58.0 50.3 61.0 50.4 Back-pressure, absolute, pounds per sq. in Temperatures Fahrenheit: 15-4 302 IS-7 3O3 15-8 303 15-2 478 In cylinder by pyrometer . 278297 279296 282300 313 Per cent of water in cylinder: At cut-off 52.2 35.9 27.9 27.4 At end of stroke . .... 32.4 29.3 23.9 18.3 7.65 12. 7 15-68 6.83 Steam per horse-power per hour, pounds, B.TJJ. per horse-power per minute. . . 48.2 796 ' 42.2 696 45-3 747 ' 35.2 631 A metallic thermometer or pyrometer was place* In the head of the cylinder. When saturated stea this pyrometer showed a large fluctuation, but when steam was used its needle or indicator was at rest part of the apparent change of temperature with sat is attributed to the vibration of the needle and th< mechanism, it is very clear that the use of super" reduces the change of temperature of the cylind remarkable manner. The effect of superheating c of the cylinder walls is also indicated by the per < . in the cylinder at cut-off and release. The apparent gain by comparing the amounts c per horse-power per hour in favor of superheated 272 ECONOMY we must compare instead tl giving a real gain of 696 546 696 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 ^ pressure. Though we have no test condensation on engines o it is probable that a very r use of superheated steam u heat were as much as fiftee] consumption to a larger < and would be likely to give steam per 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 SCHKOTKK TESTS which places It a little beyond the performance oi engine mentioned. But since the uncertainty of the tion of power by the indicator is probably two per o reasonably conclude that the effect of lining superh in a compound engine is to place it on a level v engine, and the* question is to be decided in prat relative expense and trouble of supplying and using a of a third cylinder and higher 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 them, TAHI.K COMPOUND HORIZONTAL \IILL KNUU4I %Ntt jj witt't; j;|,5 , tt'ft f*| P|i>4, By Pwfijt*r M. '' t > * i } *'| ft ' ; . . im iw p'i Ktuwftf re^jf 1 w i II , Hi IV ' V i VI '*<*>*** *M. flirt, in 1*1 1 ; f#* M' 17 V n 1 <i |i ! lift Itfftltrt ftl II?' Hi U ' y it V ** ft 1 ti * ti i, ii C Vtt I*, ? 11 D si i i' i t i i* 4 i i 274 ECONOMY 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 expansion. The stationary comjxnu have about 20 expansions, that for highest economy quired. In practice advisable. Variation of Load. If VARIATION OF LOAD In the next chapter; and the second is evident from i of curves of 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 276 ECONOMY OF STEAM- 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 Al'TOMATK* AND THKOTTLK KNdlNKS by gravity* When tin* engine is running steadily speed the forces acting on the governor are in eqm the hulls revolve in a certain hori/ontal plane. If the engine* is reduced liir engine speeds up and the outward ami upward until a new position of eqi found with the halls revolving in a higher hori/< Through a proper system of links and levers the upv of the halls is made* to partially close a 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 easily. Automatic engines, tike tlu* (\rliss engines, ha\e two for admission and two lor rxhaiist of ^team. Hi relea.se*, ant I compression are tt\ed f but tlie cut otT i by the ftovrrnor. t*su;tll> an ;ulmixsin valvr is att; actuating mrcltanism by ,i lait It *r similar device, w opened by the ^ovenor\ and then the valve is < lose* by a spring or by some other independent device, of the governor i* to ttmtroi ftie position of a * which the latch strikes and by which il is opened I valve. Corliss and other automati* eiifjne^ have long h;u reputation for cnonomy, which is commonly attrthi; method of regulation. Il t- true tltat the valve gc enginc\s are adapted t< i*ivr an early cm oi'f, winch i elements of the design of an rn*rni<'al simple rngti ECONOMY OF STE from the steam to the exhaust side of similar construction. Every 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 EFFECT OF SPEED OF RE^ Considering also that automatic en built and carefully attended to, while often cheaply built and neglected, th the one and the bad reputation of tl counted for. It is, however, far from certain that ai have a decided advantage over a throttl latter is skilfully designed, well built and < to run at the proper 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 sfa 280 ECONOMY C "surfaces exposed to steam in fact, all engines which for \ to run at very high rotative economy, in part from the r fact that piston- valves are co to the kind of leakage descri page 234, even when they z monly the engine has a fly- 1 valve to be very free with the Willans invented a 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 BINARY KXUINK 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 le.ss than of the total Meuni supplied to the engine, The pc the engine is given in Table XXVIII in terms < 282 ECONOMY TAJ BINARY ENGINE, ST By Professor E. JOSSE, Royal Re volutions per minute i39- Steam-Engine: 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 BINARY ENGINE 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. 0-55 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 284 ECONOMY 01- Finally ii appears probahl binary engine* could he obt; compound engine, using sii] good results might be expect 175 pounds gauge* pressure v already been called to the f but little with highly superl unnecessary and illogical. CHAPTER XIII. FRICTION OF ENGINES. efficiency and economy of 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 ' 286 FRICTION < 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 above. The following table gives tl number of engines, determined 1 TABLE INITIAL FRICTION AND LOAD FRICTIOI pumping- engines, by measuring the work done i water. Initial Friction and Load Friction. A part of th< an engine, such as the friction of the 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 governor. The main dimensions of the engine were : Stroke Diameter: small piston larere Diston 288 FRurnor T\\\ FRICTION OK (' WALTHKK MKUNIKK am! Luimiu Hortr I*owrra with l air pump, j -Ml 7 7 iH with Sf, | ?i 7 ft^ *, INITIAL FRICTION AN!) LOAD FRICTION brake (numbers g, 18, it), 28, and 2oJ were irregular tain. The first nine tests were made with the engine wo: pound. Tests 10 to 10, wen* made with the high -pre.* der only in action and with condensation, the low pn 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 abns.su* and the friction h< for ordinat.es. Omitting tests with small power* (for brake ran unsteadily), it appears that each series of t 2()0 FKICTI normal net or brake horse j to deliver, and may be rep where a is a constant to IK (>o. If 1* is the net horse time, then the load frietior when* h is a second consta; The total friction of the er /*' so that the indicated powei l.H.P. /' r / The* mechanical efficiency I The compound ctntdeii! sented by Kitf. 60 devc-loju 1 power to the brake, so tl friction. Thr diagram si INITIAL FRICTION AND LOAD FRICTION 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. TABLE XXXI. FRICTION OF CORLISS ENGINE AT CREUSO' 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 Revolutions tion of Stroke Cut-off, Kilos per Sq. Cm. per Minute. Indicated. Effectiv I 0.039 0.64 64.0 27.8 16.3 2 0.044 2.40 68.5 60.0 37-6 3 0.044 2.90 65.0 67-2 45-2 4 0.065 4.90 64.0 117.0 88.7 0.065 6. 20 61.0 138.5 106.3 6 0.065 7.10 64.0 163.2 129.2 7 0.065 7.60 64.0 185.0 144.6 8 o. 100 .16 58.0 21. 10.6 9 0.106 55 60.0 6l.9 42-3 10 o. too .82 57-3 82.7 61.0 ii 0.090 .80 58.3 135-3 106.7 12 0.128 .82 58.3 154-5 124.8 13 o. 142 -76 62.0 42.3 28.4 14 0.137 7i 60.6 44-3 28.7 *5 0.132 50 54-0 79-5 59-8 16 0.147 .60 61.6 IOO.O 78.2 17 o.iSS 65 60.0 177.2 145-0 18 o. 167 .22 61.0 40.2 27-9 19 0.197 55 57-2 no. 8 83.3 20 0.273 4 62.3 50.2 33-8 21 0.264 57 63.3 89.1 6r.8 22 0.240 .64 62.0 87-2 63.1 23 0.245 25 56.0 145.0 116.0 24 0.260 76 58.0 209.4 178.0 25 0.335 25 59-0 47-2 32.5 26 0.339 94 58.3 in. 7 90.0 27 0.338 97 6r.o 161.8 133-0 28 I 47 59-3 81.3 67.2 29 I 47 61.0 80.8 67.9 3 I .60 61.6 148.5 128.4 31 I .70 61.5 216.5 191.0 32 I .70 61.5 215-5 191.0 33 0.50 .70 61.5 15-8 o.o 34 O.I2O 6.00 60.0 132.5 107.5 35 0.106 7.00 53-0 125.0 " 103.0 2<)J FkKTiO! Table XXXI gives the rt tests made on a Corliss en^ both with and without a pressures and cut oil. The on Fig. 01, and those withe In both figures the abscissa* the ordinates are the friclio: are represented by dots; tho most ^economical cut oft itn 40 1 lot INITIAL KRKTION ANU LOAD FRUTK friction than the other tests. The tests on this clearly that both initial ami load friction are aff cut-off and the steam pressure, and thai friction be made at the eut otf which the rngine is expeeU service. tti The initial frit lion w.i*. Hj,*!tt horsepower h< without condensation* Hut IMJ;. 61 shows tlui with condensation #a\r the ltv*t economy wher 160 horse power; the f rut ion was then ,<<* horse j: the net horse power wsis i,<o, which will he taken f hor.se power /*. ronsecjuently |i i $4 -* H ! ; t^'* 1*47, shows the Iir?4| eccjii indicated IIOIM* JHW i% leaving iKci fur the In lik<* condensation^ for ahout the friction is , hcit^e mm I'h I, 294 FRICT in friction, when developi sation it had 20; conseque] (36- of the indicated power, to the high vacuum maint Thurston's Experiments. tests on non-condensing e with his advice, Professo for engines of that type load, and that it can, in ing the engine without a FRICTION OP 1> STRAIGHT-LINE ENGINE, 8 No. of Diagram. Boiler- Pressure. Revolutio I 5 232 2 65 22Q 3 63 230 4 69 230 5 73 230 6 77 230 7 75 230 niSTKlWTioN OK KRICTION lubrication and other minor causes rather than c of load. Distribution of Friction. As a consequence of in tin* preceding section, ProtVssor Thurston dec friction of an engine may In* found by driving : external sourer of power, with I lie engine in sul same condition as when running as usual, hut witho cylinder, and by measuring the power required t aid of a transmission dynamometer. Extending the distribution of friction among the several nn engine may be found by disconnecting the scvt one after another, and measuring the power requi: remaining members. The summary of a number of tests of this sort, fessor R, C. Carpenter and Mr. (1. B. Preston, Table XXXIII. Preliminary tests under noni showed that the friction uf the .several engines \ the same at all loads and speeds. The most remarkable feature' in tins table is the main bearings* which in all cases is large, lx>th absolutely. The coefficient of friction for the n calculated by the formula ^ftftn H.jP. ft n is. given in Table XXXIV. p in the [iresHure <m t pounds for tlu* engines light, ami plus tlte mea the piston for the engines loaded; c is the circuit: bearings in feet; n is flu* number of revolution and IL P. Is flu* horse -power required to overeor *!$'* . m\:.i ffl^rt * 4 '. i '% * r*i : ll'^/l v : ', 296 FRICTK TAB DISTRIBU-: Parts of Engine. \O rt 00 Main Bearings Piston and Rod Crank Pin Cross Head and Wrist Pin Valve and Rod Eccentric Strap 47- 32- 6. 5- 2. 5- Link and Eccentric Air-Pump .... Total TAI WSTKIW'noN OF FRICTION The second and obvious conclusion from Tab that the valve should be balanced* and that nine- friction of an unbalanced slide valve is unnecessary The friction of the piston and 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 piston-.ro< too tightly. The packing of both piston and rod tighter than is necessary to prevent perceptible le more likely to be too tight than too loose. ClfA INTKKN'Al. <' RECENT advances in the | been found in the develop!) and of 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\ STIRLING'S ENGINE page 39) It was pointed out that to obtain the ma ciency all the heat must be added at the highest prac perature, and the heat rejected must be given up at temperature. The 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 300 INTKRNAI. C< inner is pierced with holes t displaced by tlu- planter. pipe through which rold wat has free communication u cylinder, and eonseifucitily : l)c parked in tin* usual man In the actual engine tlu then* art* two displacrr rylin cylinder. If we neglect the action cylinder // ami the loinimi ideal eyrie. Supper the w of the forward strokr, ami its cylinder, so that \vr may part of thai t ylintlrr or in i perature T y the condition by tlu* point /> *>f Kii-t- ! quit k!v ,K strokr; \ litllr tlu Ilir air ; of thr ili ratt*r, fr* STIRLING'S ENGINE stant temperature, as represented by the isothermal completing the cycle. To construct the diagram drawn by an india assume that in the clearance of the cylinder H, 1 eating pipe, and refrigerator there is a volume of ai back and forth and changes pressure, but remains a ture jT 2 . If we choose, we may also make allowan lar volume which remains in the waste spaces at 1 of the displacer cylinder, at a constant temperature In Fig. 65, let ABCD represent the cycle of ope out any allowance for clearance or waste spaces; volume will be that displaced by the displacer pis maximum volume is larger by the volume displaced ing piston. Let the point E represent the maxin the same as that at A ; and the united volumes of at one end of the working cylinder, of the commu FIG. 65. of the clearance at the top and bottom of the disp and the volume in the refrigerator and regenerate of this combined volume will have a constant te that the volume at different pressures will be repr< hyperbola EF. To find the actual diagram A f any horizontal line, as sy, cutting the true diagrar 302 INTERNA:L-COMBUSTION E 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 STIRUNcrS KNGINK isothermal expansion, and />.<! and ,#(.' take the constant volume lines on Ki#. (14. To six lines are properly drawn, we may consider the eq which was deduced <w page 07, Kor the lit BC the volumes are constant, so that the equati or transposing, but this last expression represents the tangent of the the axis (M* and the tangent to the curve. This a (but with a dimin ishinj*; ratio} with the temperati is constant for a #UN, the anj'je <lipends only on th 1\ so that the curve JIC is itlentual in form with 1 and is merely set oil further to the nght ; in cons* like W X and ZY between a pair of constant ten are identical except in their positions with regard t< . SujJpose now ibal ibe material of the regene temperature* 1\ at the lower end, and 1\ at tht* u] that the temperature varies regularly from bottom pose further that the air when &ivmK heat to tl (or receiving heat from if i differs from it by only able amount,. Then the diagram of Fi#. 67 will ideal action correctlv, and it is eusv to show that 304 XNTKRNAI.~C< Moreover, the small amount ZY at the temperature 7' heat yielded during the openi so that. there is no loss ot ft mentioned are represented In It. can In* shown that onr u at random, provided that tlu tical and stl off further to importance enough to vutrnt In practice a regenmttor temperature than the air frt; !iiglu % r temperature than thai of air is rapid. The loss of of the original Stirling en^in ten per cent. H may le pn state thai regcnenitors ;irr r at the prest*nt day. 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 GAS-ENGINE WITH SEPARATE CO1 engine itself; the second type of engines, engine is an example, is the only successful time; the other type has some advantages wt development. 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 atmosphere. This type of engine has been used as an oil- the fuel in the form of a film of oil to the a compressed. In such case the compressor and there is not an explosive mixture in Brayton engine when run in this way could bu or, after it was started, could burn refined ' defect appears to have been incomplete con mip.nt. frmlmo- of the cvlincler with carbon. '^ ! mi- ^00 1NTKKNAI, U*mpiTatuiv> I'onvspondin hrat added from A ti / !- *'v and flu* 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 <;AS-KN(;INK WITH SKPARATK COMPRKSS< above the atmosphere the eiliciency is JL42ir:-l. / 1.1.7 "* e i (T;^'^ -- When the cycle is incomplete the expression for t? is not so simple, for it is necessary to assume cooling volume from G to // (Fig. 68), and cooling tit const! from // to />; so that the heat rejected is <- c'V nv ><, CA- TJ, and the 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 14,7 provided that. the temperature of the atmosphere is 6 j The temperature* at G is i T T MiV"* /r \ 4 s I and the pressure at (.7 is \ MY i ^-'^i^l " f'^-7 + \ so that the temperature at // is m I Mm, 308 INTERNAL- 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 strokes. The most perfect ideal GAS-ENGINES 'WITH COMPRESSION IN 1 and withdrawing heat at constant pressure fr with the adiabatic expansion and compressic The heat added under this assumption is c v (T a - T d \ and the heat rejected is c p (T, - T c \ so that the efficiency is c (T t - T f ) _ If the temperature at A and the pressure then it is necessary to make preliminary temperatures at D and at B before using equ adiabatic compression from C to D gives at D T d = T c in like manner adiabatic expansion from A T b = T a *)" . pj 1 'lA^l J< ' 310 INTERNAL-CO provided that the temperatui 2<OO = 104-7 nil == (2500+ 460) nc 1 ~ i -4os : If th atmosp' shows * as in ] conside heat as by wit; to can F:G. 70. G > anc stant represented by GC. The he and the efficiency is GAS-ENGINES WITH COMPRESSION IN THE CY: For example, let it be assumed that the expai when the pressure becomes 20 pounds above the the other conditions being as in the previous examp 0.405 and _ T I53 6 - 6 5 + 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 14-7 times the volume at D, and 'that the volume at B is =5 times the volume at A. When, as in common practice, the four strokes of the piston are of equal length, the diagfam takes the form shown by Fig. 71; the effective cycle may be 7! 2 lNTKRNAIrO The heat applied is and the heat rejected is so that the eflieieney is M7'a - 'i Sinee the expansion and the* equations 7V TV* * '/Via*" ' but the volumes at /! and / at B and C; i'onseijtirntly It; V j consecjuently and the expression for elTki GAS-KNGINRS WITH COMPRESSION IN THE ( pounds absolute, or 8iS.4 pounds by the gauge, ' efficiency is therefore not much less than the eflieiei other examples; it is notable that the efficiency same as that calculated on page ^07 for an engine compression to <)O pounds by the gauge. For the however, the pressure after explosion, which dt temperature, may exceed 300 pounds per square i The diagrams from engines of this type* re.s< which was taken from an Otto engine In the lal: Massachusetts Institute of Technology. I Hirh stroke, the pressure in the cylinder is less than th;c INTERNAL i' of ;20tothi'inrh, ami iih * pisttm; tlu- upl*'*' pan i appear In tlu' m^n-. 'H^ pounds, and liuMvdtMiHiin HI* thrrr ami f*ur p*mml. l'- Ihr influriu'c' of Oi** riri^.i! imUfutnl hursi* powrr will Tin* i'uinin-.sNin lin* *!* or in rralicy from an ;iilitl In* rXjHHlni to rtnrivv hr.it llu- lirst pan <f thr i ompn during l hi" lattrr part, T to I hi* ailialulir li* for *4 fur lart* rftiprtr%; hut in jirr vrrv <lit'frrvnt f fr thr i CHARACTERISTICS OF GASES and, if the gas is to be used for generating power, and adjuncts must be adapted to the conditions, gas is made from coke, anthracite, or from 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 ANALYSIS OF MANC'HKSTKU COAL <;/\S. (Hunsen j Hydrogen, li ....... 45. > 45-5H, Methane, C*H 4 i 34, <) | <xj,8 j 104.7, INTERNA COMPOS! Hydrogen, H Methane, CH 4 .... Carbon monoxide, CO Carbon dioxide, CO 2 . Oxygen, O Nitrogen, N details are given on pag< original paper, which ar Rich non-caking bitur larger proportion of hyc In a paper on the use < gives the composition ol Scotland, and Germany, following table were de< COMPOSITIC CHARACTERISTICS OF GASES The amounts of oxygen required for the combustion volume of any gas can be computed from the foi resenting the chemical changes accompanying c< together with the fact that a compound gas occupies tw if measured on the same volumetric scale as the < gases. Thus two volumes of hydrogen with one oxygen unite to form superheated steam as represent formula 211 +0 - H 2 O, and the three volumes after combustion and redact original temperature are reduced to two volumes; in to have the statement hold, the original temperature v to be very high, to avoid condensation of the steam i But in tlie application to 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 AFTKK BURNING are and remain the same as those of gases at. orcli tures, can he taken as a first approximation only. In conneetion with tests on a gas engine (see pi illuminating- gas. Professor Meyer makes a careful of the temperature which might he developed it of a 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 made. On the assumption of constant specific heats Pi finds that complete combustion should give ,p5c conducting cylinder, hut using Mallard and 1 equation for specific heals at high temperatures hi Those experimenters report that dissociation of cai begins at about, pocf 1 K M and of steam at about 320 INTK time. The actual e: for gas, and for lar represented by the 1 but a part of this ; carbon monoxide* an< may reduce the expc Water- Jackets. engines have the h 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 ECONOMY AND EFFICIENCY 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 estimated. 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< 3.84 nominal theoretical efficiency; consequently the efficiencies is nearly 0.60, By a somewhat intricate method Professor Me; the efficiency for two tests on the engine for \vhi< given on page 350, on the assumption that eomplel occurred in a non-conducting cylinder. The ratio 222 INTERNAI^-COMBUS' heat, be taken as the basis of cor the ratio of actual to theoretical efi 0.253 -*- 0.398 = 0.64, or If, however, we take his second val we have 0.253 + 0.297 = 0.85, or c Professor Meyer uses these coi importance of better knowledge of substance in the cylinder of an because, if the nominal theoretic* basis of comparison, there appe; improvement in the economy of second set of computations is tak< prospect of improvement. In co] the fact that these tests were on a only ten brake 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 KCONOMY KFFK;.IKNC:Y the indicator piston from rising too high which effects of an idle cycle and other features. A po expansion curve is shown, with oscillations due t< suddenly leaving the slop. The exhaust of the sj shown by the curve <//*, after whirh the engine dm of air (without gas) and compresses it on the uppe: c to d] on tin- return stroke* the indicator follow curve from d to r, so that tin* loop represents work engine; finally the air is exhausted^ while the ind the line cc. Tn explain the dtflVrenee between tin* ab and ce with spent gas and with air onlv, it mav 1 INTERNALr w : 1)5 rll } ' > time considerable import out spent gas, but it atte engines. In indicating a 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 STARTING DEVICES remaining closed during the compression, exj strokes; but very commonly the admission and for gas (when the latter are separate) trolled, and for very high speeds this action ; From what has been said, it will be evid< problem of the design of the 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 '' lii'V 326 INTERN the operations of cha formed, whereupon tl for very small sizes, i. into action, and whi piston has completed which the charge is p; compression is much this manner the ignit past the 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 GOVERNING AND REGULATING 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 service. 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 INTERNA: tures should occur befoi that even though the ex] the beginning of the woi The tests on page 3Jc varying from i : 8 to i brake 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 KiMTlON small power the negative work of idle cycles ver the brake economy of the engine 4 . Now, a sin cycle engine has only one working stroke in four nish between times the work of expulsion, filling sion, and even with a very heavy fly wheel will < lurity in speed of revolution that is very objectio purposes. This difficulty is very much increase is governed by omitting* explosions on the hit or i (4) Delaying ignition is one of the favorite w the power of automobile engines on account of i it is little used for other engines, and is very \s as there is not time for proper combustion. Ignition. The ignition of the charge may one of three methods: f i by an electric spark, {.' or (3) by compression in a hot chamber. (V) The electric spark may be produced in o: ,,, ],y the make and break method, or by the jum] For the first method a movable piece is worked. der walls, which doses a primary circuit some t tion is desired; the slight closing spark has no proper time the moving mechanism breaks tin good spark is made between the terminals, wl with platinum. A coil in the circuit intensifies opening spark. The spark obtained by this n to be better than tin* jump spark, but there is 1 venience of a moving nurhanism in a cylinder < high pressure, and the motion must be comr piece which enters the cylinder through a stuflm] The jump spark betm'een two platinum termu lated spark' plug, screwed through t lie cylinder ~ , INTKRNAl. Tin* divtilt may la* MIJ generated by a small dyn supplied from any tonvri plied* the engine is usuall; The rlrtlf'ti' nirthoil ol history 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 Illii GAS PRODUCERS 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 lij: f N : w j' I ^/ 1^ 51ft >f?f iNTKKNAI, tin* prvst'iH time tin- Hirl. caking hituminou-, ial. . tion, at St, l.oui*. in tu-^t, a raking bituminous i'o;il and pla.nl, ami if is likrly thai ustd in prartii'f. Ilg. 75 fjvrs fhr srt lint i .-1 i 4 " tlir i',ratr t ;irr\!f rfnf- ';': if. 11 i ; r ri%mrit f'ttr tiitti" /,. f* fl OTHER KINDS OF GAS cite; those that burn bituminous coal must have of dealing with tarry matter. Sometimes this is by passing the gas through a sawdust cleaner centrifugal extractor is added. Some makers r by care in cooling before the gas comes in conte Others pass the distillate through the fire, and into light gas or burn it; with this in view, some j with a 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 scale. 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*; 334 INTKKNAI, t 1 Gasoline. Thr lighter < Iim\ an* mulily vapori^nl the must rratlv means if M uf several hundred hotse have been built for small of gasoline has bent littntt i' raft ami tt aut>nu*bilr^; for husini'ss nthrr thin> r ,N tion of thr rnj'int's. Tin- tivrly .small [u\\rr IIMI! f*! Tltr m*>t uta! fVaturr or farbuivtnr, ami ihi*' < t'spiH-'ially for autnnjtbilf SjHH'll. ThtTt* an- thtvt' tyjt*^ t* thcisr that 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< Ihtitt, llir Ilitift* rrtrnt i arht supply lit'ing drawn fwJ lint* i.s stippliril itit! IIMH ninrr or I-H^ in riiurti KKKOSKNK OIL A third form of carburetor is illustrated by the gasoline is supplied by a pipe K to a valve t to give good average action. Below Is a fine c the end of a vertical rod which is held up by a light spring; at the middle of tin* spindle is a disk- valve which lit slooscly in a sleeve. At aa are air inlet valves, and at A is the entrance* to the cylinder. During the suction or tilling .stroke the spindle is drawn down, opening the valve at the top of the spindle and allowing the air ft* draw gasoline by aspiration, Some* of the hot products of combustion from the exhaust are circulated around tin* aspirating chamber to prevent undue reduction of tem- perature. This type of carburetor works well enough at moderate |l speeds, but at very high speeds the inertia and disk- valve cannot be* overcome rapidly enoi which is consequently throttled, so that there is r vapon/ri itolteil ! em! i-. of this engine i> MIUUII in j of the cylinder head ' the eitFJ fniu a the **u|.;im* is running. T! tltis Itiif mi! nf the vaj with thr Iit! .spent jaM" ; ! Mrokr thr i hari'r f ;iii i n'ssfd rut ITS lin* vapiri/i the* va nn i*" 1 tltr fulfil ailhrfritl tirptrat ad is put on for a * y i utilrulliii^ if; hypuss valvr oil thr ctil sitp t* tlir lank, Thr hli *r ni \"iJHri/.rr Wiitilil brromr IH THE FOUR CVCLK KN r (;iNK appears to be no reason why there should bo troul of some form of carburetor like those used for gas The 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 3.;S IN '11' KNA1 thai ran le moved !<;, 1 to t !?j\r any desired nil areas for t f a> aiul air areas remain niuhani^ piMon valve to *i\r ih clrniandri! h\ tin- l*ad * ihr r\hati>l vahr 1 A" ,ttv iiulicatctl. I In- tains in, rwulntiun <*t % thr 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-\-.tj. lm\rr than th.it | thr , atlvanta^f |*i'utini the nihi-r uay. The iir^i / \\UN that ly Inii^ili! <*! TWO-CYC 'I,!'*. KNCHNKS regularity of rotative velocity. The engine could twice us much power for its si/e as a four cycle er certain tests by Mr. Clerk, shown! a slightly bet than the older type of engine. But the operation the remnants of the spent charge by the fresh char| of this type is rather delicate, there being a chance the spent charge will remain, or that some of the will be wasted; it is likely thai the charges mingle engine experiences both defects. Eventually the ( was withdrawn from the market, but the principles two types of engines: ( i ) small gasoline engines for other small craft, and (!) large engines built for b' furnace gas. Gasoline engines of small power and moderate r< have been made on the two cycle principle by e crank- and connecting rod in a casing, so that the pi: ,as the compressing pump. On the upstroke a r] and gasoline is drawn into the crank rase, and it. is pressed on the down stroke. There are two sets < through the cylinder walls near the em I of the dow are opened by the piston; these an* on opposite* cylinder; one set, which is opened slightly earlier th; forms the exhaust -ports ami the other the inlet 'ports communication with the crunk case, and therefore and gasoline to replace the spent charge. A barri the cylinder- head which prevents tin* fresh charge directly across from the inlet to the* exhaust, but ne\ action Is probably much inferior to that of Clerk's t had the charge supplied at thr cylinder-head. Then 340 INTERNAL-CC 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 burned. 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 THE DIESEL MOTOR 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'01 } f L'v m\':{ i H m, 342 INTERNAL-COMB ger. Atmospheric air is drawr pressed from b to c to a p: square inch and a temperature is injected in a finely divided excess it burns completely at by the injection mechanism, is petroleum or some other oi interrupted, and the remainde is an adiabatic expansion. The at e and a rejection of the proc The cycle has a resemblance differs in that the air only is c the combustion is accompaniec his theoretic discussion of his of combustion shall be so regul not rise during the injection of therefore be very nearly an isot the fuel is added during the o] cd, the weight of the material i physical properties change, so ' isothermal. The fact that then THE DIESEL MOTOR rise of temperature, or that there is any great advj a regulation if the temperature is not allowed to ris The diagram from an engine of this type is sho^ which appears to show an introduction of fuel : or 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: 344 INTERNAL-COMBUSTI 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 TUK DIKSKI. MOTOR A theoretical discussion of thr efficiency of th simple engine us represented by Fig. 70. may 1 considering that heat is added at constant tern] to d and that heat is rejected at constant volun bearing in mind that be and dc represent adiabat From equation (75), p*W u k i? the expressioi supplied from c to d is, for one pound of working Q, - At> f v f \w,~t ART, }<>&- 1 1 . 11 e The heat rejected at constant volume is Since the expansion </r is adiabatic, (i ^. t' r but since the compression be 5s also adiabalic, and consequently ' mK'ratutv /'? I ' lr * prrssuiv at tu- '* * ill !' : jlr l lip; li; ZnjirtrtL llut i>, lv rrilu liy it writ's uf i.tlruLiffM Tliis JN a MTV impnt'Lini will hau' in prat tin- litiU It>atl^ [I is 11 pnM* *l !ha*. i rill i*' .t J *a'* f? ' m 'v .ii thai ill*- Iraian* KNG1NKS FOR SPECIAL PURPOSES The equation for efficiency gives in this case ( I f \ a jin e 778 X 0.2375 X 530 (^^~) ' - i ( \o.07<)6/ e ' J ~x-^___ 1.405 X 53.22 X 1480 log, ^iLZli 0.0796 Engines for Special Purposes. - - Small engines < to give any required degree of regularity for elect] purposes, by giving a suflicient weight, to the i large power the same object can be attained by usi of cylinders, by making the engine double acting, struction of 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 am ihr Economy ECONOMY OF GAS-ENGINES (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 ( * ! ' ECONOMY OF GAS-ENGINES 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 *M, Ml 35** 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 jninuti Tlti * *tj|*t i .u i .hurt thi- arnr ir nil Int la Illliti -!! ii*!i', Tffr |Ut 4i*fl a > f> 1 rniiirs has JMVU tHir-.ii rsl rrMlU ttut i. r tif l)ir lli-.lift) tiHikr !iti|',r JiMttrl. 11 VtihilUr ," Hvill'i'M 41 I*HN MrtltiUlr CH* A PRODUCER-GAS PLANT 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 354 INTERS TEST Duration, hours . . . Total coal fired in prod Coal equivalent of stean Coal equivalent of powe Total equivalent coal . Thermal value of total, Total gas (at 62 F. anc Thermal value of total \ Efficiency of producer . Electrical 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 TEST AT CH Duration hours, . . . Coal required by plant, Thermal value of Georj Heat abstracted from 01 Efficiency of boiler . . ECONOMY OF A IHKSKL MOTOR correspond to one pound per brake 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 I ml ffi I IIP;' 1 - ill Ife 356 INTER* 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 Clerk.* Dimension of Engine. 6.75 X 13-7 9.5 X 18.0 26 X 36 ? WASTE-HEAT ENGINES first question to be determined is the mean ef that is desired or can be obtained. This must fuel and its mixture with air, and on the degree There does not at' the present time appear to that will serve as the basis of a working theory the mean effective pressure even when thes determined. It is desirable', in order that the engine shall li compart, that the mean elTeetive pressure shall b engineers commonly make use of go to 100 pound pressure; but German engineers who have had very large engines for which pre ignition is dange content with 60 pounds or less. 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 Durt)oses. 1; W i I' 1 ' I ii ( [*:. 4,;.; COMPRESSED air i energy, and for pi pressure, produced b; of iron and steel; an< than that of the blowers) are used to for producing forced be given mainly to th production and use < ceptible of but little be reserved for anotl A treatment of the involves the discussi through pipes, and c storage of energy difi the compressed air, FLUID PISTON-COMPRESSORS 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 MOLSTURK IN THE CYLINDER ing water into the cylinder, but experience has work of compression is not much affected by : only effective way of reducing the work of coi use a compound compressor, and to cool the ; from the first to the second cylinder. Three- stu are used for very high pressure 1 ,,. It is, howe^ air which has been compressed to a high pres density is more readily cooled during comp v cssior Moisture in the Cylinder. - If water is not ir cylinder of an aireompres^r the moisture in the on the hygroscopic condition of the atmosphere the air were saturated with moisture the ubsolut tive weight of water in the cylinder would 1: Thus at 60 P. the pressure of saturated stean fourth of a pound per square inch, and the weig foot is about o.oooH of a pound, while the weig' foot of air is about o.oK of a pound. It is pn only effect of moisture in the* atmosphere is to the exponent of the equation (77), page 64. sion probably holds when the cylinder is cook jacket. When water is sprayed into the cylinder of of operations rrpivsriHt tlu* air is rompivssrd, , If s|ll*i 1 ' I ffhrr VUlfl cif tin 4 otmprt-ssor vvl that tlir !'iiiii|nvs>itiri i nrntial i iirvr haunt; il thru rk {' * ujj Thr \vtrk ff %rlL ' , EFFECT OF CLEARANCE in which the subscripts refer to the normal proper 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; I anil thi . t i without t lit 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 VOLUME OF THE COMPRESSOR CYLINI pressor to the plan* where it is to he used. The lo will ht k discussed under the head of the flow of air it should not he large, unless the air is carried a ] The loss of temperature causes a contraction of v ways: first, the volume of the air at: a given pressi as the absolute temperature; second, the moistu (whether brought in by the air or supplied in the < excess of that which will saturate the air at the lowes in the conduit, is condensed. Provision must draining off the condensed water. The method the contraction of volume due to the condensatio will be exhibited later in the calculation of a specia Interchange of Heat. --The interchanges of the air in the cylinder of an air compressor and th cylinder are the converse* of those taking place bctw and the walls of the cylinder of a 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 360 If thr will to- the rlraramr rxprrssrtl in uli ^ HI thr air i'- r\|rll'i! it i! is iirltvi'frt.1 I'IMII fill" I ilfflfifyv.Mt ill fiitfii it*. tiiiftf"f!:,SHit^ t . as i.ili ulatol, vJiriln i rra^nJ l?y m .un**M COMPOUND COMPRESSOR The work of compressing one pound of air fr p i to the pressure p' is n I The work of compressing one pound from the is n_ 1 M ( //> TF,= ll w - i I \p f l ) n - i\ \p' because the air after compression in the first c] to the temperature t^ before it is supplied to the and consequently p f v' = pj) r The total work c \_ | rif JL and this becomes a minimum when becomes a minimum. Differentiating with re| equating the first differential coefficient to zero, Three-stage Compress* iTfftiifvtl, as \\hnr air * to UM- ;t t whit h flu- aii' ' pa-^ vva\ frtni uiu* an* /, ami /, in way: Thr \vurk of iomjrr it**, ftil'il tt-iil'i iif ii FRICTION AND IMPKRKKCTION. 1 and l "._! Equations (206) ami (207) k*ad to from which by elimination we hav / and Sinrt* the temiH*rature is the sanu* at the ad of the three cylinders, the volumes of the eylr inversely proportional to the absolute pressures As with the compound compressors, this meth a 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< RATIO OF ACTUAL fe Piston speed, feet per minute . So 1 60 200 240 280 This table does not nor is the clearance fc EFFICIENCY OF COMPRESSION would be 2 but pjV t = p t v t for an isothermal change, and const w = ^ 10 ^; Some investigators have taken the work of isot! pression, represented by equation (214), as a basis o: for compressors, and have considered its ratio to the of compression as the efficiency of compression, together into one factor the effect of heating during and the effect of imperfect 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 : ARBITRARY EFFICIENCY OF COMPRESSI HYDRAULIC AiR-COMPRESSOl 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 Air-Pump**. *r* \ufti tin itM.tiii i tump, lilt- mri|,ii! *4 tft jr ?s liy tilt" f ftf tip. fit Mil J'.itfr irtil it i- 1 * t u*<ft*m.tr* ?*+ : DRY-AIR PUMP 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 pump. He also gives the following table of ratios o pump cylinders to the volume of the engine cyli discharging steam into the condenser : RATIO OF ENGINE AND AIR-PUMP C Description of Pump. Description of Engine. Single acting vertical Double-acting horizontal . Jet-condensing, expansion Surface- " " Jet- Surface- " " compound Jet-condensing, expansion Surface- " Jet- 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 770 If ih< an 1 tn i* ;,! / I ,, |!U t tli^ * i iti Ml ,!, n t ulltlrliNlHi* II CALCULATION FOR AN AIR COMPRE 85. J Lj.8s X 7 7;-- 2080 e 51.9 0.878 Assuming the air pump to be 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 37* If thr if thr r\|rnl "< *'*' the uir in ihr tlr-if^ 1 whivh ihr lUlfirira^n- /4^-l t \t H:) trVfilll!i' % Will tir thr i Mini*!"*"-'^ 1 *'* & tit > ii.: CALCULATION FOR AN AIR COMPRES! The calculation has been carried on for a simple but there will be a decided advantage in using a coi pressor for such work. Such a compressor should pressure in the intermediate reservoir X 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 H.r. {"fir !r!Sl]*f!4f?4l'r 4! ft' will !* i'^r ;>" I 4 '. a!ui**, FRICTION OF AIR IN PIPES which last term is obtained by dividing the a: by its perimeter. For a cylindrical pipe we ha m = ircd 2 nd = id . . The expression (215) represents the head of lie overcome the resistance of friction in the pipe w of flow is u feet per second. Such an expression be applied to flow of air .through a pipe when th ciable loss of pressure, for the accompanying inc necessitates an increase of velocity, whereas the ( the velocity as a constant. If, however, we cc through an infinitesimal length of pipe, for wh may be treated as constant, we may write for 1 due to friction P u 2 dl 2g m This loss of head is the vertical distance throu| must fall to produce the work expended in ove] and the total work thus expended may be founc the loss of head by the weight of air flowing tl It is convenient to deal with one pound of air, so sion for the loss of head also represents the wor] The air flowing through a long pipe soon '< perature of the pipe and thereafter remains at a < ature, so that our discussion for the resistance oi made under the assumption of constant tern much simplifies our work, because the intrinsic < remains constant. Again, the work done by t ing a given length dl will be equal to the work when it leaves that section, because the produa But tlu* vrlwifv f ;iir ian !> n Thr ai Irngth ill if pij 1 *-, anil work must lr tiihtT r f liriitl i> rtUiil lei thr Bui frttttt lli' * hir;u i FRICTION OF AIR IN PIPES But from equation (221) the velocity at the entrai where the pressure is p l will be WRT . rrr MI= __ and w so that equation (223) may be reduced to gRTm p, 2 Equation (224) may be solved as follows : The first two forms allow us to calculate eithi or the loss of pressure; the last form may be us< values of f from experiments on the flow through ] From experiments made by Riedler and Gut fessor Unwin f deduces the following values for f: Diameter of pipe, feet. 0.492 0.00435 0.656 0-00393 0.980 0.00351 with ;- ! ? - ,,,,,,, s . FINAL TEMPERATURE steam was used in it. The full line ah is a hypcrb line ac is the acliabatie line for a gas; both lines are dn the intersection of the expansion lines of the two dk Power of 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 v.th> .U' found bv thr r*juuiin if thr r\{;WMtn nit! if r\pitMsit>n fi in ** hit !i T, ;> ?hi ^ i*!i4 <, / r j. ?hr ,;* iiiil / i . th* !rn$|' :tt thf vijtjK I'M'*"- jtii'*Mtir tins in th i**f Ilfii ll t/ f l< 4 !h iii|* fin!* h 4 . il i * th*' frWJtiM"jJ< III In i'i ii mj t.tMa* in MOISTURE IN THE CYLINDER the walls of the cylinder of a 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 calculations. Moisture in the Cylinder. The chief disadvant use of moist compressed air and it is fair to a compressed air is nearly if not quite saturated whe to the engine is that the low temperature experie the range of pressures is considerable causes the i freeze in the cylinder and clog the exhaust-valves, cultv mav be overcome in Dart bv making the valves ar CALCULATION FOR A COMPRESSED-AIR EN 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 CUMi'KKSSX!) AIR 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 lurgrr, 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 ul.it 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 AIR 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 imperfections) W - 3 X 464-7 X 144 X 75 20520000 foot-pounds. I 394 4 lit If thr prrssiirr i% rrtliitri IM >i* j*ufnl." bv ttu- g.aii'i' before it usttl, thr voiumr of -iir will ! 75 * -|*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. C'HAITKR XXT. .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! tli.il the rritkmi le {irrAturr k M a , Air "Hit' general arwft^rmeRl i,itlBr ! t htMin tv i ; 'ii?. *. ft ttiftsf oi u. c.umju.mwu-<.,yuHu<-u /i, nu 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, tlt;KKATlM; MAl'WNKS is replaced ly .m app.ir.itti-. 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 (231) Were the compression also adiabatic the temperature t 2 could be determined in a similar manner; but the air is usually cooled during compression, and contains more or less vapor, so that the temperature at the end of compression cannot FIG. 8 7 . be determined from the pressure alone, even though the equation of the compression curve be known. RKrKI'ifcKATISti M.\* HtM-.S It* ihr nir paving through ihr tHstifrr.tting. machine p minutt* U* J/; thru ihr hr.si wiihtiruwn from ih? n>ttiroom Tht* work *f compressing -M {mimd* ui ur from the pre&urc to ihr prom i! re ft in *i fomprr^ur wjtltntsi ilriiraritr is (Fig, 8 W f - vll f p.r. * f it* || ^ ? f t t I* a '** I " * i Vlf "r I ir ii *. , * f .* . , , < s I \,f I Ihr In* fi 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; ~ I H -- 1 t w me auierence between the works of compression and expan- sion is the net work required for producing refrigeration; conse- quently or, replacing M by its value from equation (232), W = 2i *i + ^ Ji ~" V / t / 4 (237) (238) The net 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) Qi ^1 ~ ^4 (242) If the initial and final temperatures of the cooling water are 4O2 REFRIGERATING MACHINES tt and t t) and if <? and q k are the corresponding heats of the* liquid, then the weight of cooling water per minute is G - ^7. = <2t (t -oifo- gi ) ' ' ' (243) The 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 (246) 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 ; MAi JUNK til- of thr air rowing i'mm ih- uiit|rrs^t*r ami tlimU-r will l- /, - 7*4 - Ufo * Tltt- rortt Stif* . U VM; gitl from tfc .', /,a54l i i " ir tt }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. 11 of th f I 1 4 * t '1 ' * i IV" '* ^ ^-.'li * "- * .jo rittiic f?t, /, W If lilt* tlruriimr tf ll$r iiSll|*frw%t.if i yiiftt)rr i* of it 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 i 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 0.963, 100 \i4.7/ 100 which makes the piston displacement i\9o * 0.963 s= 1.97 cubic feet. If now we allow ten per cent for imperfections, we will get for the dimensions: stroke a feet, diameter of the 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 hr.il 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 thr 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 k This equation may be used because it is equivalent to the assumption with regard to entropy on page 121. The value of a is i for ammonia and 0.22 for sulphur dioxide as given on pages 119 and 124. As has already been pointed out, the vapor approaching the compressor may be treated as though it were dry and saturated, each pound having the total heat H 2 . The vapor discharged by the compressor at the temperature t, and the pressure p l will have the heat r ft f \ 4. IT p v i/ ' -^ r The heat added to each pound of fluid by the compressor is consequently c f (t, - t,} + H, - H v and an approximate calculation of the horse-power of the com- pressor may be made by the equation P = 778M \c v (t, - Q + H, - HJ 33000 or, substituting for M from equation (249), 7780 \c (t t } -{- H H \ 33000 (251) The power thus calculated must be multiplied by a factor to be found by experiment in order to find the actual power of the compressor. Allowance must be made for friction to find the indicated power of the 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 408 REFRIGERATING-MACHINES must be carried away by the cooling water per minute is co: sequently <2 2 = M (H 2 - ?1 ) + M\c p (t s - g + H,- HJ; where r t is the heat of vaporization at the pressure p r If the cooling water has the initial temperature t w and the fin temperature t' m and if q w and q' w are the corresponding heats the liquid for water, then the weight of cooling water used p minute will be If the vapor at the beginning of compression can be assum to be dry and saturated, then the volume of the piston displae ment of a compressor without clearance, and making N strok per minute, is D -^ (25 To allow for clearance, the volume thus found may be divid by the factor as is explained on page 363. The volume thus found is furtt to be multiplied by a factor to allow for inaccuracies a: imperfections. The vapors used in 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 minute. The heat of the liquid for water at 80 F. is 48 B.T.U., and the heat of liquefaction of ice is 144, so that the heat which must be withdrawn to cool and freeze one pound of water will be 48 + 144 = 192 B.T.U. If we allow 50 per cent loss for radiation, conduction, and melting the ice from the 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 N _ X 80 _ v feet 4io 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 table: t ti HP 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* ammonia. Absorption Refrigerating Apparatus. Fig. 89 gives an ideal diagram of a continuous absorption refrigerating appara- tus. It consists of the following essential parts: (i) the gen- erator B, containing a concentrated solution of ammonia in water, from, which the ammonia is driven by heat; (2) the con- denser C, consisting of a coil of pipe in a tank, through which cold water is circulated; (3) the valve V, for regulating the pressures in C and in 7; (4) the refrigerator 7, consisting of a coil of pipe in a tank containing a 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 It III ilir tiT%!b, $l i'f'iiiiiirf's, il ! flit ff*ft it it i' by ft Uf-j rfr nH4* lir-4 1u c4i ll rll| f B||*rf4iWfr f llir ,f %'a. 1 * it ill r4 ill*- ijf vhn*trf, 1 fitt flic 4 ir i %iii|rn *h<w for lite ci llt?lft .! |*fr-fjiifr *|lir$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. TABLE XXXVI. TESTS ON BELL-COLEMAN MACHINE. 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 : Steam-cylinder Compression-cylinder 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.: Headend Crank end Volume at admission, per cent of piston displacement : Head end Crank end Weight of air discharged per stroke, kg.: Head end Crank end Weight of air discharged per revolution, kg Calculation from expansion diagram : Absolute pressure at release, kgs. : Head end Crank end Absolute pressure at compression, kgs. : Head end Crank end Volume at release, per cent of piston displacement : Head end Crank end ._ . . Volume at compression, per cent of piston displacement: Head end Crank end Air used per stroke, kg. : Head end Crank end Air used per revolution Difference of weights, calculated by compression and expansion diagrams, kg In per cent of the former Mean weight of air per revolution, kg Elevation of temperature at constant pressure, degrees Centigrade. Heat withdrawn per H. P. per hour, calories I. 6 65- os 19.3 27.3 19.00 -47.0 2.263 2.230 I. OCXS 1.869 1.502 1.615 85.12 128.85 60. 10 3-35 2.82 0.53 1.04 0.783 0.765 6.15 8.50 0.2744 0.2716 0.546 1.32 1.45 1.14 1. 20 104.65 106.1 16.5 19.8 0.234 0.254 0.058 10.6 0.514 66.3 371 n. i.6 3 61.2 17.5 26.8 16.6 -47.0 2.336 2.294 1.861 1.825 1.589 1-594 82-35 118.55 56.12 3-25 2.83 0.42 1.04 0.788 0.749 S.os 8.41 0.2764 0.2742 0.551 1. 14 1. 19 104.7 106.3 16.0 rg.6 0.233 0.254 0.487 0.064 n.6 0.519 64-S 354 III. 2.92 63.5 19.1 27.2 19.1 -47.0 2-343 2.301 1.870 1.906 1.626 1.624 85.71 126.01 59-46 3-40 2.84 , 0.56" 1.04 0.764 0.765 6.03 7.91 0.2750 0.2730 0.548 1.33 1.46 104.8 106.4 16.6 20. 6 0.238 0.255 0.493 0.055 10.0 0.520 66.1 363 TABLE XXXVII. TESTS ON REFRIGERATING MACHINES. BY PROFESSOR SCHROTER. Number. System of the machine. Dimensions of the steam cylinder. Dimensions of the compression cylinder. 3 31 10 5<: 4 3. 8. ii Diameter of piston, mm. Diameter of piston-rod, mm. a a ! c/3 Diameter of piston, mm. Diameter of piston-rod, mm. eS I Linde. t Pictet. 37^-25 1? 330 45 55 -S 'if?' 68 800 602 740 poo 325 250 43 -ft # 4 54.0 420 poo 3 g 7 ' .. a::::::::::::::::;:: o I<J 12 Number. Revolutions per minute compressor. Indicated horse-power of steam cylinder. Indicated horse-power of compressor. Absolute pressures of vapor, kilos, per sq. centimeter. Initial temperature. 8_ u 'W In compressor during expulsion. In condenser. In compressor during admission. In vaporizer. 64.8 59-8 54.7 55-1 53.6 66.1 2.76 45-9 26.27 27.30 9-S8 9.31 13-66 2.50 2.64 4.85! 4'S5J 4.90 4-53 4.91 4-55 4-27} 4.8 3 J 2.63 3.24 0.82 1.03 ''S i. 06 ii. ip It. 2 II. 2 II. I III 10 15 10 I 10 15 10 3 3 * 4 s 59. i 2p,23 14.11 6 7 49.6 65.15 65.8 64.2 64.7 64.S 26, i 34-5 91.2 94-5 99.2 24.49 18.1 25-8 52.01 61.70 66.42 75.02 8.13 10.68 3-77 4.11 4-23 5-8i I3-78 7-87 10.41 3.22 3-5 3-62 S- ii 2.36 2.07 0-45 0.63 0.73 0.67 8. ....... IO ......... 12 Number. Ice formed. Temperature of water or brine cooled. . ' t Temperature oi water supplied, degrees C. Per compressor horse- power, per hour, gross, kilos. Per compressor horse-power, per hour, net, kilos. At entrance. At exit. i -a , 9.0 8.3 34.8 3i-7 -~4-4 5-9 li. ip II. 2 II. 2 II. I 9.5 18.2 IO.O 9.7 6. 05 4.4 S.9 a-95 2,38 9.24 4.71 9.97 =^ 3 IO.O -9.7 6,05 6 .... ... . . 7 . . ... 1 Q "3 ir.s ii. 3 ii. 3 16.8 25.0 28.2 20. 6 15-2 22.6 25.9 I8. S 10 II 12 the data and results of tests on three refrigerating- machines on the Linde system using ammonia, and of a machine on Pictct's system using Pictet's fluid, all by Professor Schroter. The tests on machines used for making ice were necessarily of considerable length, but the tests on machines used for cool- ing liquids were of shorter duration. The cooling water when measured was gauged on a weir or through an orifice. In the tests 3 to 6 on a machine used for cooling fresh water the heat withdrawn was determined by taking the temperatures of the water cooled, and by gauging the flow through an orifice, for which the coefficient of flow was determined by direct experiment. The heat withdrawn in the tests 7 and 8 was estimated by comparison with the tests 3 to 6. The net production of ice in the tests i and 2 was deter- mined directly; and in the test 2 the Ioss 4 from melting during the removal from the moulds was found by direct experiment to be 8.45 per cent. By comparison with this the loss by melting in the first test was estimated to be 7.7 per cent. The gross production of ice in the refrigerator was calculated from the net production by aid of these figures. In the tests 9 to 12 on the Pictet machine the gross production was determined from the weight of water supplied, and the net production from the weight of ice withdrawn. A separate experiment on the machine used for cooling brine gave the following results for the distribution of power : Total 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* gr.ir . . . . . 16,6 " ** grar, ami puwj . In t.sHH comparative* tr*r %trrrc made !y i*rtilr,Mor Schrfitc tm a Ltfifir and on a i*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 tf if, i y 8 MI |S 44 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 TESTS ON RKFRIGERATING-MACHINES. By Professor M. SCHKOTER, Vergleichende Versuche an Kallemaschinen. Piclet machine. One vaporizer. I II III IV V Steam-engine : S7-o 21. 8r 16.82 0.771 3-99 1.47 6.10 3-o8 0.850 6.09 3.03 6. 1 1 3 os 9-fiS 19 72 IS.J 9-57 19.71 9.67 IQ.7I + 0.6 3S07 56.8 20.88 16.10 0.771 3-9t 1.05 1.96 4.98 0.847 2. 02 4.99 2.O4 4 .08 9.6O 19.70 15.6 9.64 19.72 9-S7 19.64 + 0.6 2SS6 57.1 18.75 14.26 0.761 3 84 0.68 9.92 13.01 0.845 9.91 T2.9I 9-94 12.88 9.61 19.59 16.8 9-58 19-37 9.61 19-35 +0.4 1852 57.6 15-93 11.83 0.743 4-25 0.17 17-93 20.96 0.841 18.00 21. OO iS.OO 21. OO 9.68 19.51 l6.7 9-68 I9'52 9-73 19-59 -1-3 1075 59.3 27.56 22.91 0.831 6.39 i.5 2.04 5.01 0.846 1.99 5.02 2.05 4.96 9.68 35-i8 18.6 9.73 35.o8 9.72 35-01 + 8.9 1708 Compressor : Mechanical efficiency Pressure in condenser, kilograms per square Pressure in vapomer, kilograms per square Vaporizer : Mean temperature of brine, entrance . . Mean temperature of brine, exit .... Initial temperature of brine, entrance . . Initial temperature of brine, exit Final temperature of brine, entrance . . . Condenser : Mean temperature of 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. Steam-engine: 44.9 18.14 15.53 0.856 9-S2 3-8p 6,00 a 89 0.850 5 9 2,89 S-97 2.94 9-5*5 19.76 9-S6 19-74 9-S7 19.74 1.8 4308 4S.I 18.26 15.20 0.833 9-34 3. 95 2.02 5.02 0.846 2.05 5-02 2.04 5.04 9. 54 19.63 9-SS 19.42 9-S4 19-45 1.8 3182 45-1 17-03 14.31 0.840 9.00 2.13 9-99 12.91 0.843 9-95 12.94 9-97 12.89 9.61 19.84 9.61 19.82 9.60 19.89 1.9 2336 44-8 15-70 12.63 0.805 8.89 1.56 17.92 20.82 0.840 17.97 20 . 83 17. 96 20.83 9.61 19.72 9.64 19.79 9 -5$ 19.88 2.1 1711 4S-o 24.41 21.86 0.895 14-03 a.95 2.03 5.01 0.845 2.03 5.00 2.03 5-01 9.68 35-33 9.68 35-45 9-65 35-44 + l 2O2* Compressor : Mechanical efficiency Pressure in condenser, kilograms per square Pressure Jn vaporizer, kilograms per square Vaporizer : Mean temperature of brine, entrance . . Mean temperature of brine, exit .... Initial temperature of brine, entrance . . Initial temperature of brine, exit Final temperature of brine, entrance . . . Condenser : Mean temperature of 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 Kl' HilUI'KATIMi MAt'IHNtCS 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 tmrra.nr 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 increased. TABLK XXXIX. TKSTS ON AMMONIA RKFRKJKRATnSTG-MACHINR. By Professor J. 1C. DKNTON, Trans. Am. .S'c. Mcch. Kngr., vol. xii, p. 326. 1 II in IV Preatuira above ntnionplmrn, poiuiibi por Hqunro lunh : Iftt aH H.a ay ,H7 Temperature, dugrucm Fnlirnnholt : jH.80 ao^ a .ao 38.4? ,|,| .6^ 0.6*f S4 ,OO outlui ...,,,,.. ,.,,,,...... 8? ,ftft ^,4' Hi ^6 Ba.86 Jack^t-wtvtart Inlaid, ,..,.,,,., ,..,,..,..... ,\,\ ,6 j <s6.7 S*t J t .0 ^y .a si? irf 313 a 60 ttnterl UK tutndonBttr .,,.... 910 108 Brino, paumlN per inhiuCw, . , . aaHi tua H Specific ntutt.. ,....,.,..,...,,,.,..,,.....,........, o.Ba a. To 0.78 Q*?H T4-6H 16.67 aH.ia from <H>fii]>rti;ie>r clinplm'iHmwi, , Heat aooount, H.T.W, per minute ; 14776 918^6 HH^4 97800 351:8 140 tAT ift? 6oK 6^6 jHa rtH a;o Total t.ako.n from tumiHwin., jH*> (a 10160 108 s^i 18017 3. c Power, ota. : 17.88 sB.Sy H<(.tt 7' 7 7t .d 8 .6 OB. 7 54 7 <i*O, A Tr t a O.Ht o,tt,i IM Q.HI Kefrigerativo lfot: 74.8 3^^J 44.64 74. "j6 B.T.U. abBtraatfed from brine pnr nriKjwr minute . 74 34 . I 107 14. x 97 106 aj , ^7 Table XXXIX gives the data and results of tests made by Professor Denton on an ammonia 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 tli.tl 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 ilii.fi 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<| hr.it ffi*fll llir I'Cllf ttl ihr MRintuttU. W-ii'J ilrlrfltiillrrf |.% slifn I r%|*rlllt"fit, SEVEN DAYS' CONTINUOUS TEST, SEPT. 11-18, 1888. fGenerator I S-77 Average pressures! above atmosphere^ Cooler inlbs.persq.in. [ Abgorber 23 . 4 Atmosphere in vicinity of machine ... Generator 2 7 2 ^ . (I nlet 2I ' 2 Bnne {Outlet 16.16 _ , (Inlet S4i Condenser Qutlet 8o Average tempera- j let _ _ 8o tures in Fahren-< Absorber JQ ^ ' ' II;t heit degrees. rU ppe r outlet "to generator .... 212 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 " * 20 432 KKKKlM-'KATINli-MAl'ltlNKS brine chilliti am! th- M4titK w.tirr usetl were measured with mt'tfis, which were afterwards ie>ir*t umler ihe conditions of the exjK'rimem. It k intcrrsiing uftmiwr** tlu* rrfrirraiivr rflrris expressed in. pitinei.s l kr IHT jHumtl *! ru4l. On ilir* lianU ihr c machine Iralttl by !*roCrvor t**ntn h;t.-* an atlvanuigc of * tow ' 1 1 j jwrf ft'fll, But lilt's tttirffift i realty unfair to the on machine, for if steam -nt^ine ii <i vat met I IM re<|utre a ronsump- tion cf three jKUintb f *'al l^'f hr-* jH%vrr JUT hour,, while the calculation fr tin* al?ir|>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, CHAPTER XVII. FLOW OF FLUIDS. THUS far the working substance has been assumed to be at rest or else its velocity has been considered to be so small that its kinetic energy has been neglected; now we are to consider thermodynamic operations involving high velocities, so that the kinetic energy becomes one of the important elements of the problem. These operations are clearly irreversible and conse- quently the first law of thermodynamics only is available, and if any clement of computation involves reference to equations that were deduced by aid of the second law, care must bo taken that such computations are allowable. It Ls true that all prac- tical thermal operations are irreversible for one reason or another; for example, the cycle for a steam engine is irreversible, both because steam is supplied and exhausted from the cylinder and because the cylinder is made of conducting material. But all adiabatic operations in cylinders (which serve as the basis of theoretical discussions) are properly treated as reversible and all the deductions from the second law may be applied to that part of the cycle. In particular the limitations of the discussion of entropy on page 32 have been observed. Three cases of continuous thermal operations have been discussed (i) flow through a porous plug, (2) the throttling calorimeter, (3) friction of air in pipes; to which it maybe well to return now. In all, the velocity of the fluid has been so small that its kinetic energy was neglected; in none of them was any reference made to equations deduced by the aid of the second law of thermodynamics. Rather curiously, all the operations were adiabatic, using the word to mean that no heat was taken from or lost to external objects ; in the case of transmission of air in pipes, this comes from the natural conditions of the case 423 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 (257) If the difference of pressure is due to a difference of level or head, h t we have p l p^ - hd, where d is the density, or weight of a unit of volume, and is the reciprocal of the specific volume; consequently equation (257) reduces to *, (258) ft us which w lh* iMi small orituc. Flow of i\r Thr imrititu mrrgy of u unii of which clrprrol* only * ilir tt.fniiituft tf the ;aH and not on that flint* takrn *r uy lair filtfr, The flow f 'A grt' llirf-t'ltifr li-j *tnr-i ' rf -I'v jv s 5 - J|f * S thin plut* if is i M--.jMin.il % }. -** 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$f moi<ir. If iliii ti ill JWfiiifi C^5*l' SO i* * _s '?' I "" JV > | , | * *' 9 - "*u v-vjwu.i.iv.u. 1110, y cUSU UC UCU.UC.eCl JLOf work of air in the cylinder of a compressed air motor (Fig. 91). The work of admission is A v i> tne wor k of expansion is by equation F ' G - " (81), page 65. to. and the work of exhaust is so that the effective work is iV,' * 1 1 which is readily reduced to equation (261). For the calculation of velocities it is convenient to replace the coefficient p t v^ in equation (261) by RT V since pressures and temperatures are readily determined and are usually given, thus 7 2 p If the area of the orifice is a, then the volume discharged per second is aV, and the weight discharged per second is aV w = when v 2 is the specific volume at the lower pressure and is equal to H.oW !' H I* from npuiiMit I^,H ani i', from anc miming " " j;, v 1 1. Thr rqualitms tlrtltitrti for iltr tlmv nf air apply la the flov from a largr i-ylimlrr r rrsrrvoir ifii. .1 nuitl straight tub through at r*umlrl rilur, Thr l\vrr |n%>airr i iht premtm in thr small tuU* ;uul tiitf*'^ itutrrt.tUy from llir |*rrs*urt' af thi (4jtir int witii It ihr hjU- iiwy Mivrr, In tr|rr that tht? to shall mil U* inu* It ullninl In fri. iitn ii|f,.iiti-4 ihr s?i of thi Hib- it *hmthl In- *h*rt mi mir llt.nt mt r r iv\ii r tUtHametet Thr flow cU-t Mii .t||-,if ! U- ;iln tr*I 1> iiwkiiig the tub vwy shrl, ami sSir ili-rn- of mutitUtiK i- mi imixtrtnnt; th i*c|Uti(rbi fr Ihr lUw f iilj ir anl -iram nwy b* appliet with it fair ttt'tcrrr tf Ap|n>\imitit*n ! ntiiitr.-. in lliin filtto am It* irrri*iii;ir uriiwt*. i*rIr-i-Mr Flw-gfii-r * mat|* 4 I*iri* numU-r *f rs Iliw f uir from n rr--fv**ir into ih- iiiMit'|itirfr, with in Ilir rr*rrvoir vdiytnu ttnm J4-*M IMW. f m-r wry to 3366 mn Hr iiM'il two tliilrrrnl unfit r*, ur -i.tiHs; iilttl tltr clhrf 7,314 mtt III liiiilttflrr, tmlh Writ runt*-l Hi tlw rlllriilirr, fir fiHifiti ihr prr-viun- i ihr r$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 /** II. pressure .less than twice the atmospheric pressure Fliegner found the empirical equation iv = 0.96440; 4/W v* - A.) (266) where ^ is the pressure of the atmosphere. These equations were found to be justified by a comparison with experiments on the flow of air, made by Fliegner himself, by Zeuner, and by Weisbach. Although these equations were deduced from experiments made on the flow of air into the atmosphere, it is probable that they may be used for the flow of air from one reservoir into another reservoir having a pressure differing from the pressure of the atmosphere. Fliegner' s Equations for Flow of Air. Introducing the values for g and R in the equations deduced by Fliegner, we have the following equations for the French and English systems of units : French units. t > 2p a , 10 = 0. t < 2p a , W = 0.7900 a (Pi - Pa} English units. pt > 2p a , W = 0.5300 Pi < 2 A> w - p l = pressure in reservoir; p a = pressure of atmosphere; 7\ = absolute temperature of air in reservoir (degrees centi- grade, French units; degrees Fahrenheit, English units). 430 In thr Knj?U*h 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. dynamic's. 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 s * %-pi, r lir it- In wttltli llir vrlmitv i* 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 x,r I'JU 4. T, X rp "I" * 2 the acceptance of this method infers that the flow of steam through a nozzle differs from its action in the cylinder of an engine in that the work done is applied to increasing tho kinetic energy of the steam instead of driving the piston. Values of the 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 w (268) The equations deduced are applicable to all possible mixtures of liquid and vapor, including dry saturated steam and hot water, In the first place steam will be condensed in the tube, and in the second water will be evaporated. rm'pUu'lr, anil ruinr* f* IT**!, ihr i-tin>:> f iiuiim will U? turned into hr.it ;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 oriiitr. 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 .t 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. Fr 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 FLOW OF SUPERHEATED STEAM rOO on the flow of steam, and that when the pressure is less than that required by the formula the flow can be represented by a curve which has for coordinates the ratio of the back pressure to the internal pressure and the ratio of the actual discharge to that computed by the equation on the preceding page. The following values were taken from his curves : Ratio of back pressure Ratio of actual to computed discharge. to internal pressure. Converging orifice. Orifice in thin plates. 0-95 o-4S 0.30 O.QO 0.62 0.42 0.85 -73 o-S 1 0.8o 0.82 0.58 Q-7S 0,89 0.64 0.70 0.94 0.69 0.65 0.97 -73 0.60 0.99 0.77 o-55 0.80 o.45 0.82 0,40 0.83 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 2 = cdt The accompanying equation for finding the quality of steam x 2 is r cdt + it. 4. - *i 4. o J ~7p ~r ~r i j, T- 2 A * * i * 2 Here ^ and T are the thermometric and the absolute temper- atures of the superheated steam, t l is the temperature of saturated steam at the initial pressure, and / 2 the temperature at the final 434 pressure. ami the letter. r, and r f and I 1 , ami <i, represent the t: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 nov.ir w i> very high, rraihinj; #!<*.* fn-s Hi*- velmity tf air or steam h a i.it|*r iiiieremr in %r mul in \riir fi rtotjiirrttiy the enV* t of friitinn K mailed even* in short tuba by Iliii liitrf * tit* sit straight tuhe j,i long ami o.t5X of an in h internal diameter, under an pressure of t'l'j jMiund** to ihe *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 FRICTION HEAD 435 the cone may be one in ten or twelve; this will give for the total angle at the apex of the cone 5 to 6; if the entrance to the nozzle is not well rounded there will be a notable acceleration of the steam approaching the nozzle and this acceleration outside of the nozzle appears to diminish the amount of steam that the nozzle can deliver. The expansion should preferably be suffi- cient to reduce the steam to the pressure into which the nozzle delivers; otherwise the acceleration of the steam will continue beyond the nozzle, but the steam tends more and more to mingle with the adjacent fluid through which it moves, and a poorer effect is likely to be obtained. If the expansion in the nozzle is not enough to reduce the pressure of the steam to (or nearly to) the external pressure into which the nozzle delivers, sound waves will be produced and there will be irregular action, loss of energy, and a distressing noise. On the other hand if the expansion in the nozzle reduces the pressure of the steam below the external pressure at the exit, sound waves will be set up in the nozzle with added resist- ance. This latter condition is likely to be worse than the former, and if the pressures between which the nozzle acts cannot be controlled it should be so designed as to expand the steam to a pressure a little higher than that against which it is expected to deliver, allowing a little acceleration to occur beyond the nozzle. Friction Head. - In dealing with a. resistance to the flow of water through a pipe, such as is caused by a bend or a valve, it is customary to assume that the resistance is proportional to the square of the velocity and to modify equation (258), page 425 to read where C is a factor to be obtained experimentally. The term containing this factor is sometimes called the head due to the resistance or required to overcome the resistance, and the equation may be changed to Kl.ti\V A' it bring understood ikti of the available head A, a certain portic A* ij. UM'd | in 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, BUCHNER'S EXPERIMENTS 437 (3) The reaction of steam escaping from a nozzle or an orifice may be measured. (4) The jet of steam may be allowed to impinge on a plate or curved surface and the impulse may be measured. (5) A Pitot tube may be introduced into the jet and the pressure in the tube can be measured. Of course two or more of the methods may be used at the same time with the greater advantage. It will be noted that none of the methods alone or in combination can be made to determine the velocity of the steam, and that all determinations of velocity equally depend on inference from calculations based on the experiments. Formerly the weight of steam discharged was considered of the greatest importance, as in the design of 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 * o.ij All thr rttu'u'tr* It4l ; iviffuirit.il ffiit fur whit h thr hmfj !* givrii in thr itl*v* uMr *m fading ihr t'Mumiing ai rntraai lifiii-'i thr jJkiMtirf ,ii ilir fhr<nit 4tii !||-,ir- in h*ivr had consi fl'14r tnllurflir tfl ihr 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 Bt)CHNER'S EXPERIMENTS 439 results. The discharge was also computed by GrashofPs equation on page 432, and the ratio to the actual discharge is that set down in the table ; the variation from unity is not greater than the probable maximum error. The method of the compu- tation of velocities at throat and exit by the experimenter is not very clear, but it was made to depend on the equation (268), using the proper pressure and the discharge computed by GrashofFs equation. TKSTS ON FLOW OF STEAM. Du. KAKI, BifcriNKR. Numlxsr and designa- Prewmre IKIU ids ulwolulc. itUio of hrtmt to initial. charac pouncm Ratio of actual in com- putecl Velocity it thrtmt Velocity at exit. Ratio >f actual to com- putcd tion. Initial Thnmt. Kxll. Hxirrnul Hcctmil. din- charge. velocity. I-2E l3 104.4 a 5. 3 n.fi 0-573 0-0503 i8eo 3030 0.928 a-aa 160.5 9 j . 4 ai.7 y'.6 0-577 0.0449 jf {S 179 3030 0.930 3~aa 147-3 83.0 20.7 *3-8 0.564 0.0411 0* l820 a ggo 0.926 4-2 a 131 .3 75' ' 18.5 0.572 0.0370 1790 aggo O.cpg S-aa 117.1 6*7 . 6 16.8 13.8 0.577 0.0331 1780 296 0.925 33-2!) 180.2 ga. t 16-5 14. t 0.511 o . 0494 1940 3260 0.930 __. 140-0 76.8 91.2 13.6 0.529 0.0394 1860 3060 0-957 37 _ 3 a 131.5 70.4 10-5 13. 8 0-S3S 0.0363 *&3 *& 1850 3020 0.950 3 8-3a "5-7 62.0 17.4 13-8 0.536 o.oaig d d 1850 3020 0.944 39-3!) 183.6 99.6 _ 18.5 0.541 0,0501 ,,. 1830 51 0.987 __. 103,0 68.6 38.1 IS -4 O.66o 0.0481 1550 2 1 go 0.932 43 -5 b 89.3 S-7 32.8 14.9 0.658 o.o4tg ao w 58 o S 1 SS 2180 0.932 43 -5 b 75.3 49-3 27.9 14.7 0.656 0-0343 &> S o 1560 2150 0.923 44-5 b fil .0 37.6 33.3 14-5 0.643 0.0283 H 1560 2160 0.939 4S~Sb 4S-4 23.0 16.9 14-5 o.6t8 o.oait 1630 3130 0.933 47-Sc 102.5 65.4 __ 15.0 0.637 0.0549 1630 2520 0.937 48-51- 8.8 SS 7 32.3 14. H 0.635 0.0410 * w 1630 M 53 0-931 74.2 46.9 l8'5 14.6 o , 63^ 0.0344 S 3 8 1620 2530 0.935 5~Se 50 -a 37-1 14.9 14.4 Q.62J 0.0277 W 1. 1630 2490 0.933 The nozzles 30 and 3?? had tapers of 1 17.2 and i -.4.9 which were probably too great, so 4hat they may not have been filled with rni ti ferrf,,-* ' > 'I } ! > I !,%> ^ t'M'iiS strum; thi> might aacmni for tw- small ratio of thr throat to t! initial |imsMirr; the- m/./!r st* t whn h ha>i .1 taj*rr uf 1:13, al .show-* a small ratio ot' throat to initial |n-^.tjf', Tlsr moot 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 tlflftcfl*4-f, * -*^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 ROSKNHAIN'S EXPERIMENTS 441 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. Sj.o 135 105 75 45 61.5 Ratio, o . 606 0.585 -550 0.546 Calculated Veloc- ity at Throat. 1407 1448 1504 Stodola's Experiments. In his work on Steam Turbines, Professor Stodola gives the results of tests made by himself on the Jlow of steam through a nozzle, having the following proportions: diameter at throat 0,494, diameter at exit 1.45, and length from throat to exit 6.07, all in inches. The nozzle had the form of a straight cone with a small rounding at the entrance; the taper was i :6.37- Four side orifices and also a 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- su-.im i-rrvurr wa, * ontrolled U'' liui ihn.- w.i* -, t iur numtUR under similar ,-unliii"n- a ihrottlf-vaUr. It - I't A Ihc -.IMHI PRESSURE IN THE THROAT 443 a direct calculation cannot be made, but a curve can readily be determined from which the pressure can be interpolated. The velocities corresponding to these pressures have been taken from Rosenhain's curves and the velocities were calculated also by the adiabatic method. Since the diagrams in the Proceedings are to a small scale the deduction of pressures from them cannot be very satisfactory, but the results are probably not far wrong. The table on page 442 gives the coefficient of friction obtained by this method. Lewicki's Experiments. These experiments were made by allowing the jet of steam to impinge on a plate at right angles to the stream, and measuring the force required to hold the plate in place; from this impulse the velocity may be determined. It was found necessary to determine by trial the distance at which the greatest effort was produced. One of his nozzles had for the least diameter 0.237 and for the greatest diameter 0.395 of an inch or a ratio of 1.28, which is proper for a pressure of 80 pounds per square inch absolute. His experiments gave the following results as presented by Biichner: Steam pressure 77 99 108 Ratio of computed and ) . 96 0.96 0.955 expt. velocities ) y * yoj Coefficient of friction . . . . 0.08 0.08 0.09 These experiments like those for reaction are liable to be vitiated by expansion and acceleration of the steam beyond the orifice. Pressure in the Throat. Some of the tests by Biichner show rather a low pressure in the throat of the nozzle, but in general tests on the flow of steam show a pressure in the throat about equal to 0.58 of the initial pressure provided that the back pres- sure has less than ratio 3/5 to the initial pressure; this corresponds with Fliegner's results and should be expected from his com- parison with molecular velocity on page 430. The following table gives results of tests made by Mr. W. H. Kunhardt * in the laboratories of the Massachusetts Institute of Technology: The excess of the throat pressure above 0.58 of .the initial * Transactions Am. Soc. Mech. Engs., vol. xi, p. 187. 444 ,,,,.,.,...;' fur flu* 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 j.s-<a* |* Iwgf, J > -1 3 *- i 5 li ! * " l! 'H i > w * V.* 14 ., n ) I , t* * < I fat ">'* 8s I *, , t ! * ''"' 1 * i . * * ;**' *' i ii. . .- $ j ' i . * s , * . * t ' * ''-t% is* f" 1 * sf 5 1 4 * ** * ? M 5 % , *l I r- w^ 44 5 * 6 * S 4 i* a 1 a- . i 4n S8f* * s i * 5fc .' H -; *.! WS ; l*, in i *J tutMivrr 150 I*V Till* tiii'tittft! of *ft i irnt lo J al 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 DESIGN OF A NOZZLE 445 The quantities just obtained are the amounts of heat that would be available for producing velocity if the action were adiabatic. In order to find the probable velocity allowing for friction, they should be multiplied by i y, where y the coeffi- cient for friction may be taken as 0.15 for the determination of the exit velocity V v As for the throat velocity, there are two considerations, the frictional effect is small because the throat is near the entrance, and all experiments indicate that orifices and nozzles which are not unduly long deliver the full amount of steam that the adiabatic theory indicates; therefore we may make the calculation for that part of the nozzle by the adiabatic method. The available heats for producing velocity may there- fore be taken as 434 and (i 0.15) 288,5 245, and the velocities are therefore (see page 436) K s - ^644 X 778 X 434 1480. K 8 - V644 X 778 X 245 - 3500. The quality of steam in the throat is ^ 3 - # a r, + r 3 - 855.1 + 885.9 - 0.967. To find the quality of steam at the exit we may consider that if x 9 f is the actual quality allowing for the effect of friction we have + 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 44 144 The iJiami-tm art-, M.l'Il'S 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 0,0597 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; 175,1 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 CHAPTER XVIII. INJECTORS. AN injector is an instrument by means of which a jet of steam acting on a stream of water with which it mingles, and by which it is condensed, can impart to the resultant jet of water a sufficient velocity to overcome a pressure that may be equal to or greater than the initial pressure of the steam. Thus, steam from a boiler may force 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 447 4- Ki lks through ihr Jnilurmv t* ^r.tviiy, A /I///MJC injrrtor hm a a dt'virr for making a uutiuw l ilr.iw tvairr frmn a reserve 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 lli.il 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 f THEORY OF THE INJECTOR 449 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 A. 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 V ' 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 have y ~ (2 450 IStH'luKs 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 I 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 THEORY OF THE INJECTOR 451 For practical purposes we may calculate the weight of water delivered per pound of steam by the equation y = (270) This equation may be applied to any injector including double injectors with two 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 loss. For example, if dry steam is supplied to the injector at 120 pounds by the gauge or 134,7 pounds absolute, if the supply- temperature of the water is 65 F,, and if the delivery-temperature is 165 F., then the water pumped per pound of steam is 867.?; f -p -i :.-;\ .-.<...*!.. ..... .. V ft 10.5 pounds. From the conservation of energy we have been able to devise an equation for the weight of water delivered per pound of steam; from the conservation of momenta we can find the relation of the velocities. The momentum of one pound of stearn issuing from the steam- nozzle with the velocity V t is K, + g', the momentum of y pounds of water entering the 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 |r.it 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$*|llS *ii llif *w5f i- VELOCITY OF THE STEAM-JET 453 sized by Roscnhain's experiments, the steam will expand and gain velocity beyond the nozzle, if it escapes at a pressure higher than the back-pressure. For an injector this last action is influenced by the fact that the jet from the steam-nozzle mingles with water and is rapidly condensed. Some injector makers use larger tapers than those recommended in the preceding chapter for expanding nozzles. The throat pressure may be assumed to be about 0.6 of the initial pressure; with the informa- tion in hand it is probably not worth while to try to make any allowance for friction. The calculation of the area at the throat of a steam nozzle by the adiabatic method will be found fairly satisfactory; the calcu- lation of the final velocity of the steam will probably not be satisfactory, as complete expansion in the nozzle seldom takes place, but it is easy to show that the velocity is sufficient to account for the action of the instrument. For example, the velocity in the throat of a nozzle under the pressure of 120 pounds by the gauge or 134.7 pounds absolute is {2 X 3 2 -2 X 778 (867.5 - 0.967X894.6 - 1430 feet per second, having for x z 7' / f \ T # 9 . ~a./-o. + <9 t ~- # 2 J = ~- (1.0719 + 0.5032 0.4546) - 0.967, provided that p 2 - 0.6^, 80.8 pounds absolute. If, however, the pressure at the exit of an expanded nozzle is 14.7 pounds absolute, then (1.0719 + 0.5032 0.3125) 0.877, and J-439 bX 32.2X778 (867.5-0.8775X966.3+321.1-180.3)}* 2830 feet per second, 454 INItttTUKS whirli U nearly fwirr ttu! j-.i c.tlrui.itn) fur ihr \T|K ity at the jimultr.Hl SIT lit n uf ttu* *4r,ifti .'/ tr. Sin* r thrrr is usually vacuum Ir)inl thr ?lr;un m*v.!r, ihr ttruil -.fr.tm velocity fe Ukrh to tr otnnitlrralijy Urgrr, luil ffni-. Mi|$tirt| iriucity will Millar ft n r*j4,iii|* ihr t)yrunu< -* *l ihr .. Velocity of Entering Water. Thr \rlnt iiy f tht* water in ihr t'tintliililrill Illfw whrrr tl titin^Ir^ wilh ihr 'tr;m 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- s 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 SIZES OF THE ORIFICES 455 V 2 X 32.2 X 5 = 18 feet. It cannot be far from the truth to assume that the velocity of the water entering the 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 - 62.4 , , = 305 feet. Now the velocity of water flowing under the head of 305 feet is V2gh Va X 32.2 X 305 = 140 feet per second. The velocity of steam flowing from a pressure of 120 pounds- by the gauge through a 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 losses. Sizes of the Orifices. From direct experiments on injectors as vrell as from the discussion in the previous chapter, it appears that fhr quantity of 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 fi whrrr T i lisr %-rl** sH In i llir H llir iPfriftif *f 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 SIZES OF THE ORIFICES 457 In trying to determine the size of the orifice in the delivery- tube we meet with two serious difficulties; we do not know the velocity of the stream in the smallest section of the delivery- tube, and we do not know the condition of the fluid at that place. It has been assumed that the steam is entirely condensed by the water in the combining- tube before reaching the delivery- tube, but there may be small bubbles of unconclensed steam still mingled with the water, so that the probable density of the heterogeneous mixture may be less than that of water. Since the pressure at the entrance to the 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 w (274) for each pound of steam mingles with and is condensed by y pounds of water and passes with that water through the delivery- tube; w t as before, hi the number of pounds of water drawn from the reservoir per second. For example, let it be assumed that the actual velocity in the 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 458 INJECTORS clear water the diameter would be only 0.183 of an inch; this i to be considered rather as a theoretic minimum than as a prac tical dimension. 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 ifir r *;f ill llir 1 iflC lift* llf. placed higher than the reservoir a special device is provided for lifting the water to start the injector. Thus in the Sellers' injector, Fig. 92, there is a long tube which protrudes well into the 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 th.il 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 SELF-ADJUSTING INJECTORS 463 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- pipe. 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 -.i.it 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 vwlv itir ilrlilrfy llllr lil'th 'brrr is al.M a slit] ifi<l an ovfrflttf wi*l* rt*' *>wI iiwkrs n varuut y ul* wmlrr utt tonclitionH; til i lulir ml *MI in llw m "tlir %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 INJECTORS 465 SU annular >tr;tm no<v.h- /, .nul ihr annular tlrliviT rounding ilu- iio^-lr i. Thr proportion*, art- MU h that the lifti ran always prtHlwr a in lion in ihr fm{ pipr r\rn when the: is a UiM'hargr fr*ni thr main *>lram mwlr, ami it is this fa, that rM;tMi.hrs tSir fr?4 4 tiling fi'.iiitrr, Whrn tin* 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 EXHAUST STEAM INJECTORS 467 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 boiler-pressure. 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. 966.3 180.3 113.0 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 pressure 0.6 X 14.7 = 8.8 pounds. This will givr f 954,6, ! " * ' I t *"* *' ^* "'ijj *4/" ihr wltH'iiv 4 ihr water riitrfing ihr rnmbining Itiiir will givr for ihr \rtti!y<f lltr |r! in ihr ttt$Itt ing- tube \\ " ?l "' *"' I i' frrl, I t j,tj llib vrlw-'ily i** rtjuivalrni in iSi.il ^trtfliiirtl ly \\ t*!tllr |rrssur( til !*'...' f4 -'^ l(5 f4. 4 * >44 imitndft atM*iiilr of a 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*w.lr 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 WATKR-EJECTOR 469 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 (// + *); v Substituting In equation (375), "i -\- yVx -* Vll It is evident from inspection of the equation (276) that y may be increased by Increasing x; for example, by placing the injector above- the level of the reservoir HO that there may be a vacuum in front of the orifice A, _, If the weight G of water is to be lifted per second, then- pouncls IKT second must jmwt the orifice A, G pounds the apace at JV, and ft 4- -) G pounds through the section at 0; which, with the Hevcral velocitiw* v, v v and v,, give the data for the calculation of the required areas, PROBLEM. Required th calculation for a water-ejector 47 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* f. 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; frrt, The ili4iinirr"s Mtrrr^)*tintifl^ I** Stir vritw -. i- am) r i t| ti.iS *( ft ill* It; tl s t.i,0 *f silt int. It, Thr afrit *i ? i f iiftiniliif (tm, having tltr ^nM 0,4 of u inrti, Ejtctor. - Whrn flu* rj itir t% isrl fur 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 EJECTOR-CONDENSERS 471 Ejectors are commonly fitted in steamships as auxiliary pumps in case of leakage, a service for which, they are well fitted, since they are compact, cheap, and powerful, and are used only in emergency, when economy is of small consequence. 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. CHAPTKR XIX, 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 *< IMPULSE 473 and such a head will give a velocity of V Vs x 32.2 X 376 = 156 feet per second, But so great a hydraulic head or fall of water is seldom, if ever, applied to a single turbine, and would be considered inconvenient. One hundred feet is a large hydraulic head, yielding a velocity of 80 feet per second, and 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 STKAM- I't'KlitSKS /* f < ; A 1 I/* li'J U im(>ortant io keep flrarly in mind that we are dealing wil vrlinily* flutnge f 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* r n. Tltb furcr in one %rr*fti will m**i.e the dittamr i* feet and w tin ihr work '* .ft* fli / 1 I I 1 , , , (37. * * * ' 1 7 footjxnmth. Since the vane would "** move heymd the of the ji it would he neie^-wiry, in *fder to *Iii4tii Mntinuoitii action on mtitor, it* provide 4 . teuton f v;itte't, whi Ii nti^ht IK* mount (in lip* rim of 4 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 IMPULSE 475 For if we differentiate the expression (276) with regard to V and equate the differential coefficient to zero we shall have and this value carried into expression (276) gives for the work on the vane LJy a ; 4 $ but the kinetic energy of the jet is i w so that the efficiency is 0.5. If the flat plate in Fig. 99 be replaced by a 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 be t and neglecting friction this velocity may be attributed to the water where it leaves the vane. This relative velocity at exit will be toward the rear, so that the absolute velocity will be j/ _ fy _ y) s aV V . The change of velocity or negative acceleration will be V t - ( 2 V - V,) - a (V l - V), and the impulse is consequently PW /T/ T/\ s* .2 (V j V ). o The work of the impulse becomes - .2 (V, - V) V - 2 ~ (V,V - V 2 ) . . (277) o o The maximum occurs when . Jl (V v - V 2 ) - V, - 2 V - o or V - i V.. i * VI i/ 1 ** a7 476 STEAM-TURBINES 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 made. Reaction. If a stream of water flows through a conical nozzle into the air with a velocity V l as in Fig. 100, a force (278) FIG. too. will be exerted tending to move the vessel from which the flow takes place, in the contrary direction. Here again w is the weight discharged per second, and g is the acceleration due to gravity. The force R is called the reaction, a name that is so commonly used that it must be accepted, Since the fluid in the chamber is at rest, the velocity F t is thai imparted by the pressure in one second, and is therefore an acceleration, and the force is therefore measured by the producl of the mass and the acceleration. However elementary this maj appear, it should be carefully borne in mind, to avoid future confusion. x If steam is discharged from a proper expanding nozzle, whici reduces the pressure to that of the atmosphere, its reaction wil be very nearly represented by equation (278), but if the expansior is incomplete in the nozzle it will continue beyond, and the added acceleration will affect the reaction. On the other hand, if the expansion is excessive there will be sound waves in th( nozzle and other disturbances. 1 GENERAL CASE OF IMPULSE 477 The velocity of the jet depends on the pressure in the chamber, and if it can be maintained, the velocity will be the same rela- tively to the chamber when the latter is supposed to move. The work will in such case be equal to the product of the reaction, computed by equation (278), and the velocity of the chamber. There is no simple way of supplying fluid to a chamber which moves in a straight line, and a reaction wheel supplied with fluid at the centre and discharging through nozzles at the cir- cumference is affected by centrifugal force. Consequently, as there is now no example of a pure reaction steam turbine, it is not profitable to go further in this matter. It is, however, important to remember that velocity, or increase of velocity, is due to pressure in the chamber or space under consideration, and is relative to that chamber or space. General Case of Impulse. In Fig. 101 let ac represent the velocity V l of a jet of fluid, and let V represent the velocity of a curved vane ce. Then the velocity of the jet, relative to the vane is V^ equal to be. This has been drawn in the figure coincident with the tangent at the end of the vane, and in general this arrangement is desir- able because it avoids splattering. If it be supposed that the vane is bounded at the sides so that the steam cannot spread laterally and if friction can be neglected, the relative velocity F 8 may be .assumed to equal F 2 . Its direction is along the tangent at the end e of the vane. The absolute velocity 7 4 can be found by drawing the parallelogram efgh with ef equal to F, the velocity of the vane. The absolute entrance velocity V i can be resolved into the Fio. ior. 4/8 STEAM TrtltsiNfr'.X two cmfKJiirf* tit and i at right anglrs to ant) along the direc- lion of motion of the vane. The former nay t*r called the velocity of How, I*/, ant! the latter the veliHtty t$f whirl, F,,. In likr manner the aimolute exit velocity may br resolved into the 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 'F. and the thrust i* to U9 7* ..... 4- I f f,: ** " I * / ~ * / which be ?* - ^ (I* sin tt I" 4n 7i , S ' If is mi velwity f whirl al the rxil the i **' t* I* I , tti** r ,.>.. I* delivered to the vanr | r srttintl Is it* *^*i* If ~ ;- I 1 I , *%, ...... GENERAL CASE OF IMPULSE 479 and since the kinetic energy of the jet is wVf -4- zg the effi- ciency is V - cos a (284) e 2 To find the relations of the angles a, /?, and 7, we have from inspection of Fig. 102 in which el is equal to ef, V l sin a = F 2 sin /? ...... (285) V = F 2 cos 7 ....... (286) V = Fj cos a F 2 cos /?; from which cos a- sn a cos = sn a cos 7 and - 1 sin p - sin // .'. sin p cos a cos p sin a = sin a cos 7 sin (P a) = sin a cos 7 (287) The equations given above may be applied to the computation of forces, work, and efficiency when w pounds of fluid are dis- charged from one or several noz- fl_ zles and act on one or a number of vanes ; that is, they are directly applicable to any simple impulse turbine. Example. Let V v the velocity of discharge, be 3500 feet per second as computed for a nozzle on page 444, and let a = 7 = 30. By equation (287) sin (P a) = sin a cos 7 = 0.5 X 0.866 = 0.433. .'. p - a = 25 40'; p = 55 40' = 2020 ,. r , sn a y y -- 2 J sin p 0.866 V = F 2 cos 7 = 2020 X 0.866 = 1750 e = 2 X 1750 X 0.866 -s- 3500 = 0.866. 4^o Ho Axiiti Thrust. llir butltlrrt of itttfniUr >tc;im lurl ultriimtr nun Is im(iort;uu uvtmlmj* ;t\u! thrust, whirl: In- ilow In- i,ikii|| the rntt iin*l cvit 4iiffSr- of ihr \ r|u.tl f jrnvi|n| that fri tfut uthtT f"r"j:4iif!t"r*t 04 i Iril. Thi** is v in llii-% i =.'" t l I", -.in 7 kl t w I 1 *V I'* fii.iftr lMIH.ll III ,1 iifti ^ f * 8 < > 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 rijsi.il ! /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 DESIGN OF A SIMPLE IMPULSE-TURBINE 4 8r If this value is carried into equations (283) and (284) the work and efficiency become w W^} j K t 3 cos 2 ( 29 o) and This freedom from axial thrust appears to be purchased dearly unless the accompanying reduction of velocity of the wheel is to be considered also of importance. Example, If as in the preceding case the velocity of discharge is 3500 feet per second, and if a. is 30, we have now the following results, cot/9 ^ \ cot a - j X 1.732 " 0.866 /. /? - 49 10' V | Fj cos (v | X 3500 X 0.866 = 1515 e =* cos 3 30 0.75. Effect of Friction. The direct effect of friction is to reduce the exit velocity from the vane; resistance clue to striking the edges of the vanes, splattering, and other irregularities, will reduce the velocity both at entering and leaving. The effect of friction and other resistances is 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 482 STEAM-TURBINES foregoing discussion to a simple impulse turbine of the de Laval type. 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- power. 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 be 0.262 X 0.75 X 0.85 X 0.9 X 0.9 = 0.135; which corresponds to 42.42 -f- 0.135 = 3*4 B.T.U. per horse-power per minute. DESIGN OF A SIMPLE IMPULSE TURBINE 483 Now it costs to male one pound of steam at 150 pounds by the gauge or 165 pounds absolute, from feed water at 126 F (2 pounds absolute) r i + ^ ~ & = 856.0 + 337.6 - 94.3 = 1099 B.T.U., consequently 314 B.T.U. per horse-power per minute correspond to 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 supplied. Not uncommonly turbines of this type are run under speed as a matter of convenience. Sup- pose, for example, the speed of the vanes is only 0.3 of the velocity of whirl, instead of 0.5; that is, in this case take V = 1050. This case is represented by Fig. 104, from which it is evident that v Vf = V/ = ai = 7, sin 30 = 3500 X 0.5 = 1750 V u V l cos 30 = 3500 X 0.866=3030 tan /? = ai -=- id = 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. 484 STEAM-TURBINES consequently the exit velocity of whirl is W/ = ek = 1050 - 1980 = 930. Consequently the work delivered to the vane is IV IV PV = -[3030 - (- 930)] 1050=- 39 6 X I0 5 S S , w 416000 g But the kinetic energy is wV* * 2g, so that the efficiei 416000 X 2 -T- 3500 = 0.68. The combined efficiency of the turbine therefore becomes 0.262 X 0.68 X 0.85 X 0.9 X 0.9 = 0.123 instead of 0.135; and the heat consumption becomes 42.42 -f- 0.123 = 345 B.T.U. per horse-power per minute ; and the steam consumption inci to 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 TESTS ON A OK LAVAL TURBINE 485 !..! inches out of 62.8 inches (the perimeter), or somewhat less than tme-lifih. The section of the nozzle is shown by Flu. Fig, 105, and the form of the vanes may be like Fig. 106. In this case thr thickness of a vane is made half the space from om vane to the next, ttr 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 !> Snall.t \V. \V. Amm<*n ami II, A, VAI MMttt. i< hri )| 1 -i% i *1 3 >i Slrasti jrf If *!.", t< 9 f- |*v*'f it?,!* |*if Wait* lt?! r*r.,..rf jirf wiwrtr lii ?!" !,' 1"; VrS* ity *4 t'^ws i >' I s ", Vrl<* III* *f |*"i Mi, 4rs 6 .J rlr. Ifi,, ! .* i ! ' i i .;* . . < s > s . . t 1 f4,| 14 .4 I* 4 ** i i >* ||4 *"; ii*" i;?" 'Tlfrfr nfr I lift irm ltit%'r 5, t : i if IIP a iiii'rT?itrn of movtfi}* '*! : i!$^fi ; ,;tfi may flw thruugh * ir r-%*t *| in it >nr iiti|*Ir *i mt^thmU l* Piilr llir lr>tm of rhamt>rn in f ii *IB % ; anr, Thr fir*! tint an i% l*f iltr I*., of ih Citriw Thr H titrlitnr, Iw* f Tin* third U In llir f*ijfii% wtiitfi !IAI two to sspvrn iiinitili*r In *! air lf*i iw. t |*nif til f'evwlwtff taR*%, Till* !*ar*ll tllfliillr, i% ^ft fr:j|ifw ttrhrr!, toi a vrry numltrr ! M-H f *n*^ ,r., t$fif to ctttf hundred iind liffy. III fcttiit'r llir to i in tti f ihr vaflr^ llir J*rf l I*. VELOCITY COMPOUNDING 487 Velocity Compounding. In Fig. 107, let V t represent the velocity of a jet of steam that is expanded in a proper nozzle down to the back-pressure. Suppose it acts on an equal- angled (/? = 7) vane which has the velocity V. The relative velocity at entrance to that vane is F 2 and this velocity reversed and drawn at F a may represent the exit velocity, neglecting friction. F 4 is the absolute velocity at exit from the vane, which may be re- versed by an equal-angled .stationary guide, and then becomes the absolute velocity F/ acting on the next vane. The diagram of velocities for 'the second moving vane is composed of the lines lettered F ' K i ' F ' Y 2 ' F/ and the last of these is reversed by a .stationary guide, and the velocities of the third vane are F/', F 2 ", F 8 " and F 4 ". The diagram is constructed by dividing the velocity of whirl V w V l cos a into six equal parts, and the final exit velocity F/' is vertical, indicating that there is no velocity of whirl at that place. It is immediately evident, since the velocity of flow is unaltered in Fig. 107, and since there is no exit velocity of whirl that the efficiency neglecting friction is the same as for Fig. 103, namely e = cos 2 a .as given by equation (291) page 481. S'tT.\M Tt"li; , 5nlrfr"",|ifi|f !"* itrtcf tliiilr llir tttlk lrnr tin rar ; It Is vanr; tin- MUM *I tlii- wrk- !" itfw lr.i In Fig. 107 thr vrlii isy *4 whir! at n'U,ttur 1 t U'8 and the vrlinily l lfl -l *'*it fitl llic wutk li*!ir *n ih- *-,ir t-. r I* Wa-s iliiillr attil ft ' . SC tlliil Ihr r, Thr tfi%tftitii%-r the til Ihr t*n A in%'r*ili|!4i$*fi ftmr v4Ht"*i in Thr iitfiifr in jf vunr-n A ^fir-. i% r4*i ; ,iifirj| l% an , r. s ihr lriritiu-< tion VKMU'ITY COMPOUNDING ^o 409 ll is considered that this type of turbine cannot be made to give good rtlit -iency in praetiee on account of large losses in passing through a succession of vanes and guides, especially as the steam in the earlier stages has high velocities. The turbine, however, has rertain advantages when used as a backing device for a 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 velcK.it y ml exit from the preceding vane, thus F/ m equal to V,, etc. Thr I^t absolute velocity V" is equal to ai the constant vclwily of flow. Thr ft, n t , ^j, it, and /f, art* properly indicated as may be ern by 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 tun nn i I ros , etc., ; 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*, lli lite **i|ic's I* | ? ,iir ilfitwil in tJ |||:;|||fii:f, I*, '4.lf |,| 1"^ ||| C i" 4 $> 1,1 i<i off 1 r -^lltsr Imr AH r, Irffrfrit I*/ " mil-. f fif I^", tin- lt,4Vt* Thi lltiri K T UK FRICTION ^ and a* ihr intrinsic rnrrgy tif thr jet is I A' thr 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 rrquirnl, 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, 3030. Starting With l\ ihr Vrlm'llV f ihr is tlfitwu i* Ir!rfffttt!r ittr tnil9.il 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| tti *"iic- Thb antl iiiiiilr-i, inti t>f lit if-;i Is* Tti lO t PRESSURE COMPOUNDING 493 Fio. no. In Fig. no an attempt is made to avoid axial thrust on the vanes, and at the same time to retain a fair efficiency by making the delivery angle of the guides constant. A calculation like that on page 492 indicates that an efficiency of 0.76 might be expected in this case. It is quite likely that in practice there might be difficulty in making the delivery angle of the guide as small as 30, but it appears as though the common idea that it is practically impossible to make an economical turbine on this principle is not entirely justified. Pressure Compounding. The second method of compounding impulse turbines with a number of chambers each containing a single impulse wheel like that of the de Laval turbine requires a large number of stages to give satisfactory results. For sake of comparison with preceding calculation we will take the same initial and final pressure and the same angle for the nozzles, namely, 150 pounds by the gauge and 26 inches vacuum, and a - 30. Nine stages in this case will give approximately the same speed of the vanes as in the problem on page 490. The temper- 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 f ;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\ i| M| fc'ffijw'faf lit ! If! If the Ji"fi|hrf.al '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 ifii.fr ifto frrt I*- if* i ft4tft!j(f% itiilc.rtsi fif ? i'KKSSUKK COMPOUNDING 495 This will give fur the avuilahlc heat for each chamber 8 thermal units, and using as before y 0,1 we shall have T, - \ j X ^j X 778 X 8 X 0,9 600 feet IKT second. With n ~ jo the velocity of whirl is now 520 feel ami tin* 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: N <IF PRKSSURK. 4 * tttn !*.. *Mi Ratiw *( prsur. l*S 7.V5 47. 0.68 0.66 0.65 0.64 18.6 0> 01 o.fit u-J o!J7 i 0. The taut t'olumn give* the ratio of any given pressure to the preceding |irrtirt% i.e. us : 165 0.68. These ratios indicate that ftimplr utntral t'tm verging noxzicn will be sufficient for all but ihr fast With the uutt! number of stages, twenty or ronrr, thr nttiii* art* certain tci be larger than 0,6 in all cases, indicating flit* uc of converging throughout, sriufti To determine the si,*r> of tin- m.;4ir% or thr 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 * |* PKKSSUKK COMPOUNDING 497 FIRST rOMI'trrvriONf OF QUALITIES AND VOLUMES. 5 i "-i f I IU, S } t \i 1 1 ; 4 j ,|y i til ! j|f ! 16? V4jStfi Miin 5S y i S j w,$ yt*i i toio Quality 0.078 0.076 a. 78 3.78 3-QS 3-90 5-79 5,66 8- ft 5 8.44 '3-3 19.7 at .0 it). 8 34.1 31.8 55,8 52.2 1)7.0 88. 3 "75 158.0 By Ihr nid of thr trm[H*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 ,' Li 498 STEAM-TURBINES though y shall be varied from stage to stage. For example, 01 choice of o.i for both y and y i gives 32 X 0.9 X 0.9 = 25.92 B.T.U., which ^multiplied by 0.75, the efficiency due to the angles ar velocities, gives 19.44 B.T.U. as above. Let it be assumed f< the moment that the above product shall be kept constant, so i to obtain the same velocity of jet in each stage. Then tl following table exhibits a way of accomplishing this purpo while varying y and y 1 : Stage i 2 3 4 s 6 7 8 -y 0.08 O.oSi; o.oo O.OQC; O. IO O. IO? O. II o. ii<; O. I y 0.088 O.OOI O.O04 O.OQ7 O. IO O. IO3 o. 106 o. 109 O. I (i-y) (i-yj 0.839 0.832 0.824 0.817 0.81 0.803 0.796 0.787 0.7 B.T.XT 30-9 31.2 31-5 31-7 32 32.3 32.6 33-o 33-2 The last line shows the proper assignment of thermal uni for this condition. For simplicity both y and y l are assume to vary uniformly, but other variations can be worked out wi a little more trouble. Evidently the sum of the figures in tl last line should be equal to 9 X 32 = 288; it is a trifle larger in the table. Now it is probable that the best values of the factor for frictic and resistance are to be derived from investigations on turbin rather than from separate experiments on nozzles and vane and it is evident that the use of the methods of representii the friction by a factor y is rather a crude way of trying to atta in a new design favorable conditions found in a turbine alrea( built. Since the general conditions of this problem are the same those on page 481, the efficiency due to adiabatic action will 1 the same as is also the efficiency due to the angles and velocitic Taking the factors for friction in the guides and blades as eai PRESSURE COMPOUNDING 499 o.i, the corresponding factors are 0.9 and 0.9. The efficiency due to velocities is 0.75, and the mechanical efficiency may be estimated as 0.9. The combined efficiency of the turbine is 0.262 X 0.75 X 0.9 X 0.9 X 0.9 = 0.143. A computation like that on page 483 with this efficiency gives for the probable steam consumption 16.2 pounds per brake 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 diameter 260 -*- 2o?r =4.14 feet. The remainder of our calculation will be carried out on these .assumptions, namely, that the power is to be 500 brake- 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, FttV vH t'lj /M ii. |ffj*tfiifii, ills Mtnjnllr.il if| |*; wr Likr r f sr l|$r rllr live |**fiffirtri li*f*lr| Is, !|4 list- r f| r | ; i> ken S*i bt '', llic isr |-5 ;iiftiis.'nifi 1** Iltr ?!ilc 41 ,!|n.r tf| l.KAKACiK AND RADIATION Conversely, If desired, the thickness of the vanes could be adjusted^ give the same length. Such a construction as this leads to if* likely its give UKJ sharp a curvature to the backs of the vanes, and it may !x better to givp only the thickness demanded for strength and take the chance that the passage between the vanes shall nut IK* filled. If allowance is made for f rift ion and the consequent reduction in velocity the lengths of the vane* should br correspondingly increased. The lengths of the guides fur the other stages will be directly proitortional to the 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 excessive, ad Radiation. This type of turbine, as will be seen In the description f iht* Raltmu turbine, hus a number of wheels each in it* own chAmbrr mrici the rhamtx^n are separated by stationary dink** thai extend to the shaft. Reduction of leakage be tttlMinnl by a small clearance between the disk and the shall for a |rojT Iit-.iiing r slulhm: ln * .inhui In* fl.tmt in so inariTssihK' a J'lair, "I'ltr l%*ka>*r * ,ifi la- r.<fitfui! hy aid of Riinkimvi. rptoit**ii tm la^r 4,4-* r fru tt,iir4t! on |gr -i.y; J'tit l*th tw'i!*h ;r*' 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 t* In IM." any lilt* l fr 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- ts -'S ;Sft*t V 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 rtiiifin, *tir rt ihr %d*ii>, If aiiioi i ft'jc*|i|ri1< r llli I i it ai ill! p- ?lifrt KATKAU TURBINE 503 Let **/* 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 r* lll* - till will U- Y In lik a |Ktim in the trajeetory of the particle of steam. . V The i will dlfVif / may lie taken as the trajectory of the steam, and r/ in the Ir.ttl *s defined almve. I*ro{a>rly a similar construction TthnuUt t*r made *il*o fur the bark of the vane, and the mean path fthnultl fir taken to e*!atiti*h the lend, Kxtremi? refinement is protfciMy neither net > e.H?ary nor justifiable in this work. r t'oniitrurtton of this turbine, which is * *** of the pure 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. tl.vi"'-. i*\ li.iri. .ir tt s 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-?* !f Hi jifr^aiifr til a j**r is fr, i*r liwt Jm^I f *i* nicfif.it! 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- * SIDE THRUST 505 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. \ioo/ Wheels with vanes H.P. = [0.02295 a. D 2 - 5 + 1.4346 a. I 1 - 25 ] ( \ioo where D is the diameter in feet, L is the blade length in inches, V is the peripheral speed in feet per second, and 7 is the density of the medium. The values of the other factors are a 1 = 3.14 a 2 = 0.42. These formulae explain why the backing turbine for marine propulsion is always run in a vacuum when idle. Turbines which have only a partial admission must be affected by some such action for that part of the revolution during which steam is not admitted; but this matter is obscure and such a resistance must be combined with friction and other resistances. It is therefore very difficult to assign the proper value to the fric- tion factor y for steam in the vanes or in the guides and vanes of a 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 **tif twt or im- >r- . lt 'alr mtltt Ili cf tfifumii Siiur ihr jrim iilmnl)% will i |rlU- Lrl u* likr fr Walls ill rtoifka tif 0.i, wti 1*1 ihr ifitikl ! 3* ffll'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 t-*nh lit*- j4i< .ui.n - t ill j** i' m 4i ilir i* jia ih- it**- ir ill th of f, i* "O ** t' lrW|'fattifr to l ftei n.r.t?, Thr rttkirttcy tif r* for any w f* ' thr l$t>?'tr.j*iwrr jn-r Ttic rflu-irnt'y for L I s * t" 4 by the PRESSURE AND VELOCITY COMPOUNDING 507 the combined effect of losses in the vanes may be taken to be equivalent to making y equal to 25 so that i - y is 0.75; this is in effect the efficiency factor for the vanes as affected by friction. If, further, we take the mechanical efficiency of the machine as 0.9, then the combined efficiency for the turbine will be 0.285 X 0.883 X 0.85 X 0.75 X 0.9 = 0.144. This corresponds to 42.42 -^ 0.144 = 295 B.T.U. per 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 becomes V =V 2 x 32.2 X 778 X 161 Xo.85 =2610 feet per second. Assuming that we may use three sets of moving vanes the velocity for them will be 2610 -f- (2 X 3) = 435 feet per second. St'tUM Tt'Kl!\'fcS If wi' rhixwe a iltiitm'lrr ( if f<-*'t for t v;tnrs il will lr;tii to litr -' *f iM*;j r*-t*i To tiro I fill* iKirffliriifiitf" ff'vttifr Wr umtrnt* al that |rr'*%iifr *- jntth '.isrinr of 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! li.nr ihrn^lt for thr V*!IH ilii"% itttt%i I*- lrirriiiiiu'*! in r*|rr f^i the Hit* throat ifr*'4ttrr4 itwy ! t,ikrft I ! till' Srfii|*'l'4lMfr-.* 4f SiniT lilt* f it"' flt,*.?lr ?'} for friiltMfi 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'*. |nj| Tlw with fr lit*- vutumr U 44S rilttir frrt. The 4 iiii 114*1 ** 44 . II f I** thr Ttlt* f thr |u|tlt(| PRESSURE AND VELOCITY COMPOUNDING 509 The specific volume is v= (xu + <r) = 0.902 (21.6 - 0.016) + 0.016 = 19.5. With 15.7 pounds of steam per brake 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 itr.it 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$|.Ir'*, 4iii vcUi.-itim 1,883, Thr hrat ini. work w..i-> ihrrrfrr 161 *: >:' o,?i *: .*iS| ~ tjM,f ii. t ,r. ihr Ml W lh* lr<m *!> it ||fi*it:ttrs w I till - |i t|i.M ,t.f, per fwiiritl. N*w r liit* lh? valur tj^j i! ^j,i I',, sitwl y it it|i that tlw* quality t ,f -- (itaj - tit i : - iiy *>,^v*- If thu flow from thr t ih- tlif*.;i! 34 ,f,t?, to |jf iftlri wwl as f ii* tt 4iil f it t<r4 *t* .* fteftM '- if 14 1 - i it thr throat f thr wt*ml nw/^lc, Alipwifipl us lwftrr si, ic If ihr lri*!i* In* III I PRESSURE AND VELOCITY COMPOUNDING 5ll at exit from the second set of nozzles. The volume of saturated steam at 102 is 335 cubic feet, and with x equal to 0.858 the specific volume is 288 cubic feet. Consequently, with a weight of 3.36 pounds per second, and a velocity of 2610 feet, the united areas of all the nozzles at exit will be 3.36 X 288 X 144 -s- 2610 = 53.4 square inches. Now the perimeter of a circle having a diameter of 4$ feet is about 170 inches. Allowing for the sine of the angle 20 and 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 512 STEAM-TURBINES 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. Pressure. Temperature- Heat contents. Quality. Specific volume. i8.a 223 IIOO 0-95 10.6 196 1063 0.92 32-7 I.O 1 02 927 0.85 245 The apparent available heat for adiabatic flow to the throat is now noi - 1063 = 37, which would give a velocity of V = V 2 X 32.2 X 778 X 37 = 1360, instead of 1280 as previously found. The apparent available heat to the exit with 0.15 for the friction factor is now (noi 927) 0.85 = 147, which gives for the exit velocity ' V = V2 X 32.2 X 778 X 147 = 2710, instead of 2610 previously computed. This comparison shows that the intermediate pressure deter- mined by the customary method will be too high, and that to obtain the desired distribution of temperature the factors for imvr Htagi* must he modified arbitrarily as may be deter- mined ly rofttfutkmi with practice. Curtis Turbine. Fig. 1 1 4 shows a partial elevation and section of ihr rs*rwiiil failures of a Curtis turbine, which has four rhamlKT!. *intl lw wts of moving vanes in each chamber. The n*it uf liiiMurbinr is vertieal which demands an end bearing, the- tlitliftiltie* nf whirh construction appear to have been met by oil umirr im^iMurt* into the bearing, so that there is ciwijiktr liilirknitttn without contact of metal on metal. The umtirntrr i* |>Uil tlimlly under the turbine, and the electric- grnrrattr b aUw tin a 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. 514 STEAM-TURBINES 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. TESTS ON A TWO-STAGE CURTIS TURBINE. DARLING AND COOPER.* Duration, minutes I2O 120 I2O I2O 60 Throttle pressure gauge 146. 3 ixc; . -i 142 . 2 143. I4Q . 7 Throttle temperature F eia ?2O 464 "JO2 t !l2 Barometer inches 20.8 20 .0 20.0 20.0 30.0 Exhaust pressure absolute pounds . . Load kilowatts 0.82 161 .4 0-79 2<< . 7 0.92 374-O 0.84 512. o 0.85 731 .0 Steam per kilowatt hour, pounds . . Thermal units kilowatt minute . . . 21.98 440 I9-63 396 19.98 39 2 18.43 3 6 9 17-75 357 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. TESTS ON A FOUR-STAGE CURTIS TURBINE COE AND TRASK.f Duration minutes 60 60 60 1 80 I2O Boiler pressure) pounds TC2 IAD 6 I <J2 I ICO ICQ A. Vacuum inches . . 28 * 28 2 28 8 28 4 28 1 Load kilowatts 282 380 C27 ega 788 Steam per kilowatt hour pounds . . 21.4 20-3 18.8 19-5 19-3 Thermal units per kilowatt (minute) . 394 37 352 360 357 * Thesis, M. T. T., 1905. f Thesis, M. I. T., 1906. TURBINKS 515 & iraiure the 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 units, Rttctton TurbittM. -The. essential feature of a reaction turbine, in a fall of pressure and a consequent increase of veloc- ity In fiir (Mintage* among the vanes of the turbine. Since surh wheel* rommonly are affected by impulse also they are sometime-, railed 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 |t.tt llir irifirr eruU f the whtt h art- l.o o(H'n; ihi* to '4itiwft hy Fig. 1 1 5. Tlu* reafiion turbine in always made 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$, frti the guide* or the vanes is only 4 lltilt? Sr ihun the enlrant-c prtmsure, and the passages Thrrr h mi uttrmpt to awld axkl thrust, and therefore the rxil 7 from tin* vam-s* may be made small; it is commonly rtjtiat ui the rxit angle a from the gulden. A common value for lltr-ir angles is Ji**. llir giiitlr% ami vanw follow alternately in close succession leaving only the nrersHary flearancp; the kinetic energy due to thr ntiiliiir c-xli vrluc'ity from a given set of vanes is not lost but I in the nrt''t of guides. The turbines are usually if -I nuidr in twt or ami ii ' inly *tt lu llir ,ltm*lis!r tltis kinrtii rtit- ftttrcr M- un^ in shown lv t>'s?. 11 im- mil 4 *i >**! *u UMI ihr iiitrfis i-nrrgv ttttt* M! wU*a> -. firjirt !<<!, at ihr rm| M| 4 lirfr ifr 4i'*Wj|% illliiit'ilt " **( lltr ilfirli.* *'rf>t* l'.'| lt%T |*rf i'rfi! it f;i% |f|'il'i thr giitfli"'! ami tiin* 1 - fiUj in?h-nr-i r tf Iir;t! sill** mrl 4 i|*l*i!*:4 !<i *Jsr !tlsfif of m* rrdiir lite r til Hfr^m .;!! lll*!";i-\ifr, ilir rill iil*%ilUt!r %rl<.$!% driving ilir >l*'aiii ttti** tlir '%,! ^- SH V*-J*nllV l an lilt* tin- ititli | lltr Tlw* *lrifll rflirfa a -?rl #l if till' al*%*|tr grimily lf* I III w| iltr lt*i tf j*frA* uf k tif VfttMtlV I* I** S r%il vrl'ily * life It i** *j t^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 < CHOICE OF CONDITIONS 517 the gain of velocity in the vanes is equal to the gain in the guides. In Fig. 116 let 7 1 be the velocity of the steam leaving the guides and V the velocity of the vanes; then F 2 is the relative velocity of the steam entering the vanes. V a is the relative exit velocity which is greater than F 2 on account of the change of heat into work. F 4 is the absolute exit velocity from the vanes with which the steam enters the next set of guides. If the con- ditions for successive stages are the same, V 4 is also equal to the entrance velocity to the set of guides of the stage under discussion, and if ce is laid off at ac' then cfb is the gain of velocity in the FIG. 116. guides. Consequently to construct V s we may lay off ce' equal to ac and e'd equal to c'b. Now a and 7 are commonly made equal, and therefore the triangles abc and cde are equal. Consequently the angle 3 for the entrance to the guides is equal to /? at the entrance to the vanes. In fact the guides and vanes have the same form. Choice of Conditions. The foregoing discussion shows that the designer is given a wider latitude in his choice of conditions for the compound reaction turbines than appeared possible for impulse turbines, though if the restriction of no axial thrust were removed from the latter the comparison would be quite different. Ttlr II! in prat li'r ' in a ja|rr ! mation in I** fl'ii'liwtl krfiv.iifr w'9&$a * ^ $.'JSMki3*' j ' $& fHUlCK OF CONDITIONS PARSONS TURBINE - MARINE WORK. Hift* *|*mt Intrrmwlifttr wall *ir*wrr* t'hAttwt 'sirawrt^ . . , |titttirhi|n tttl Smatt * f tir* Prf, fal . p stwntl. Ratio of velocities, Number of H.P. L.P. vanw to steam. ahafls. 70-Ho 110-130 0.45-0.5 4 ite-q 110-135 0.47-0-5 3-4 ijo-toj 130-150 0.37-0.47 3 83-100 US-MS 0.48-0.59 4 105-110 130-160 0.47-0.5 3-4 t 10-130 160-310 o. 47-0.51 3-4 The VVrattnghouHr 0<>m(mny have used much higher veloc- ities f vane for I'ltt'triful work than given in the above tables; m mut'K an 170 fi.Ht IXT sct'ond for the smallest cylinder and 375 for iltt* krgrst cytimittr, Tttr liliiclt* liright nhouUl t % tit least three per cent of the elkftiricr of ftir tytlmlrr In orcUfr to avoid excessive leakage over iitr lifw, Mr, SjRitkinan siys that leakage over the tips til the liliitlrs U |M'rha| not so detrimental on account of actual lew by as tKrcnuatf it upsets calculations regartoig by inrrnt^inK the steam volume, The ftilliiwlng equation reprcnenta Mr. Speakman'a diagram for ttearaerrs over ill of vtnes. rlearance In inchen 0,01 + diam. in feet. The t>ro|xirtmn f may be taken from the Mowing table ; " ' ~ HCHE8. WMih at 24 Mr. i*a n%* i\et for the efftricncy of the steam in the turbine ttltti*-* themielvr* 0.70 to 0.80. * /nil. ,V<*wl 4rA., 1903, S ! 1ft i|iiti ! tt !* ilw Ir4ij|t" JM'** llu- fa ft fit *S in |fiitllir tic --9rn.il 1 iilnl ill tlirfr U likrJv S K~ A *cM'istlrr*it*h? fI'iiH wliis It uU ! t|"*H i iW*! in Tlii"* iligr i"4 in iSic m*| iUrr*l i* tit*- firnl IK- f si ill llir ti*-*n|fti nf l but alltiWiinrt* 'ltll t*c i i jfti i frsiilt'i i4 trsf-v. f**r A Rwctifttt Tutfein*. I <" .11* < *hr I ltl| ft F. Thr irfiry wf ,$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 ffi.j iff |tt tir tl lr*U f tf llir f sir tltf ffir l f*r? 14 | - mr*! ill ir rl ihr | lit* lift J*rf sci'i.ifltl, |r! iltr FOR A REACTION TURBINE 521 cylinders be i| and aj times the diameter of the small cylinders. Let the {teripheral s|>eed he 0.75 of the steam velocity, then the latter will ! joo feet per second. If the exit angles for guides and vanes tie taken us ao* and if the degree of reaction, is 0.5, the velocities ami angles will be represented by Fig. 116, page 517, In that figure $b y $ CO8 20 o a 0,940 F t ; ami as V is 0,75 K t , we have |<' ^ (0,040 - 0.75) V v 0.190 7 r Hut J? - y, sin 20 0.343 V t ; Ian ^ -* o.j4^ J " 'P ^ 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., 522 STEAM-TURBINES 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 DK8IGN FOR A REACTION TURBINE 523 the number of stages assigned above. In that table is given also the number of the stage counting from the 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- CC IMPOUND REACTION TURBINE. It t it tjft 7 t>t 8 As 7 II?J iMV.,1 1 1 JO . ? + o nr.7 wo 184 MU toy ft7 UHfl jmft .001 984 075 ft3 OS 037 ,00 Sped Ac vmumw. J. SO 4- SO 6. !) 0-04 j 6. o 34.8 47.t 190,4 S7 3,97 I S B 0.38 0-S7 15- 33-3 230 0.415 o.fiio 4.673 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 524 STKAM I dividing thr frtwtirjtlrr by **. Finally lltr "ijitrttir volume an by I lit* rqu;ittttn but in fiRtrtki* * itwy In: ntrgUi'lctl Ijecnune we have either x nearly e*}tul !* unity nr t*! 1 will be wrttjanrt with , llir strain velnt ily for I tie I'm! rylindrr r> |" Irrl jvr s tlt" weight of Htenni jer 'u*'n*l i** .}.t4 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*' tine-fount It* 4 Tilt" iliiittirtrrm <i| ihr iiiirffftnliaf*- and Kw |f r-^-s 'ill l*r n. tlir tif ii! Itir ^rvr DESIGN FOR A REACTION TURBINE 525 ant! this length will be assigned to all the blades of the first barrel. The blades of the second and third barrels will have their lengths increased in proportion to the specific volumes at the middle of those barrels, as set down in the table. The effect ' of increasing the diameters of the intermediate and 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 IT X MINKS U - A f i , f !< gli whtfh llw* ^traits ttni'il |M'^ wii lltftilllr llir *4ra? .- $1 jM-*n-?4 lw-r, fltir is It* ki tirtff."% 'slrijitt *if hftivt int lh<* sUffiirr w! llir fvliftilrr rtfiil ilif* ill*' -nit km- if list* ?w* thill till" ;4**iifH i'* ilfiififtlv lllftsilli'4 &>. ll | M .'j.w IH rr|itrtt'il lltiil llir Uhvrtttiti *|r-|fann* t-i rnttrrly rrtiiistfig liir 1caka||r llir fvlintjrf !* a ammin It i> {ifiiniit) mil ly Mr, Jmlr iln- i'ti cilrtitwr thruitltn fa al llir k.st *t titfii f llir labyrinth, lltr trtlirf srtliof rr t't}IH|ira!i%"rly intliitiriil. Thit |riltifr mill ttr rvidrnt If a I'* In lUlll tif*tir llir l*r\ t >i|*{U(.'4tit4l t Miifiktfii?'* -sji, t>( mr-r -i%nii A t but TIIt!i% yet il> itltiilttfi*s Itr Irakagr whii It >hmiM I**- ^m*i){. Wlirfi a||4inl I |ifnjni|'ii}fs |Jir tiittitteti ami llir *ibl lliri^l i? iiwlnlli" ;i|i|*!fn| It* the iliafl, Stm-r- at! alrwiltilt" liaLtmr t*mt*t lr tsliiaificil, a to |rtviU-) Irtil if fffcii' lfci%r iiciif *ft|,f Wi hiAVr litlt lilllr ffittiwft, Sutititury lufbillr."* 4!" h^vr IttT ufiliakfirwi lliiti'tl, A irM <n A TEST ON A PARSONS TURBINE 5*7 Parsons turbine in Savannah was made under the direction of Mr. B. R. T. Collins and reported by Messrs. H. O. C. Isenberg and J. Lage,* which is interesting because the steam consumption of the auxiliary machines was determined separately. The data and results of tests on the turbine are given in the following table. The tests made at full load with varying degrees of vacuum show clearly the advantage obtained in this machine from a good vacuum, which amounted to a saving of 289 279 _ TESTS ON WESTINGHOUSE-PARSONS TURBINE. COLLINS, ISENBERG AND LAGE. J load. } load. I -ull load. ii load. i load. 60 60 60 60 60- 45 4 1 ! Steam pressures, gauge . . . 131 129 128 127 128 127 "5 28.1 28.1 2?. 7 26.7 28.0 26.7 26.6 Revolutions per minute . . 3616 3601 3602 3612 3562 3540 3537 Load kilowatts 260 370 493 501 499 629 733 Steam consumption, pounds per kilowatt-hour .... 24-3 21.2 20.7 19.8 19.7 19.8 20.2 per electric h.p. per hour . 18.1 iS- 15-0 14.8 14-7 14-7 IS-I Heat consumption B.T.U. per kilowatt-minute per horse-power per minute 462 345 403 301 494 289 375 284 374 279 373 278 3*i 283 A great importance is attributed by turbine builders to obtaining a low vacuum, in many cases special 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 Tt'RHINHH 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 HHi at J This Ulal was riftiiv^ilrtt! l o.t i% of iltt* turbinr at fwll I,nl am! with f turhint* iitailitl$tto f lit*' rtm*um|tfon imhr-* vai ttttw, S<ic <jr tliii INDEX. Absolute temperature 56 Absorption refrigerating apparatus 41 1 Adiabatic for gases 63 for liquid and vapor 100 lines *7 Adiabatics, spacing of ..... 31 After burning 3 X 9 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 function principle Characteristic equation for gases for superheated vapors .... Chestnut Hill, engine test . . . . Compound air-compressor . . . air-engine Compound-engines cross-compound direct-expansion indicator diagrams low-pressure cut-off ratio of cylinders total expansions with receiver without receiver Compressed-air calculation 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 . . " compound consumption final temperature ..... interchange of heat moisture in cylinder . ' . . . volume of cylinder Condensers cooling surface ejector 5 2 9 22 28 26 2 55 no 239 366 384 156 169 163 162 161 162 1 60 159 158 .358 377 366 363 369 372 365 39 2 3 6 4 39i 384 388 388 385 385 386 3<5i 386 149 15* Carburetors .... Creusot, tests on engine Critical temperature Cut-off and expansion Cycle, closed . non-reversible reversible . Delafond . Denton Density at high-pressure Dryness-factor Designing steam-engines Diesel motor economy Differential coefficient dp/dt Dixwell's tests Dynamometers INDEX Entropy Contimied. due to vaporization ..... expression for ........ of a liquid ........ of a liquid and vapor . . . of gases ......... scale of ......... Exponential equation .... First and second laws combined First law of thermodynamics . application of 245 257 256 255 268 23? 247 99 35 9/ application of vapors 8 Flow in tubes and nozzles Biichner's experiments Economy, methods of improving. compounding expansion increase of size intermediate reheaters .... of 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 . Ejector condenser Engine, Carnot's compressed-air friction of hot-air internal combustion . . . oil reversible .... Entropy 39 us- 470 4?i 22 384 285 335 24 3 2 43 43 design of a nozzle 44 experiments friction head Kneass' experiments Kuhhardt's experiments . . - Lewicki's experiments .... Rateau's experiments .... Rosenhain's experiments . . Stodola's experiments . . . Flow of air, Fliegner's equations in pipes maximum velocity through porous plug . . . Flow of fluids of gases of incompressible fluids . . of saturated vapor of superheated steam . . French and English units . . . Friction of engines distribution initial and load Gas-engine after burning blast-furnace gas . . - - economy and efficiency . . ignition starting devices . . temperature after explosion valve-gear water jackets 3 20 > INDEX 53* 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 INDEX 533 Steam turbines Continued. t'urtln . ......... 513 effect t>! friction .... 481, 491 impubr .......... 473 " general cure .... 477 frkticm til rotating tUnkn . . 504 lead , .......... ^oa ami radiation .... 501 thrust ,.,.,.. 480 Rateau .......... 503 reaction ...... 4?f'i 5 "5, S^o .Stirling's 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 3 diagram 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 SHORT-TITLE CATALOGUE OF PUBLICATIONS Of JOHN WILEY & SONS, NEW YORK. Lmm ; CHAPMAN & HALL, LIMMJSD, ATUUNOKD XTNDKR RUBJECTS. lirM|.uvr iti.uUro *ni ,.. rtp}<H (!,. n. Hunks marked witli sm jitneritik (*) are sold At */ j.fhft iinly, XII tHink*4rr (tumid in rliKh unless (ilherwbie Milted. AGRICULTURE. Annuity ' Manual ol Cattte-fwtdlnR. . , , , , nmo, $r 75 Prirtcipfoa nf Alumni Nutrition, ... , g V o, 4 oo tittdd Mill *' AmritM(t Uurticutiurtil Manual; Pttn I, PrMpttjtttUnfi, Culture*, arid Improvement iamo, i so Part II, Hysltimmie IHimulogy. ,.,.,,,,,,,,,.,, .jtamo, i so Knirwrii for Land lralnagt. . , , , ', '. . [ jame,' j 50, l*eticl Fwrm I)rlnAK*> . - . - , iamo, i oo- Svo, 4 oo 0rwtt' Principle* of American Forntry. , ,,..,...,,,,,, larao, i s<>' Orinfh'K Prlntipta of Madirrn Dairy Pmctic*. (Wall.). iamo, a oo. H8JlttJtk'8 Mlcrecpy ol Technical Produett. (Winton.) 8vo, oo Iferrirk'w DrnmiiriM) or Iniiuntrlitl Alcohol ,.,......,.... . 8vo, 400- Cittrdntni ti AppUd to Home Decoration. . , , , , lamo, i 50 Pthwiplti nd Pretlc of Butttr-making ,..,.. .8vo, i 50 IniMct* InSurlflus t Ht^pte Crop. , , , .iamo, i go * J4tiwr#*i t.iiKlflif I'inmin Virgin Forest , iamt>, i 35 fteekt and Soito. ... , , Svo, a 50 , 8vo, 7 go ARCHITECTURE, fleam HMtint for JiulMhigs, ,,,,,,.. xamo, a. go iamo, i oo. MtiiMttiK fu4 Utructurm ttf Amrdcsut RuiljtiadB. 4 to, s oo t%rwing and Ctmitructitm of American Theatres. , Hvo, 3 oo. Arcbiitunil lr and ileel, . , ,8vo, 3 so Compttmii Rivvt*^ Cftrdn m Appiled in Bufldtnp. , .Svo, a oo Mmrnittg ASJCJ t'titiHtruetifltt of High Offiet Building! 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(In Press) Hopkins's Oil-chemists' Handbook 8vo, 3 oo Jddings's Rock Minerals 8vo, 5 oo Jackson's Directions for Laboratory Work in Physiological Chemistry. .8vo, I 25 Johannsen's Key for the Determination of Rock-forming Minerals in Thin Sec- tions. (In Press) .Keep's Cast Iron 8vo, 2 50 iadd's Manual of Quantitative Chemical Analysis izmo, i oo Xandauer's Spectrum Analysis. (Tingle.) 8vo, 3 oo * Langworthy and Austen. The Occurrence of Aluminium in Vegetable Products, Animal Products, and Natural Waters 8vo, 2 oo Xassar-Cohn's Application of Some General Reactions to Investigations in Organic Chemistry. (Tingle.) izmo, i oo Xeach's The Inspection and Analysis of Food with Special Reference to State Control 8vo, 7 50 Lob's Electrochemistry of Organic Compounds. (Lorenz.) 8vo, 3 oo Lodge's Notes on Assaying and Metallurgical Laboratory Experiments 8vo, 3 oo Low's Technical Method of Ore Analysis 8vo, 3 oo Lunge's Techno-chemical Analysis. 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Baker's Engineers' Surveying Instruments I2mo, 3 06 Bixby's Graphical Computing Table Paper 194X24* inches. 25 Breed and Hosmer's Principles and Practice of Surveying Svo, 3 oo * Burr's Ancient and Modern Engineering and the Isthmian Canal Svo, 3" 5 Comstock's Field Astronomy for Engineers Svo, 2 50 * CorthelTs Allowable Pressures on Deep Foundations I2mo, i 25 Crandall's Text-book on Geodesy and Least Squares Svo, 3 o Davis's Elevation and Stadia Tables. 8vo, i oo Elliott's Engineering for Land Drainage I2mo, i 50 Practical Farm Drainage I2mo, i oo *Fiebeger's Treatise on Civil Engineering 8vo, 5 oo Flemer's Phototopographic Methods and Instruments Svo, 5 oo Fohgeilfe SewiCEage. . (Designing. and Maintenance:). Svo, 3 oo Frej tag's Architectural Engineering, ad Edition, Rewritten Svo, 3 So French and Ives's Stereotomy 8vo 2 So Goodhue's Municipal Improvements izmo. i 50 Gore's Elements of Geodesy 8vo a So * Hauch and Rice's Tables of Quantities for Preliminary Estimates I2mo, i 25 Hayford's Text-book of Geodetic Astronomy 8vo, 3 oo 6 Bering's Ready Reference Tables (Conversion Factors! i6mo, morocco, 2 50 Howe's Retaining Walls for Earth i2mo, i 25 Hoyt and Graver's River Discharge 8vo, 2 oo * Ives's Adjustments of the Engineer's Transit and Level i6mo, Bds. 25 Ives and Hilts's Problems in Surveying i6mo, morocco, i 50 Johnson's (J. B.) Theory and Practice of Surveying Small 8vo, 4 oo Johnson's (L. J.) Statics by Algebraic and Graphic Methods 8vo, 2 oo Laplace's Philosophical Essay on Probabilities. (Truscott and Emory. ).i2mo, 2 oo Mahan's Treatise on Civil Engineering. (1873.) 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(In Press.) fl Searles's Field Engineering i6mo, morocco. 3 oo Railroad Spiral i6mo, morocco, I 50 Taylor's Prismoidal Formulae and Earthwork. gvo, I 50 * Trautwine's Method of Calculating the Cube Contents of Excavations and Embankments by the Aid of Diagrams. 8vo, 2 oo The Field Practice of Laying Out Circular Curves for Railroads. i2nao, mor.occo, 2 50 Cross-section Sheet Paper, 25 Webb's Railroad Construction i6mo, morocco, 5 oo Economics o.f Railroad Construction Large I2mo, 2 50 Wellington's Economic Theory of the Location of Railways Small 8vo., 5 oo DRAWING. 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Voi II it* l**fl I. t'r> It. **4 I* <>* If I J , t JO ,*%tt*Jt4 llttiu, | SM fiiiiu, a on .f UM Wrl4'* |ln lltf mufti* it 5 **, J S !<M, 4 too *vw, 4 Me t, I IKt !*, j no t*m, 4 wo Svjs, s no s < I mi i*tw, 75 *, i f *, j **, ? S Htr>. 4 *tt Hw, .4 no *!*i, S * ** 8 f tt- K*M>li *f Alt, RpM**tti* t , ftV, 4*4 < ti*i** ^ ftst tlf l .. , , * . J *t i tn tttm, 4 no <, Htf I a go Sitt tiilifimt. l^^l^^ | J<|jf|||i M ^0 Ssisri, I! M t, J tt* 8W I III, } HM..W(Kltl HT , 1(4, W,| rf M* Miw*. , . . , , (A. W,t ** Mstteim , Ml l J '**' t * ... , J 00 ^w^ilW^fw ^fflW' . ie I 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 <>> * MEDICAL. * Bolduan's Immune Sera 12mo, 1 50 De Fursac's Manual of Psychiatry. (Rosanoff and Collins.). . . .Large I2mo, 2 50 Ehrlich's Collected Studies on Immunity. (Bolduan.) 8vo, 6 oo * Fischer's Physiology of Alimentation Large I2mo, cloth, 2 oo Hammarsten's 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. 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' 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 Sections. (In Press.) * Martin's Laboratory Guide to Qualitative Analysis with the Blowpipe. lamo, 6 Merrill's Non-metallic Minerals. Their Occurrence and Uses 8vo, 4 01 Stones for Building and Decoration gvo, 50 * Penfleld's Notes on Determinative Mineralogy and Record of Mineral Tests. 8vo, paper, Tables of Minerals svo, * Richards's Synopsis of Mineral Characters iamo. morocco, * Ries's Clays. Their Occurrence. Properties, and Uses gvo, 3 < Rosenbusch's Microscopical Physiography of the Rock-making Minerals. (Iddings.) gvo, 5 01 * Tillman's Text-book of Important Minerals and Rocks .8vo, 2 01 s< 1 MINING. 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 a S< x 2; SANITARY SCIENCE. 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, 18 y I 1 - * Towler's Sewage Works Analyses _ ^ i2mD, 2 oo JFuertes's Water and Public Health. .f .T. A . ! I2mo, r 50 Water-filtration Works i2mo, 2 50 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 Control , .8vo, 7 50 .Mason's Water-supply. (Considered principally from a Sanitary Standpoint) Svo, 4 oo Examination of Water. 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