PRACTICAL THERMODYNAMICS Published by the Me Grow- Hill Boole Company 5ucce>ssons to theBookDepartments of tKe McGraw Publishing Company Hill Publishing Company '.Publishers of Books for! Electrical World Jhe Engineering and Mining Journal Engineering Record Power and TKe Engineer Electric Railway Journal American Machinist Metallurgical and Chemical Engineering >T IT u y g ir IT irif t ir >T a ff IT g irg gju PRACTICAL THERMODYNAMICS A TREATISE ON THE THEORY AND DESIGN OF HEAT ENGINES, REFRIGERATION MACHINERY, AND OTHER POWER-PLANT APPARATUS BY FORREST E. CARDULLO, M.E. MEMBER OP AMERICAN SOCIETY OF MECHANICAL ENGINEERS PROFESSOR OF MECHANICAL ENGINEERING IN THE NEW HAMPSHIRE COLLEGE OF AGRICULTURE AND THE MECHANIC ARTS McGRAW-HILL BOOK COMPANY 239 WEST 39TH STREET, NEW YORK 6 BOUVERIE STREET, LONDON-, E.G. 1911 COPYRIGHT, 1911 BY MCGRAW-HILL BOOK COMPANY fHE SCIENTIFIC PRESS RT DRUMMOND AND COMPANY BROOKLYN, N. Y. PREFACE IN writing this volume the author has endeavored to present the natural laws and physical principles which underlie the action of thermodynamic apparatus in such a manner as to enable the student not only to compre- hend the principles upon which the apparatus depends for its operation, but also to assist him to correctly design such an apparatus, to operate it, and to judge of its value. The book is intended primarily as a text-book for the use of junior and senior classes in mechanical and electrical engineering. It there- fore attempts to present the subject of thermodynamics from the physical rather than from the mathematical standpoint. While the treatment of the subject is rigorous, a minimum of higher mathematics is used and the methods employed are those which appeal to common sense rather than to a knowledge of calculus. The writer believes that the higher mathe- matics are to be regarded merely as a set of tools by the use of which the engineer may accomplish certain results. Hence the methods employed in developing the mathematical part of the work depend upon the objects to be accomplished, and are the simplest and most effective possible. They are usually methods which lay stress on the physical phenomena rather than those which appeal to the accomplished mathematician. The writer has not hesitated to present new methods whenever these methods seem to be simpler and better than the older ones. Much of the difficulty of teaching thermodynamics arises out of a misunderstanding on the part of the student, of the phraseology usually employed, and from attempts to introduce the abstractions of the ancient philosophers into the concretions of modern science. Accordingly, no chapters are devoted to the first or second laws of thermodynamics and no puzzling or trouble- some analogies are offered for entropy. Many definitions differ radically from those offered in other text-books, but the changes made are con- sidered advisable in order to make the presentation of the subject more logical or more simple. It does not seem to the author that it is any longer necessary or desirable to give credit to the originators of methods of thermodynamic 267486 vi PREFACE investigation, or to the discoverers of physical truths long known, in a work of this kind. Accordingly, he has refrained from distracting the student's attention by continual reference to names which are strange to him and which, while they are of historic interest, should have no place in a text-book. While this book contains very little that is new, and is principally a presentation of truths long known, yet authorities are quoted but seldom. The effect of such references and quotations upon the student's mind is usually to divert his thought from the principles to be considered, and they are therefore omitted unless some unusally good reason dictates their insertion. The author has separated all reference to the temperature-entropy diagram from the body of the text and placed it it a separate chapter (the 25th) in order that it may be used or not as the judgment of the teacher shall dictate. The material in the 25th chapter is so arranged that it exactly parallels the remainder of the book, and the temperature- entropy analysis of any type of thermodynamic machine may be found in its proper order. It is the author's opinion that the temperature- entropy diagram is not illuminating to the average student, who is con- tinually seeking for some physical analogy for entropy and who is continually plunging himself into difficulties by seeking to carry his analogy further than the truth will warrant. The use of the entropy function in developing the .theory of the adiabatic expansion of vapors, on the other hand, involves no difficulties whatever, and the author has therefore presented this matter in the body of the text. The writer has attempted at all times to bring most of the work well within the comprehension of the average technical student. In some places it will seem as if he had made his treatment of the work absurdly simple, as, for instance, in the description of the steam engine. He believes, however, that many of the difficulties encountered by students arise from a misunderstanding of facts which seem to the teacher to be perfectly obvious and which the teacher mistakenly believes that the student thoroughly understands. Another difficulty often encountered in teaching thermodynamics arises from the fact that an inadequate preparation precedes the study of the phenomena of heat engines and other thermodynamic machinery. The author has therefore endeavored to present in the first seven chapters of the book the fundamental physical principles upon which a further study of the subject must depend, in such a thorough and simple manner that no trouble need subsequently arise from a misunderstanding of these fundamentals. In order that the book shall be available to the largest possible num- ber of classes, the author has included many items, which, while they are of great interest, can be profitably taught only to advanced students or to classes in which the amount of time available for the subject is greater PREFACE vii than that usually taken. These items have been printed in smaller type than the remainder of the text, and the teacher can omit any of them that he may see fit, without omitting any of the essential parts of the work. The problems have been carefully chosen to illustrate the principles treated in the text. The author believes that a student has a true knowl- edge of his subject, not when he can make a recitation of the substance of a statement in a text-book, but when his knowledge can be applied to the solution of problems. The problems have been so arranged as to advance the student one step at a time in his work, only one new element being introduced in each problem. By concentrating the student's atten- tion upon the new element, the problems are made more easy of solution and are more valuable from an instructional standpoint. The problems are not intended as examination questions to show the student's grasp of his subject, but are rather intended to be suggestive to him and to assist him in the comprehension of the text. The answers accompany the problems in each case. In working the problem it will in many cases be necessary to make use of a steam table. The reader should therefore procure such a table. Either Peabody's tables, published by John Wiley & Sons, or Marks and Davis' tables, published by Longmans, Green & Co., will be found to be admirably suited for the work. Peabody's tables are preferable for some kinds of work, while Marks and Davis' tables will be found preferable for other kinds. All the values given in the book, except those specially noted, are from Marks and Davis' tables. In the first edition of any work of this character, it is difficult to entirely eliminate errors, even by the exercise of the greatest care. Accordingly, the author will be very grateful to any of his readers who will point out to him errors of any kind which he may find, whether in the statements made or in the answers to the problems. In conclusion the author wishes to express his thanks to many friends who have assisted in the preparation of this work, particularly Professors Charles James, L. S. Marks, and C. H. Peabody, Dr. William Kent and Mr. Geo. Orrok. He also wishes to acknowledge his indebtedness to the firms mentioned on page x for material furnished. ERRATA ^ Page 7. Fig. 1. Ordinates should be -0.20, -0.10, 0.0, +0.10, +0.20. Page 11. Prob. 3. Ans. 3.2174. Prob. /1 3 i Ans. 13.998. Page 15. In equation (4) substitute R for C'F. not for C". Page 23. Prob. 4. Ans. 200.4. Page 36. Last expression should be ~-j- WP(V 2 -Vi). Page 37. Equation (2). Insert a minus sign before -5-. Page 38. Art. 51. P in equation should be Pi. Page 46. Equation 6. Insert brackets after and at end. Page 49. Prob. 16. Ans. 123,000. Prob. 18. Ans. 25 and 510. Prob. 27. Read 26 for 24. Page 50. Prob. 40. Ans. 0.809. Prob. 41. Ans. 0.0081. Prob. 42. Ans. 0.0142. Prob. 43. Ans. 1.10. Page 57. Line 3. Read 4 for 3. Page 63. Prob. 6. Read ft.-lbs. for B.T.U. Prob. 15. Ans. 42.8. Page 71. Prob. 3. Insert 161.1 in ans. Prob. 5. Ans. 333.0. Prob. 6. Ans. .002851. Prob. 9. Ans. 798.1. Page 77. In paragraph 4, line 2, read 0.0886 and so in line 5. Page 80. In equation read 1.4094. Page 87. Prob. 6. Ans. 24.11. Prob. 7. Ans. 0.0415. Page 88. Prob. 28. Ans. 10,495. Prob. 32. Ans. 1.6020. Page 95. Prob. 7. Ans. 14.956. Page 96. Prob. 16. After " air " insert "in Problem 15." Page 108. Second line from bottom, read P' for P. Page 130. In second equation read 25.36 for 25.0. Page 139. Prob. 4. Ans. 25.4. Prob. 5. Ans. 26.6. Prob. 6. Ans. 1.064. Page 140. Prob. 9. Ans. 99.7. Prob. 11. Ans. 12.9. Prob. 14. Ans. 122,800. Prob. 15. Ans. 15.7. Prob. 17. Cannot be solved since compression cannot be complete. Prob. 18. Cannot be solved. Page 156. Prob. 1. Ans. 85. Prob. 5. Ans. 10.5. Prob. 10. Ans. 0.0276. Prob. 11. Read "cylinder" for "piston." Ans. 19.6. Page 177. Prob. 2. Ans. 0.20 and 0.18. Prob. 3. Ans. 0.400 and 0.447. Prob. 9. Assume 120 r.p.m. Prob. 12. Ans. 23,100. Page 185. Inequations at bottom of page, read 1.1778 for 1.1178. Read 0.964 for 96.4. Read 1186.3 for 1183.3. Read 7.40 for 7.45. Read 0.726 for 0.505. Page 198. Prob. 5. Read 17.9 for 16.9. (Over] CARDTJLLO'S "PRACTICAL THERMODYNAMICS." Page 214. In article 223, paragraph 2, line 8, read seventh for sixth, ar in line 9 read sixth for seventh. Page 215. In col. 11 read 11.60 for 11.50, in col. 12 read 8.93 for 8.83 and i col. 14 read 2.748 for 2.848 and 3.48 for 1.212. Page 217. Sixth line from bottom. For 0.217 read 0.189. Fourth line frc bottom. For 3.792 read 3.683. Page 218. Fourth line. Read 3940 for 3830. Sixth line. Read 4030 for 3900. Art. 226. Par. 2. Line 6. Equation should be 9X1052.3 = 9471. Line 10. Equation should be 62,032-9471=52,562. Line 12. Read 3500 for 3290. Line 13. Read 3570 for 3360. Page 219. Par. 3. Line 6. Equation should be 62,032 X T V = 4770. Line 14. Read 18,170 for 18,250. Page 232. Prob. 3. Ans. 21.1. Prob. 4. Ans. 2560. Prob. 6. Ans. 2120. Prob. 7. Line 2 read CO for CO 2 . Page 233. Prob. 19. Ans. 2970. Page 251. Prob. 7. Ans. 60.3. Page 256. Equation 6. Read .74 for .75. Page 263. Prob. 4. Ans. 11.0. Page 273. Prob. 7. Ans. 3.83. Prob. 8. Ans. 1290. Prob. 10. Ans. 15,100. Prob. 11. Ans. 3,130,000. Page 290. Equation (2). For ^y read |^. Page 295. Line 11. For P read E. Page 301 . Answers contain some errors in third significant figure. Page 319. Prob. 2. Ans. 2.26. Prob. 3. Ans. 71,700. Prob. 4. Ans. 1002. Prob. 5. Ans. 573. Prob. 6. Ans. 40.5. Prob. 7. Ans. 232,500. Prob. 8. Ans. 160,800. Prob. 9. Ans. 13,660. Prob. 11. Ans. 2.52. Page 343. Prob. 2. Ans. 41,400. Page 344. Prob. 4. Ans. 6900. Prob. 5. Ans. 8590. Prob. 14. Ans. 0.0066. Prob. 15. Ans. 0.00503. Prob. 16. Ans. 503. Page 367. Prob. 3. An&. 32.5. Prob. 5. Ans. 45,150. Prob. 6. Ans. 181. Prob. 7. Ans. 251. Prob. 10. Ans. 113. Page 369. Third line from bottom. Read isothermally for adiabatically. Page 371. Second line from bottom. Read b c for b d. Page 383. Fifth line from bottom. Read cdfg for idfg. Page 384. Last line of Art. 348. Read cdfg for idfg. CONTENTS .'TER PAGE I. INTRODUCTION. THE NATURE AND MEASUREMENT OF HEAT 1 II. THE THERMAL PROPERTIES OF GASES 12 III. THE EXPANSION OF GASES 25 IV. THERMODYNAMIC PROCESSES AND CYCLES 51 V. THE THERMAL PROPERTIES OF VAPORS 64 VI. WET AND SUPERHEATED VAPORS 72 VII. MIXTURES OF GASES AND VAPORS 90 VIII. THE STEAM ENGINE 97 IX. STEAM CYCLES v 125 X. LOSSES IN THE STEAM ENGINE 141 XI. NOTES ON THE DESIGN AND TESTING OF STEAM ENGINES 158 XII. THE STEAM TURBINE 178 XIII. CONDENSING MACHINERY 199 XIV. COMBUSTION 214 XV. THE STEAM BOILER 234 XVI. BOILER PLANT AUXILIARIES 252 XVII. WATER-COOLING APPARATUS 264 XVIII. HOT-AIR ENGINES 274 XIX. THE INTERNAL COMBUSTION ENGINE 285 XX. NOTES ON THE DESIGN AND PERFORMANCE OF INTERNAL COMBUSTION ENGINES 302 XXI. GASEOUS FUELS 320 XXII. COMPRESSED AIR 332 XXIII. REFRIGERATION 34f> XXIV. HEATING, VENTILATION, EVAPORATION AND DRYING 356 XXV. ENTROPY DIAGRAMS 368 XXVI. THE KINETIC THEORY OF HEAT 393 ix ACKNOWLEDGMENTS The author is indebted to the following firms for illustrations and other material in this book. ALLIS-CHALMERS Co. AMERICAN ENGINE Co. AMERICAN LOCOMOTIVE Co. CROSBY STEAM GAGE AND VALVE Co. DE LAVAL TURBINE Co. DIRECT SEPARATOR Co. FORE EIVER SHIPBUILDING Co. GRAY MOTOR Co. HOLLY MANUFACTURING Co. MC-KENSIE FURNACE Co. NEW YORK ENGINE Co. OHIO BLOWER Co. OTTO GAS ENGINE Co. WESTINGHOUSE MACHINE Co, JOHN WILEY AND SONS PRACTICAL THERMODYNAMICS CHAPTER I INTRODUCTION THE NATURE AND MEASUREMENT OF HEAT 1. The Purpose of Thermodynamic Machinery. One of the greatest, if not the greatest, of our engineering problems, is the transformation of the store of energy with which Nature is' so lavishly endowed, into those forms which best serve the purpose of mankind. The form of energy which men find to be the most generally useful for their purposes is that form which we term work, or mechanical energy. Unfortunately, the forms in which energy is furnished to us by Nature are seldom those which are immediately available to our purpose, or which may be transformed into work by simple mechanical appliances, such as windmills or water-wheels. The needs of society are usually such that mankind is commonly obliged to avail himself of that vast store of natural energy found in the form of potential chemical energy in combustible substances. This form of energy can be liberated, so far as we know, only in the form of heat. In order to make Nature's store of energy of use to us, therefore, it is necessary first to transform it into the form of heat, and then in most cases to transform this heat into some more useful form of energy, such as work, or electricity, or light. In doing so, we make use of certain forms of engineering apparatus which we may term thermodynamic machines. Thermodynamics, in the sense in which it is used by physicists, is that branch of physical science which treats of the effects produced by heat and the phenomena accompanying their various manifestations. When used by the engineer, however, the term thermodynamics is understood to mean that branch of engineering science which deals with the interconversion of heat and work, and the phenomena attendant thereon. 2. The Conservation and Correlation of Energy. One of the funda- mental axioms of physical science is that the sum total of the energy 2 THE NATURE AND MEASUREMENT OF HEAT ART. 5 of the universe is a constant quantity and that this energy may not be increased or diminished, created or destroyed, by any known process or power. This physical axiom, known as the doctrine of the con- servation of energy, lies at the basis of our theory of thermodynamics. As a corollary of the axiom of the conservation of energy, we may state that the different forms of energy are mutually inter-convertible, and that the amount of one form of energy which will be required to produce a given amount of any other form of energy is fixed and invariable. For instance we find that a certain quantity of work will invariably be transformed into a certain quantity of heat, that a certain quantity of electrical energy is the equivalent of a definite quantity of potential chemical energy, and so on throughout the entire list of possible con- versions. 3. Standards of Measurement. Fundamental Units. As a pre- liminary to the intelligent discussion of any engineering subject, it is necessary to' establish certain standards of measurement. Without such standards it is impossible to express quantitative relations, or to make of the physical sciences anything but an orderly array of curious and interesting, but generally useless, facts. If these standards of measurement are to be of value in engineering work, they must be those which society uses in its ordinary dealings, and with which man- kind generally, and workmen more particularly, are thoroughly familiar. Accordingly, engineers in English-speaking countries use as their standards of measurement those units which are collectively known as the Foot Pound Second system. This system, while not so elaborate, or perhaps so rational, as the C.G.S. system in use among physicists, has the immense practical advantage that its units are understood by everyone, and are those in common use in our workshops. 4. Length. The unit of length is the foot which is defined 1 as 0.30480 meter or 30.48 centimeters. The meter is defined as the length of a certain bar of metal, accepted as the standard of length by inter- national agreement. The centimeter, which is the standard of length used in physical measurements, is Vioo part of the length of this bar. In certain engineering work the inch is a unit of length. The inch is, however, never used in rational energy equations. The symbol of length is L. 5. Mass. The unit of mass, or quantity of matter, is the pound, which is defined l as 0.453592 kilogram, or 453.592 grams. A kilogram is the mass contained in a certain metal weight, accepted as the standard of mass by international agreement. The gram is Viooo part of the kilogram. The symbol of mass, when expressed in pounds, is W. 1 By Act of Congress. ART. 6 UNITS OF MEASUREMENT 3 6. Time. The unit of time is the mean solar second, invariably called simply the second (except in works on astronomy) , which is 1 /8Q4oo part of the mean solar day. The symbol of time is t. 7. Force. The unit of force is the weight of 1 pound, or the force with which the earth attracts a mass of 1 pound, at any point where the acceleration produced by gravitation is 32.1740 feet per second per second. 1 For convenience and brevity, the unit of force is also known as a pound. The symbol of force is F. 8. Relation between Force, Mass, and Acceleration. It will be noted that the unit of force (1 pound) does not produce an acceleration of 1 foot per second per second, in the unit of mass (1 pound). In consequence of this fact, in all kinetic energy equations we use for the unit of mass that quantity of matter to which the unit of force does give an acceleration of 1 foot per second per second. This quantity of matter is 32.1740 pounds and is usually termed the kinetic mass unit. The symbol for mass, when expressed in kinetic mass units, is M , which is, of course, W equal to . 00 9. Derived Units. From the four fundamental units of length, mass, time, and force, the following units of measurement are directly derived: 10. Area. The unit of area is the square foot. In practical engi- neering calculations the square inch, which is, of course, Yi 44 part of the square foot, is generally used as the unit of area. The symbol for area is A. 11. Volume. The unit of volume is the cubic foot. The symbol for volume is V. 12. Work, or Energy. The unit of work, and therefore the funda- mental unit of energy, is the foot-pound, which is the quantity of work performed by a force of 1 pound in moving its point of application through a distance of 1 foot, measured in the direction of its line of action. The symbol for energy, when expressed in foot-pounds, is U. 13. Power. Power is the rate of doing work, or the rate of expendi- ture of energy. The practical unit of power is the horse-power, which is equivalent to the performance of work at the rate of 550 foot-pounds per second. The symbol for power, when measured in horse-power, is H.P. 14. Pressure. Intensity of pressure, called for brevity, pressure, is the rate of application of a uniformly distributed force upon an area, 1 This value for the acceleration of gravity has been accepted as standard by international agreement. The symbol for the acceleration produced by gravity is g. and for the value 32.1740 the symbol g may be used. 4 THE NATURE AND MEASUREMENT OF HEAT ART. 16 and is found by dividing the total force by the total area upon which it is applied. The units of pressure are four in number. The first is the pressure of 1 pound per square foot. This is the unit of pressure employed in all rational thermodynamic equations. The second is the pressure of 1 pound per square inch, which is 144 times as great as the first. This is the unit employed in engineering tables, such as steam tables, and so on, and in engineering calculations. The third is the pressure produced by a column of pure mercury 1 inch high, at a temperature of 32 F., when g is 32.1740 feet per second per second. This is the unit generally used in condenser and gas calculations. The fourth is the normal pressure of the atmosphere at sea level, which has been defined by international agreement to be the pressure produced by a column of pure mercury 29.921 inches high, at a temperature of 32 F. where g is 32.1740 feet per second per second. This unit of pressure is termed an atmosphere. The symbol for pressure, when expressed in pounds per square foot, is P. 15. Absolute and Gage Pressure. Pressure gages of the type or- dinarily used in engineering work do not measure the true pressure exerted upon their mechanism, but the excess of this pressure over that of the atmosphere. The pressure recorded by such an instrument is called the gage pressure, and may be reduced to the true or absolute pressure by adding the actual pressure of the atmosphere as deduced from the barometer reading. In like manner, a vacuum gage registers the amount by which a pressure falls short of that of the atmosphere and the " vacuum " so recorded may be reduced to absolute pressure expressed in inches of mercury, by subtracting it from the reading of the barometer. Unless pressures are stated to be gage pressures, they are understood to be absolute pressures, in works of thermo- dynamics. 16. Effects of Heat. Energy itself cannot be perceived. We may only perceive and measure it by the effects which it produces. Heat, being a form of energy, can only be perceived and measured by its effects. We term a body hot or cold according to the effects which we feel when we are in contact with it or in its neighborhood. We find that hot bodies tend to give up heat to cold bodies, and eventually all attain the same degree of warmth, when they are brought near one another. When one body is capable of giving up heat to another body we say that the first body has a higher temperature than the second. As a result of heat exchange between bodies of different temperatures (i.e., the addition of heat to cold bodies and the abstraction of heat from hot bodies), we find that some or all of the following effects are produced. First, the addition of heat to a body almost always increases its ART. 17 THE MEASUREMENT OF TEMPERATURE 5 temperature, making it more capable of giving up heat to colder bodies, and less capable of absorbing heat from hotter bodies. The rise in temperature is usually very nearly proportional to the quantity of heat added. Second, the addition of heat to a body, with consequent rise in temperature, generally tends to expand that body, and the amount of the expansion is usually very nearly proportional to the quantity of heat added. Third, the addition of heat to a body, with conse- quent rise in temperature, quite often results in a change in the physical state of the body. For instance, the addition of heat to ice changes it into water; the addition of heat to water changes it to steam. The abstraction of heat has in each of the above cases the contrary effect, reducing the temperature, decreasing the volume, and changing the physical state from that of a gas or liquid to that of a liquid or solid. For instance, the abstraction of heat from carbon dioxide, which is a gas, reduces its temperature and volume, and finally changes it to a snow-like solid. The addition of heat to certain kinds of bodies results in a change in their chemical composition. For instance, the addition of heat to potassium chlorate, KC1O 3 , changes it to potassium chloride and oxygen, the formula for the reaction being 2KC1O 3 = 2KC1+3O 2 . Such phe- nomena, however, unlike the ones recorded in the preceding paragraph, are not usually reversible. Subsequent abstraction of heat will not return such substances to their original chemical form. In all of these cases, the amount of change produced, as measured by the quantity of material changed, is always proportional to the amount of heat producing the change, so that heat may be, and is, measured quantitatively by scientists, by means of the physical effects which it produces. 17. The "Measurement of Temperature. Since the most obvious change ordinarily produced in a body by the addition or abstraction of heat is the elevation or depression of its temperature, we must first seek some suitable method of measuring temperature. It has been found that ice melts at a certain definite temperature, provided that the ice be formed from pure water, and the fusion occurs at a pressure of one atmosphere. This temperature is known in physics as the ice- point. It is also known that the temperature of the steam which comes from boiling water at a pressure of one atmosphere is a fixed quantity. This temperature is known in physics as the boiling-point. If we may find some method of determining the temperature of a body with reference to these two points, we will have a system of thermometry, or temperature measurement. We have noted that one of the effects of heat is to expand almost 6 THE NATURE AND MEASUREMENT OF HEAT ART. 18 all bodies to which it is added. Gases expand to a greater degree upon the addition of heat than do any other substances, and are therefore better suited than other substances to the purposes of exact ther- mometry. Some gases expand with great regularity, the amount of expansion so produced being strictly proportional to the quantity of heat producing the expansion and giving a definite measure of the rise in temperature of the gas. Helium and hydrogen are such gases. Other gases, such as air, oxygen, etc., while often used in thermometry, are less regular in their rate of expansion. Still other gases, such as carbon dioxide, are so irregular in their rate of expansion as to be quite unsuited for the purposes of thermometry. It is therefore the custom among physicists, as a result of international agreement, to adopt for the measurement of temperature the indications of a hydrogen ther- mometer. 1 The method of construction and use of such a standard thermometer is described in Art. 31. The symbol of temperature is T. (See Art. 26.) 18. Thermometer Scales. In engineering work in English-speaking countries the Fahrenheit thermometer scale is in common use. One degree on the Fahrenheit scale is defined as YIRO part of the rise in temperature, as indicated by a standard hydrogen thermometer, from the ice-point to the boiling-point. The Fahrenheit zero is 32 below the melting-point of ice, so that the temperature of the ice-point is 32 Fahrenheit (generally written 32 F.) and the temperature of the boiling-point is 212 F. In countries using the metric system, and in purely scientific work, the centigrade thermometer scale is used. The centigrade degree is Yioo part of the rise in temperature from the ice-point to the boiling-point. The centigrade zero is the ice-point and the centigrade temperature of the boiling-point is 100 (generally written 100 C.). In order to reduce Centigrade to Fahrenheit temperatures, we may make use of the formula (1) In order to reduce Fahrenheit to Centigrade temperatures, we may make use of the formula - 32) 9 1 For reasons of convenience, it is not the volume of the hydrogen, but the pressure which it exerts upon the walls of the bulb in which it is confined at constant volume, which affords a measure of its temperature. ART. 19 THE BRITISH THERMAL UNIT In these formula?, C and F are respectively corresponding Centigrade and Fahrenheit temperatures. 19. Mercury Thermometers. For the ordinary measurement of temperature in engineering work, "mercury in glass" thermometers are used. The indications of a perfect thermometer of this type, (i.e., one filled with pure mercury, and having a capil- lary tube of absolutely uniform bore) depend upon the kind of glass from which it is made, and the conditions under which it is used, and are invariably different from those of the hydrogen thermometer, except at the ice-point and boiling-point. Such thermometers are, however, sufficiently exact for most engineering work, although entirely unsatisfactory for refined investigations, unless suitably handled and calibrated. In Fig. 1 will be found a graphical representation of the errors of a perfect mercury in glass thermometer at different temperatures. It will be seen that the error is so small as not to be important in ordinary engineering work. 4-20 -1-10 -20 '0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 Fahrenheit Temperature by Mercury Thermometer JT IG> i Correction curve to reduce mercury in glass thermometer readings to hydrogen therm.ometer readings. 20. The British Thermal Unit. Temperature measures intensity of heat, or in other words, it determines the ability of a body to surrender heat to, or abstract it from, a body of a different temperature. It does not, however, tell us the amount of heat which the body contains. In order to measure quantity of heat, we need another unit of measure- ment aside from that of temperature. The unit of measurement used in engineering calculations in English-speaking countries is termed the Mean British Thermal Unit, and may be denned as Viso part of the heat required to raise 1 pound of pure water from a temperature of 32 F. to a temperature of 212 F. (i.e., from the ice-point to the boiling- point) without loss of mass, under a pressure of one atmosphere. In order to avoid the use of the cumbersome term Mean British Thermal Unit, the symbol B.T.U. is used. The symbol for quantity of heat is H. 21. The Mechanical Equivalent of Heat. Since heat is a form of energy and the different forms of energy are inter-convertible, it follows that work may be converted into heat. As a result of a long series of experiments carried out by many different men at various times, it has been shown that 777.5 foot-pounds of work may be transformed into one B.T.U. This quantity, 777.5 foot-pounds, is 8 THE NATURE AND MEASUREMENT OF HEAT ART. 22 known as the mechanical equivalent of heat, and in thermodynamic equations, we use for its exact (but unknown) value, the symbol J. 22. Specific Heat. If a small quantity of heat be added to a substance without changing its physical or chemical state, its temperature will be somewhat increased. The rise in temperature produced will be directly proportional to the quantity of heat absorbed, and inversely propor- tional to the mass absorbing it. The proportionality factor, which varies widely for different substances, is known as the specific heat of the substance. The specific heat of a substance may be defined as the number of B.T.U. required to raise the temperature of 1 pound of the substance 1 F. It follows from the definition of the Mean British Thermal Unit, and that of specific heat, that the average specific heat of water between the temperature of 32 and 212 F. is unity. The term average is used, because it has been found that the specific heat of different substances, water included, is not a constant quantity, but depends upon the temperature of the substance. Therefore, in physical or engineering investigations requiring great exactitude, account must be taken of this variation in the specific heat of substances, although in ordinary engineering work it is not necessary to do so. Tables are appended showing the relation of the English, the Metric, the Electrical Engineering, and the C.G.S. systems of units, used in engineering and physical measurements. TABLE I LENGTH Feet. Inches. Meters. Centimeters. Foot 1 12 0.30480 30.48000 Inch 08333 1 0.02540 2.54001 Meter 3.28083 39.37996 1 100 Centimeter 032808 39380 01 1 Millimeter 0.003281 0.03938 0.001 0.1 TABLE II AREA Sq. Feet. Inches. Meters. Centimeters. Foot . ... 1 144 . 092903 929.03 Inch 0006944 1 00064516 6 4516 Meter 10.7639 1550 1 10,000 Centimeter 0.00107639 15500 0001 1 ART. 22 TABLES OF EQUIVALENT UNITS TABLE III VOLUME Cubic. Feet. Inches. Yards. Meters. Liters. Centimeters. Foot 1 1728 .037038 .028317 28.317 28317 Inch .0005787 1 .000021433 .000016387 .016387 16.387 Yard..... . 27 46,656 1 . 76454 764 . 54 764.540 Meter 35.314 61,023 1.3081 1 1000 1,000,000 Liter .035314 61.023 .001308 .001 1 1000 Centimeter .000035314 .061023 . 00000 130S .000001 .001 1 TABLE IV MASS . Pounds. Kilograms. Grams. Pound 1 453592 453 592 Kilogram Gram 2.04622 00204622 1 001 1000 1 TABLE V FORCE Pounds. Kilogram. Dyne. Pound 1 0.453592 444,800 Kilogram 2 . 04622 1 980,665 Dyne 0000020866 0.00000101975 1 10 THE NATURE AND MEASUREMENT OF HEAT ART. 22 si ""5 ?si"ii D T* CO S rH CO C^ ^^ HH rH t- o CO tO O eOi i ( tO O co o t^. O CO rH O 000 O odd o o o CO ^ O i i c^ 10 ,_, 05 05 rH CO (N O . r^ co oo QO rH T^ r^, O rH O I>- (N (M co o co S3 O (7) which becomes r PdV = -VdP (8) Dividing through by PF we have dV _dP J V ~ P' Integrating each side between corresponding limits - --? which becomes f (log e V-loge Vi) = log e PI -log e P, .... (11) or r lo ge ^ =log.^^ (12) whence and PF^PiF/ (14) In the above equation, P is the pressure and F is the corresponding volume of a quantity of sensibly perfect gas undergoing adiabatic expansion (or compression) when the original pressure of the gas was PI and its original volume V\. This expression may also be written PVr=C, (15) in which C is a constant. ART. 44 RELATION BETWEEN INITIAL AND FINAL PRESSURE 31 44. Relation between Initial and Final Pressure, Volume, and Tem- perature of a Gas Expanding Adiabatically. If the gas be assumed to have expanded to some pressure P 2 , and corresponding volume V 2 we will of course have the relation -PiVi r . (1) This may be written 7l /-. ........ (2) For the characteristic equation of gases, we have for 1 pound of any gas T= ~R~' and therefore P\v p For -^ in (3) we may substitute its value from equation (2), and obtain the relation 'i (Y*\ r ~ l ^(vl) ' From number (2) we may write F2 = /Pi\7 F! \P 2 ] y Substituting this value for ==- in equation (3) we have r-l Solving equations (2) and (4) for F 2 , (1) and (6) for P 2 , and (4) and (6) for T 2 we will have c. P,-,,'. 32 THE EXPANSION OF GASES ART. 45 These equations may be readily solved by the use of a table of logarithms when they are written in the form A', log ^logF^ - lo T B'. log K 2 = log Vi+j= C'. logP 2 = logP 1 + r'lo D'. log P 2 = log P l + ^ E'. log T 2 = log TVKr-l) log F. Io7^ = lo7\+ By means of these relations we may compute the final temperature, pressure, or volume of a mass of gas expanding adiabatically,. when its initial temperature, pressure or volume is known, and also the ratio of its initial and final pressure, temperature, or volume. It is to be noted that these equations will be true, no matter what system of units be employed. For instance, the temperatures may be expressed in Centi- grade or Fahrenheit degrees on the absolute scale, the pressure in pounds per square inch or per square foot, or in atmospheres, or in inches or millimeters of mercury, and the volumes in per cent, in cubic feet, in cubic inches, or in cubic centimeters or liters. So long as the same system of units is employed throughout an equation, the results obtained will be correct. 45. Work Done During Adiabatic Expansion. The amount of work done by a mass of gas expanding adiabatically will of course be equal to the heat lost by the gas. Therefore we may write U= W K V (T,-T 2 ) ........ (1) Substituting for TI the value * * and for T 2 the value -^~jj, we may write this expression, TT W u ' W ART. 46 WORK OF ADIABATIC EXPANSION 33 Clearing this, we will have P2V 2 ) . . (3) JUi From equation (6), Art. 43, we have the relation S-Fi (4) Substituting this we will have > in which C7=the number of foot-pounds of work done by a mass of gas expanding adiabatically; PI = the initial pressure of the gas in pounds per square foot ; P 2 = the final pressure in the same units; Fi = the initial volume of the gas in cubic feet; F 2 = the final volume in the same units. This same result may be obtained by the integration of the expression U=C V *PdV, (6) sVl in which we substitute for P the value obtained from equation (C), Art. 44, namely, (y v The integral of this expression is, of course, equal to the shaded area in Fig. 6, which shows the pressure-volume curve of a mass of gas expand- ing adiabatically. This curve is also, like the rectangular hyperbola, asymptotic to both axes, but it will be noted that the area included under this curve from the volume V\ to an infinite volume is not infinite in amount, but is a definite and finite quantity, as will be seen from equation (1) in this article. By such an expansion the gas will part with the entire amount of intrinsic energy which it contains, and the work of expansion is limited to this quantity of energy. 46. Graphical Construction of the Curve whose Equation is PV n =C. Any curve represented by the general equation PV n = C 34 THE EXPANSION OF GASES ART. 46 may be constructed graphically by the method shown in Fig. 7, when one point on the curve, and the value of the index n are known. Let the coordinates of point M be PI and V\, and the coordinate axes be FIG. 6. The adiabatic expansion line. FIG. 7. Graphical construction of the curve P V n = K. OP and 0V. Draw AO, making any convenient angle AO V with OF. Then let ART. 47 ISOBARIC EXPANSION 35 Determine the angle BOP, whose tangent is given by the equation, tan BOP = ^, JL and construct angle BOP. Through M draw the horizontal line Me and the vertical line Md, intersecting OB at c and Oa at d respectively. Through c and d draw ce and df, making angles of 45 with the coordinate axes, and intersecting them at e and /. Through e draw a horizontal .and through / a perpendicular, intersecting at N, which will be a second point on the curve. In like manner points I and q and as many more points as are desired, may be located. An inspection of the figure will show that if P l and V l be the coordinates of M, and P and V those of N, that ...... (1) and (2) From equation (2) we may write V n =V l n (l+tB.nAOV) ......... .... (3) Hence PV* = P 1 F 1 n = P 1 tY l (l-tan50P)(l;ftaiiAOF) n ..... (4) Dividing both sides by P^V^ we have (l-tanBOP)(l+tanAOF)=l ........ (5) From which we deduce that . . (6) Clearing (6), X-Xt&nBOP=l .......... (7) Solving for tan BOP, . . (8) JL Hence a curve constructed in the manner described will satisfy the equation P v n = P l V l n = C. It will often be more convenient to determine the angles AOV and BOP by computing the coordinates of a second point upon the curve, such as N, and then after drawing Ne and Nf, ec, and fd, and Me and Md, finally draw OB and OA through the intersections of ec with Me, and fd with Md, respectively. 47. Isobaric Expansion. The equation for isobaric expansion is P = k, a constant, since the pressure remains constant. The PF curve is therefore a horizontal line. During isobaric expansion, the quantity of heat added to the gas is of course 36 THE EXPANSION OF GASES The work done during isobaric expansion is equal to ART. 47 The amount of intrinsic energy imparted to the gas is equal to W K V (T 2 - Ti). f We may also express the amount of work done during the isobaric expansion in terms of the temperatures by the expression W FIG. 8. Work of isobaric expansion and increase in intrinsic energy. We may express the quantity of heat imparted to the gas in terms of the pressure and volumes, by the expression / If an adiabatic be drawn from the state P\Vi and another to be drawn from the state P^V^ of a, gas undergoing isobaric expansion, as in Fig. 8, the intrinsic energy of the gas at the beginning of expansion will be represented by the area under the first adiabatic, the intrinsic energy at the end of the expansion will be represented by the area under the second adiabatic, and the energy imparted to the gas will be repre- sented by the difference between these areas plus the work of expansion which is represented by the area under the isobaric line. This is, obviously, the shaded area plus twice the blackened area. ART. 48 POLYTROPIC EXPANSION 37 48. Polytropic Expansion. The work performed by a mass of gas undergoing polytropic expansion is equal to a constant times the loss in intrinsic energy. Hence we may write PdV=-aK v dT, ........ (1) by analogy with equation (3), Art. 43. Making the same substitutions as were made in the former equation and transposing the constant a to the left-hand member we will obtain ' ...... which is similar in form to equation (9) of that article. Substituting n for , we will finally obtain the relation, PV n = P 1 V 1 n = C, ........ (3) which is similar in form to equation (14) of Art. 43, and is the equation giving the relation between the pressure and volume of a mass of gas undergoing polytropic expansion. 49. The Relation between the Initial and Final Pressure, Volume, and Temperature of a Gas Undergoing Polytropic Expansion. From equation (e) in the preceding paragraph, the relations between the initial and final pressure temperature and volume of a mass of gas under- going polytropic expansion may be deduced by the methods outlined in Art. 44. By substituting n for 7- in the equations A to F and A' to F' in that article, the relation between the initial and final pressure, temperature, and volume of a gas undergoing polytropic expansion, may be computed. In the same way by substituting aK v for K v and n for 7- in the equations in Art. 45, the work done during polytropic expansion may be computed. In case the value of the exponent n is very nearly unity, exact computations of the work done during polytropic expansion are not feasible. In case it is desirable to determine exactly the work done during such expansion the area included under the expansion line may be measured, and the work of expansion computed from the measured area and the known scales of the diagram. 50. Special Cases of Polytropic Expansion. It may be noted that the isothermal, adiabatic, and isobaric expansion may all be considered special cases of polytropic expansion. When a= oo , oo 38 THE EXPANSION OF GASES ART. 51 which is the case of isothermal expansion where there is no change in intrinsic energy. When a = l, which is the case of adiabatic expansion, where the change in intrinsic energy is equal to the work performed. When a = l j-, n=0, which is the case of isobaric expansion, where the pressure is constant. When a=0, r-i+o n=- T - -fV? which is the case of change of pressure without change of volume (i.e., change in intrinsic energy without performance of work). 61. Expansion in Conducting Cylinders. Gases do not remain in thermody- namic equilibrium while they are being expanded or compressed in practical thermo- dynamic machines, since there will in general be a difference in temperature between the expanding gas and the conducting walls of the containing vessel. As a result the temperature of the layers of gas close to the walls will be different from that of the mass of the gas. It is found, however, that under these conditions the pressure- volume curve of expansion or compression is very nearly a line of polytropic expansion, and the value of the index lies between 1 and 7-. Such expansion or compression may be treated as though it were polytropic, the value of the index n in the equation PV n = C being determined from the actual expansion curve by the equation log - in which P l and V l and P 2 and V 2 are corresponding absolute pressures and volumes as derived from the actual expansion line taken from an indicator card. 52. Compression the Converse of Expansion. The process of com- pression is the reverse of the process of expansion, the volume of the gas progressively diminishing as the process continues. In order to compress a gas, work must be done upon it, which accounts for the fact that if proper substitutions be made in any of the formulae for the work done by an expanding gas, we will, in the case of compression, get a negative answer. For instance, in the case of isothermal expansion, the final volume is less than the initial volume, the ratio of the volumes is less than unity and the logarithm of the ratio is a negative quantity (see Art. 41, equation (4)), indicating that the gas does negative work during compression. If proper substitutions be made in the equations giving quantities of heat absorbed or rejected by gases undergoing compression, the answers will also be negative, indicating that in the case of compression, the heat transfer is in the opposite direction to what it is in the case of expansion. 53. The Velocity of Sound. If the pressure of a mass of gas be suddenly increased at some point, the pressure of the entire mass is not raised instantly, but ART. 53 THE VELOCITY OP SOUND 39 the increase of pressure travels from point to point in the gas with a velocity depend- ing on the nature and temperature of the gas. Assume a column of gas whose cross-section is 1 square foot and whose length is indefinite, to be confined within a tube, under a pressure of P pounds per square foot and at the temperature T. If the pressure at one end of this tube be increased suddenly by applying the force dP to the piston shown in Fig. 9 for one second, the increase in pressure, dP, will be trans- mitted to the right with the velocity V feet per second, and at the end of one second V cubic feet of gas will be compressed. The mass of this gas will be P V Since the compression of the gas is sudden, the gas does not have time to part, with its heat to surrounding objects, and the compression is adiabatic, the relation between the pressure and volume being expressed by the equation from whence dP Gas at pressure P and temperature T. FIG. 9. Differentiating this expression we have r Vr- l dV=-CP~ 2 dP, ......... (4) dv - CdP We may substitute for C its value from equation (2) and obtain *r-?g ............. (6) In the above expression dV is the change in volume of the gas, dP is the change in pressure, and P and V are the initial pressure and volume. It will be noted that if the pressure increases, the volume diminishes, as is indicated by the minus sign. As a result of the application of the constant force dP to the gas, the end of the column is moved, in one second, a distance dV, and the center of gravity dV of the column is moved in the same time a distance . The acceleration produced by this constant force in the column of gas is twice the distance which the gas was moved in the first second, or dV feet per second per second. Now, from a well- known principle in dynamics, namely, force = mass X acceleration, we have dP = _ 5 dV ............. (7) 40 THE EXPANSION OF GASES ART. 54 Substituting from 1 and 6, py dP Solving for V we will have (9) in which V is the rate of transmission of pressure in gas in feet per second, and T is the absolute temperature of the gas in Fahrenheit degrees. 64. Velocity of Transmission of Explosive Pressure in Confined Gases. The above equations will be true only when the increase hi pressure is infinitesimal as compared with the actual pressure of the gas. This is true in the case of sound waves, which are transmitted in the gas with the velocity given by the above equation. When, however, the wave is caused by a violent explosion which produces a large increase in pressure, the velocity of transmission of the pressure is higher than the above equation would indicate. If it be assumed that the increase in pressure produced by the suddenly applied force is large, the final pressure produced may be represented by P 2 while the initial pressure may be represented by P r The final volume will be, from equation (/I), Art. 44, (8) The decrease of the volume of the mass, and therefore, as has already been shown, the acceleration of the mass, will be (9) We may therefore write, by analogy from equation (8) of the previous article, Solving for T^ we will have y= jgRT(P 2 -P3 (11) which is an expression giving the velocity of transmission of pressure in a gas when the increase in pressure is great as compared with the original pressure. When a combustible mixture of gases is confined under pressure and ignited at some point, as is the case in most types of gas engines, the increase in pressure pro- duced by the local explosion is transmitted throughout the mass of the gas in the same manner as. the pressure was transmitted through the column described in Art. 53. As the pressure wave proceeds through the gas, it compresses it adiabatically. If the initial temperature of the gas is sufficiently high, so that the adiabatic compression heats the mixture to its kindling point, the flame of com- bustion will proceed through the mass with the velocity indicated by equation (11) of the preceding paragraph. If, however, the temperature of the gas is not sufficiently high for this action to take place, the pressure in the gas will increase gradually, the flame being propagated from point to point by heat conduction and radiation, with ART. 55 FLOW OF GAS THROUGH AN ORIFICE 41 a velocity many hundred times lower than that given. The phenomena of pressure transmission are of great practical importance in the theory of gas engines and gaseous explosions. 65. Theory of the Flow of Gas through an Orifice. When a gas flows through a nozzle, it will be found that as each particle of the gas passes through it will expand in volume and increase in velocity. If the ratio of expansion in volume as the gas passes from one cross-section of the nozzle to another is less than the ratio of increase in velocity, it must follow that the nozzle is less in cross-section at the second point than at the first, the nozzle being convergent between the two sections. If, on the other hand, the ratio of expansion is greater than the ratio of increase in velocity, the cross-section of the nozzle will be greater at the second point than at the first, the nozzle being divergent between the two sections. In passing through a nozzle, a gas will of course neither gain nor lose heat, on account of the small time which each particle takes in passing through. This being the case, the kinetic energy of the quantity of gas which passes a given cross-section of the nozzle in a given time, plus the work it does in displacing the gas in the region p, FIG. 10. Ideal apparatus illustrating the flow of gas through a nozzle into which it rushes, must be equal to the loss in intrinsic energy of the gas, plus the work done upon it by the advancing mass of gas which takes its place in the region from which the gas flows. 56. Flow through a Nozzle. This will be apparent from a consideration of Fig. 10, in which A is a cylinder and B a nozzle. The cross-section of the nozzle is very small in comparison with that of the cylinder, so that the velocity of the gas in the cylinder may be neglected. The gas emerging from the nozzle passes into the tube C, whose cross-section is the same as that of the nozzle at the point where the nozzle terminates. Assume that cylinder A is filled from point D with gas having a pressure PI and a temperature T l and the tube is filled to the point E with gas having. a pressure P 2 and a temperature T 2 . At E in the tube and at D in the cylinder are pistons, which, of course, exert upon the gas a pressure equal to the pressure exerted upon them by the gas. Since the pressure in tube C is less than the pressure in cylinder A, the gas will flow from A to C through the nozzle, and if the pressure in A and C are to remain constant, the pistons must both move to the right. If a certain quantity of gas be supposed to flow from A to C in one second, then its volume in A may be assumed to be V t and its volume in C may be assumed to be T 7 2 - The amount of work done by piston D upon the gas during this second 42 THE EXPANSION OF GASES ART. 57 is equal to P v V lt and the amount of work done by the gas upon the piston E is P 2 F 2 . The intrinsic energy of the gas has been diminished by the amount and the kinetic energy gained by the gas is equal to in which W is the weight of gas which flows through the nozzle in one second, and v is the velocity of the gas flowing into tube C. 67. Determination of the State of the Gas Passing the Throat of a Nozzle. At first the gain in velocity as the gas passes successive sections of the nozzle will proceed at a greater rate than the increase in the volume of the mass, and the successive sections will diminish in area, the nozzle being convergent. When a certain point is reached, however, the rate of gain in volume increases more rapidly than the rate of gain in velocity, and the nozzle from that point outward must be made divergent. The point of minimum cross-section is known as the throat of the nozzle, and the quantity of gas which the nozzle will pass will obviously depend upon the area of this cross-section of the nozzle. Let v be the velocity of the gas passing this cross-section, let W be the number of pounds passing this cross-section per second, let T be the absolute temperature of the gas passing this cross-section, let P be the pressure of the gas passing this cross-section, and let T l and P t be the temperature and pressure of the gas entering the nozzle. Then we will have, collecting and equating the terms given at the end of Art. 56, T^ v 2 l * ~^ is often used. 2 The letter 6 is often used. ART. 96 DETERMINATION OF THE PROPERTIES 69 these instruments be accurate, that they be properly calibrated, and that, in general, the work be so conducted as to eliminate errors. After determining experimentally a series of values for the pressure of saturated steam of different temperatures, it is necessary to discover an equation expressing the relationship. Many such equations have been proposed, the most accurate of which is that of Marks, which has the following form : 1 log p = 10.515354 - 4873.71 T~ l - 0.00405096T + 0.000001392964 7 1 ' where p is the pressure of the steam in pounds per square inch and T is the absolute temperature of the steam in Fahrenheit degrees. The heat of the liquid may be determined by measuring the quantity of electrical energy used in heating a known weight of water from the ice-point to any required temperature. In conducting such an experiment, it is, of course, necessary to take precautions against many different kinds of errors. No satisfactory formula for the heat of the liquid has yet been produced except the one q - (*-32) + C, in which C is a correction determined from a graphical representation of the results of the experimental work. The determination of the total heat of the steam is the most difficult part of all the experimental work in this field. The principal difficulty lies in the impossibility of obtaining absolutely dry and saturated steam. However, several methods have been used which give results known to be accurate within y io of 1 per cent of the total value of the quantity. The result of these experiments may be represented for temperatures above 212 by the equation, 2 # = 1150.3+0.3745(*-212)-0.000550(*--212) 2 . From this equation and from graphical representations of experimental work covering the range below 212, the value for the total heat of saturated steam may be computed for each degree of temperature within the range which a steam table is intended to cover. 96. The Computation of Properties not Directly Observed. All other properties of steam are determined from the pressure, temperature of vaporization, heat of the liquid, and total heat of the steam by means of the thermodynamic rela- tions of these four quantities. The latent heat of evaporation is obtained by sub- tracting the heat of the liquid from the total heat of the steam. The entropy of dh the liquid is found by a step-by-step integration of the quantity , and the entropy of evaporation by dividing the latent heat of evaporation by the absolute tempera- ture of vaporization. The total entropy of the steam is the sum of the entropies of the liquid and of evaporation. The specific volume is determined in the following manner : Assume that 1 pound of steam is caused to perform a Carnot cycle, between the temperature limits T andT dT. The Watt diagram of this cycle is shown in Fig. 18. At the beginning of this Carnot cycle the cylinder of the Carnot engine will contain 1 pound of water at a tempera- ture T, and under the corresponding pressure P. During the isothermal expansion this water will be entirely evaporated by adding to it the latent heat of evaporation 1 See the Transactions of the A.S.M.E. for 1911. 2 See footnote to article 101 for Davis' method of determining the total heat. 70 THE THERMAL PROPERTIES OF VAPORS ART. 97 at the constant temperature T and the corresponding constant pressure P. When the pound of water is entirely evaporated, it is allowed to expand adiabatically until its temperature falls by the infinitesimal amount dT. It is then isothermally com- pressed while under the pressure PdP and at the corresponding temperature TdT. When it is almost entirely condensed, the condensation is stopped, and the remainder of the compression is adiabatic, raising the -T temperature of the mixture of steam and p^ water to the value T, and condensing the remaining steam. In this process, the quantity of heat imparted to the water is equal to the latent heat of evaporation. The quantity of work done is, of course, ~~ x VdP, where V is the increase in volume of FIG. 18. Oarnot cycle for steam. the steam (i e ? the difference in volume between the pound of dry and saturated steam and the pound of water under the given pressure), and dP is the change in dT pressure. The efficiency of the cycle is, of course, . Hence we may write L ~^L=vdp (i) Solving this for V, we will have V = ^X^| (2) If we plot from the steam tables a curve showing the relation of the temperature and the pressure of steam (the pressure being in pounds per square foot), we may at any point in this curve draw a tangent, and from the intercepts we may determine dT the value of the expression . By means of this value, and the known latent heat of evaporation for the given temperature, we may compute the increase in volume V, and by adding to this the original volume of the water, we obtained the volume of the steam at the given temperature and pressure. After obtaining the specific volume for a number of temperatures, we may construct a curve or derive an equation from which the specific volume of steam of any temperature may be determined. The density of steam is, of course, the reciprocal of the specific volume of the steam. The external work of evaporation is found by multiplying the change in volume in passing from the condition of a liquid to the condition of dry and saturated steam, by the pressure of the steam in pounds per square foot. This quantity divided is by 777.5 in order to reduce it to B.T.U. The internal energy of evaporation is equal to the latent heat of evaporation minus the external work of evaporation. The internal energy of the steam is equal to the internal energy of evaporation plus the heat of the liquid. 97. The Properties of Other Vapors. The phenomena observed when other liquids than water are evaporated into their vapors are exactly similar to the phenomena observed in the case of water. The quantities ART. 97 PROBLEMS 71 of heat, the pressure, the temperatures, the specific volume, etc., will of course be different for different vapors, but the methods of determining these quantities are the same for all vapors. In the case of such vapors as sulphur-dioxide, ammonia ether, alcohol, chloroform, carbon bisul- phide, carbon tetrachloride, and aceton, which are vapors used commer- cially in refrigerating machines of various types, the properties have been determined with some degree of accuracy and are embodied in tables available to engineers. PROBLEMS Find from a steam table the properties of steam asked for in the following prob- lems. The answers are from the tables of Marks and Davis. Other answers will usually be obtained by the use of other tables. Interpolate when necessary. 1. What is the temperature of vaporization of steam at pressures of 1 Ib. absolute? 10 Ibs. absolute, and 100 Ibs. gage? Ans: 101.8, 193.2, and 337.9. 2. What is the pressure of saturated steam at temperatures of 100, 200, and 300? Ans. 0.946, 11.52, and 67.00 Ibs. per square inch. 3. Find the heat of the liquid in each case in Problem 1. Ans. 69.8 and 308.8 B.T.U. 4. What quantity of heat is required to raise 1 Ib. of water from the ice-point to the several temperatures given in Problem 2? Ans. 67.97, 167.9, and 269.6 B.T.U. 5. What is the volume of 1 Ib. of dry and saturated steam at the pressures given in Problem 1? Ans. 339.0, 38.38, and 3.886 cu.ft. 6. What is the density of dry and saturated steam at the temperatures given in Problem 2? Ans. 0.008251, 0.02976, and 0.1547 Ibs. per cu.ft. 7. Find the latent heat of evaporation of steam at the pressures given in Problem 1 . Ans. 1034.6, 982.0, and 880.0 B.T.U. 8. Find the total heat of steam at the temperatures given in Problem 2. Ans. 1103.6, 1145.8, and 1179.1 B.T.U. 9. Find the internal energy of evaporation of 1 Ib. of steam at the three pressures given in Problem 1. Ans. 972.2, 910.9, and 789.1 B.T.U. 10. Find the external work of evaporation at the temperatures given in Problem 2. Ans. 61.5, 71.6, and 79.8 B.T.U. 11. Find the entropy of the liquid at the pressures given in Problem 1. Ans. 0.1327,0.2832, and 0.4875. 12. Find the increase in entropy of 1 Ib. of water when it is evaporated into steam at the temperatures given in Problem 2. Ans. 1.8506, 1.4824, and 1.1972. 13. Find the total entropy of 1 Ib. of steam at the pressures given in Problem 1. Ans. 1.9754, 1.7874, and 1.5909. CHAPTER VI WET AND SUPERHEATED VAPORS 98. Quality of a Vapor. When a vapor contains suspended within it in the form of fine bubbles or drops a quantity of the liquid from which it was formed, the vapor is said to be wet. The vapor and the suspended liquid have the same temperature and are under the same pressure, and the whole mass may therefore be said to be in a state of thermodynamic equilibrium, since the division of the particles of liquid is so fine that during expansion or compression the whole mass will not only remain in thermal equilibrium, but it will remain homogeneous in character. The proportion which the dry and saturated vapor present bears by weight to the whole quantity of the mixture, is termed the quality of the wet vapor and is usually expressed as a per cent. The symbol for the quality of a wet vapor is q. 1 One pound of wet vapor will there- fore consist of q pounds of dry and saturated vapor, and of lq pounds of liquid. Thus 1 pound of steam of 90 per cent quality contains 9 /io of a pound of dry and saturated steam, and there is I /\Q of a pound of water suspended in this steam. If a wet vapor be thermally isolated, its quality will remain constant provided the pressure remains unchanged, but on account of the greater density of the particles of fluid, they will tend to fall to the bottom of the containing vessel, thus separating the wet vapor into two portions, one consisting of dry and saturated vapor, and the other of liquid. This process of course destroys the homogeneity of the wet vapor by separating it into two thermodynamic bodies. Since, however, the diameter of the particles of liquid is exceedingly small, the rate at which they descend through the vapor is also small, and this action goes on but slowly. Con- sequently, wet vapors when in motion, do not change their quality in any sensible degree during short periods of time. 99. Properties of a Wet Vapor. The heat of the liquid of a wet vapor is the same as the heat of the liquid of the dry and saturated vapor of the same temperature (or pressure). The latent heat of evaporation of a wet vapor is equal to the latent heat of evaporation of the dry and saturated vapor of the same tem- 1 The symbol x is often used for this quantity. 72 ABT 99 PROPERTIES OF A WET VAPOR 73 perafrture (or pressure) multiplied by the quality of the wet vapor. This may be expressed by the formula L w = qL, in which L w is the latent heat of evaporation of the wet vapor, L is the latent heat of evaporation of the dry and saturated vapor, and q is the quality of the wet vapor. The total heat of a wet vapor is the sum of the heat of the liquid and the latent heat of evaporation. This may be expressed by the equation in which H w is the total heat of the wet vapor, h is the heat of the liquid, and q and L are as in the preceding paragraph. Unless the quality of a wet vapor is very low, the volume of the liquid which it contains is only a small proportion of the whole volume. We may therefore take as the specific volume of a wet vapor the product of the specific volume of the dry and saturated vapor at the same tem- perature (or pressure) into the quality of the wet vapor. This neglects, of course, the volume of the liquid, but no material error is introduced, as this is entirely negligible. We may then write for the specific volume of a wet vapor the formula in which V w is the specific volume of the wet vapor, q is- the quality, and V is the specific volume of the dry and saturated vapor at the same temperature. The density of a wet vapor is the reciprocal of its specific volume and is therefore equal to the density of the dry and saturated vapor at the same temperature (or pressure) divided by the quality of the wet vapor. The external work of evaporation of a wet vapor is equal to the external work of evaporation of the dry and saturated vapor at the same temperature (or pressure), multiplied by the quality of the vapor. The internal energy of evaporation of a wet vapor is equal to the internal energy of evaporation of the dry and saturated vapor at the same tem- perature (or pressure) multiplied by the quality of the vapor. The entropy of the liquid is the same in the case of a wet vapor as in the case of the dry and saturated vapor of the same temperature (or pressure). The entropy of evaporation of a wet vapor is equal to the entropy of evaporation of the dry and saturated vapor at the same temperature (or pressure) multiplied by the quality of the vapor. 74 WET AND SUPERHEATED VAPORS ART. 100 The total entropy of a wet vapor is equal to the sum of the entropies of the liquid and of evaporation and may be expressed by the formula in which N w is the total entropy of the wet vapor, q is its quality, M is the entropy of the liquid of the dry and saturated vapor, and ^ is the entropy of evaporation of the dry and saturated vapor. The above properties, when determined by the methods given, will of course be for 1 pound of wet vapor. The properties of the dry and saturated vapor, in the case of steam or other vapors used in thermody- namic machinery, may be taken from tables. If the quality of the wet vapor is unknown, but its temperatures or pressure, and its total heat or total entropy, or density or specific volume, or its latent heat or entropy of evaporation is known, its quality, and from this its other properties, may be computed from the equations or by the methods developed in the preceding paragraphs. 100. Superheated Vapors. When a vapor has a higher temperature than the temperature of vaporization corresponding to its pressure, it is said to be superheated. The state of a superheated vapor is defined in practice by giving either its temperature and pressure or by giving its pressure and the amount of superheat. The amount of superheat is obtained by subtracting from the observed or computed temperature of the superheated, vapor the temperature of vaporization corresponding to the observed or computed pressure of the vapor. 101. Properties of a Superheated Vapor. The latent heat of evapora- tion, the temperature of vaporization, the entropy of the liquid, the entropy of evaporation, and the external and internal energy of evapora- tion are the same for a superheated vapor as for a dry and saturated vapor when it is of the same pressure as the superheated vapor. The heat of superheat of a vapor is the quantity of heat which must be imparted to 1 pound of it in raising it from the temperature of vaporiza- tion to its actual temperature, at the pressure of vaporization. This is equal to the amount of superheat multiplied by the mean specific heat of the vapor at constant pressure, for the given conditions. It may be noted that the specific heat of a vapor at constant pressure varies both with the temperature and with the pressure, so that its mean value, for the particular range of temperature and pressure for which the com- putation is made, should be employed. The specific heat of superheated steam has been determined with considerable accuracy by several observers. Thomas's method consists in electrically heating steam already slightly ART. 101 PROPERTIES OF A SUPERHEATED VAPOR 75 superheated, and measuring the energy required, the weight of steam superheated, and the rise in temperature. The total heat of a superheated vapor is equal to the total heat of the dry and saturated vapor at the same pressure plus the heat of superheat. This may be expressed by the formula 1 H 8 = H + C p (t s -t] in which H 8 is the total heat of the superheated vapor, H is the total heat of the dry and saturated vapor at the same pressure, t s is the temperature of the superheated vapor, t is the temperature of vaporization correspond- ing to its pressure, and C p is the mean specific heat of the superheated vapor at constant pressure for the pressure and range of temperature for which the computation is made. When the amount of superheat is not great, the specific volume of a superheated vapor may be obtained from the equation V T V * y 8 - rp } in which V is the specific volume of dry and saturated vapor of the same pressure, T is the absolute temperature of vaporization corresponding to this pressure, and T 8 is the actual temperature of the vapor. In case the superheat is great, the vapor becomes more like a perfect gas in its behavior and its specific volume may be found from the characteristic equation of gases, or better, by means of an empirical equation derived from a knowledge of its actual behavior at different temperatures and pressures. The density of a superheated vapor is the reciprocal of its specific volume. The entropy of a superheated vapor is found by adding to the entropy of the dry and saturated vapor of the same pressure the quantity obtained by a step-by-step integration of the heat additions necessary to superheat the vapor, each divided by the absolute temperature at which they occurred. 1 When superheated steam flows through a porous plug (a process called throttling), it neither gains nor loses heat. Consequently we mpy write the formula in which the right-hand member is the total heat before throttling and the left-hand members the total heat after throttling. In each member the first term will usually 1x3 large as compared with the second, and an error in the determination of C p will therefore have a comparatively small effect upon the answer when we solve for H' or H". Consequently, if the total heat of dry and saturated steam be determined for some one pressure, from a series of throttling experiments, the total heats at other pressures may be determined with great accuracy. This method is due to Davis. 76 WET AND SUPERHEATED VAPORS ART. 102 If the specific heat of superheat of the vapor be assumed to be constant, this quantity may be expressed by the equation, N. = N + C p log e , in which N 8 is the total entropy of the superheated vapor, N is the total entropy of dry and saturated vapor of the same pressure as the super- heated vapor, C p is the specific heat of the superheated vapor at constant pressure, T s is the absolute temperature of the superheated vapor, and T is the absolute temperature of vaporization corresponding to the pressure of the superheated vapor. In practical work, the entropy of superheated steam as well as the values of the other properties are usually obtained from a table. 102. The Relation between Vapors and Gases. At this point, it is proper to point out the relations existing between vapors and gases. It has already been stated that when a gas is sufficiently cooled and com- pressed, it will condense into a liquid. During the process of cooling, it is reduced from a sensibly perfect gas, first to the condition of a highly superheated vapor, then to the condition of a slightly superheated vapor, then to the condition of a wet vapor, and finally it is entirely transformed into a liquid. There is no definite line of demarcation which separates any one of these states from the next. We may therefore regard a gas as being in the condition of a highly superheated vapor even though the gas be sensibly perfect. 103. The Critical State. Experiment shows that when an attempt is made to liquefy any of the permanent gases by the application of pressure, that the attempt will fail unless the temperature of the gas is below a certain definite value. This temperature is known as the critical temperature of the gas. Experiment has also shown that the latent heat of evaporation of a liquid diminishes as the temperature and pressure increases, and that in the case of some liquids it is reduced to zero at the critical temperature. If a liquid is heated to the temperature at which its latent heat of evaporation becomes zero, it will, obviously, be vaporized without further addition of heat, and at any higher temper- ature the substance can exist only as a vapor. Consequently, the critical temperature of a substance may be defined as that temperature at which the latent heat of evaporation of its liquid becomes zero. The pressure of a saturated vapor at the critical temperature is known as the critical pressure of the substance. This is, of course, the pressure which is required in order to liquefy the vapor when it has the critical temperature. The specific volume of a vapor at the critical temperature and pressure is termed the critical volume. The state of the vapor is termed the critical state. ART. 104 THE PHENOMENA OF FUSION 77 104. The Phenomena of Fusion. It is a matter of experience that when a liquid is cooled, it will finally be transformed into a solid at some definite temperature which is known as the freezing point of the liquid, and also as the melting point, or temperature of fusion of the solid into which it is transformed. Some complex organic substances and some mixtures of simple substances do not have a definite freezing-point, but all elemen- tary substances do, as do also almost all simple compounds. In order to transform the liquid into a solid, it is necessary to abstract heat from it at constant temperature. In order to retransform the solid into a liquid, it is necessary to add to this the same quantity of heat, at the same constant temperature. This quantity of heat is known as the latent heat of fusion. The melting-point of any substance varies somewhat with the pressure, but the range is usually very narrow. 105. Sublimation. If the pressure of vaporization of a liquid at the melting-point of the solid from which it is formed is greater than atmos- pheric pressure, the solid cannot be melted in an open vessel, but will sublime at atmospheric pressure. A substance sublimes when its vapor is formed directly from its solid form by the addition of heat. When the vapor so formed is condensed, it will condense in the form of a solid. It is evident that a solid substance can be melted only in the presence of its own vapor, and the pressure of the vapor must be equal to the saturation pressure at the temperature of fusion, for, if the vapor pressure be less than the saturation pressure, the liquid will be transformed into vapor the instant the solid melts. Hence the phenomena of sublimation. The pressure of other vapors and gases present has no effect in preventing sublimation, except as the presence of such gases serves to prevent the free escape of the vapor which is being sublimed. An inspection of a steam table will show that, when the pressure of the water vapor present in the air is less than 0.0866 pounds per square inch, ice will sublime, since as fast as the ice is melted, the water formed will instantly disappear as vapor, the vapor pressure of water at the melting-point of ice being 0.0866 pounds per square inch. In order to obtain water from ice it is therefore necessary to melt the ice in an atmos- phere where the pressure of the water vapor is greater than the value given. Carbon is an example of a substance which cannot be liquefied except at very high pressures, and since the temperature at which carbon would melt is exceedingly high, it is impossible, by any means, to obtain liquid carbon. Could we do so, it would in all probability crystallize in the form of the diamond, on solidifying, just as ice crystals are formed from water at suitable pressures (i.e., at a pressure greater than 0.0866 pounds per square inch). Most solids sublime to a noticeable extent at temperatures approach- ing their melting-point; carbon, for instance, sublimes from the filament 78 WET AND SUPERHEATED VAPORS AKT. 105 within the bulb of the incandescent lamp, and is deposited in the form of a thin film on the interior of the glass. Ice and snow also sublime at temperatures far below freezing. Even a cold wind will cause the rapid disappearance of a snowbank provided the air is dry (i.e., the pressure of the water vapor present is very low) . While we cannot state positively, it is quite possible that all solid substances are continually subliming at a very slow rate, and would in the course of centuries lose appreciably in weight. We know that this is true in the case of certain substances, which gradually disappear at temperatures below their melting-point unless confined within an air-tight space. 106. Isothermal Expansion of Vapors. When a vapor is caused to expand without the addition of heat, its temperature falls. Consequently, if a vapor is caused to expand isothermally, heat must be added to it. If the vapor be wet, this heat will vaporize the moisture present as the expansion progresses, and so long as any moisture is present, the expansion will be isobaric as well as isothermal, for the least fall in pressure will lower the temperature of vaporization of the liquid, and cause it to evap- orate at such a rate as to restore the pressure to that corresponding to the temperature. For instance, if a mixture of steam and water be confined at constant pressure and heat be supplied, the water will be evaporated, and the volume will increase, but the pressure and temperature of the mass will both remain constant. The pressure-volume curve which represents the isothermal expansion of a mass of wet vapor is, therefore, a horizontal line. The work done during such isothermal expansion is, of course, equal to the product of the pressure (in pounds per square foot) into the change in volume (in cubic feet) , and is also equal to the external work of evaporation of the quantity of liquid evaporated during isothermal expansion. The quantity of liquid so evaporated may be deduced from the specific volume of the vapor and the observed or computed change in volume during the expansion. If the isothermal expansion of a vapor be continued after it has become dry, the vapor will become superheated, since the pressure will fall off and the temperature will remain constant. As the expansion progresses, the amount of superheat becomes greater and greater as the pressure becomes lower, and the condition of the vapor approaches more and more that of a perfect gas. The pressure-volume curve for the isothermal expansion of a superheated vapor resembles that of a gas and may be very nearly represented by a rectangular hyperbola. This method of vaporous expansion is not, however, of great importance in the theory of thermodynamic machinery, since it is never met with in practice. 107. Expansion without Change of Quality. A mass of vapor may be caused to expand, and to remain in the dry and saturated condition throughout the expansion, by the addition or abstraction of heat at the AET. 108 ADIABATIC EXPANSION 79 proper rate. The pressure-volume curve of a mass of steam, when it expands under such circumstances, is known as the line of constant steam weight, and it may be plotted, point by point, from a steam table, by making the volume of the mass of vapor proportional to the^ specific volume of dry and saturated steam for each of the several pressures for which the points are plotted. The plotting of this curve is a matter of importance in the analysis of steam-engine and steam-turbine tests. If a vapor which condenses by adiabatic expansion be caused to expand slowly within a conducting cylinder while the walls of the cylinder are maintained at a temperature slightly higher than the initial temperature of the vapor, it will expand in this manner, since a wet vapor quickly takes up heat, while a dry one does not. As soon as any of the vapor is condensed by expansion, the liquid formed is immediately re-evaporated by the heat from the walls of the cylinder. In certain kinds of engineer- ing apparatus it is found that this method of vaporous expansion is quite closely approximated. 108. Adiabatic Expansion. A vapor is caused to expand adiabatically when it is confined within a non-conducting cylinder or when it is allowed 'to flow through a properly formed nozzle. The successive states of a mass of vapor undergoing adiabatic expansion all have the same entropy. In the case of a vapor, we cannot write a rational equation connecting the pressure and volume, or temperature and volume, of the mass of expanding fluid, as we can in the case of a gas. It is therefore impossible to compute directly the exact effects of adiabatic expansion upon the temperature, pressure, and quality of the vapor, although numerous empirical equations have been given by different investigators which give results which are approximately correct for limited ranges of expan- sion. However, by means of the relations between the total entropy of a vapor and its other properties, we may compute for any particular case, the properties of the vapor when its initial temperature or pressure and quality and its final temperature are known. Thus if vapor of known properties (i.e., temperature or pressure, quality and total entropy), l)e caused to expand adiabatically to some other temperature or pressure, its total entropy at the new state will be the same as it was initially. From the known total entropy and temperature or pressure at the new state, we may compute the entropy of vaporization, the quality of the vapor, and any other properties which are desired. For instance, if steam of 350 temperature and 98 per cent quality be caused to expand adiabatically to a temperature of 110, we may find its properties at the lower temperature in the following manner: The entropy of the liquid at 350 is 0.5032. The entropy of evaporation of the wet steam is 0.98 X 1.0748=1.0533. The total entropy of the steam at 110 will, since the expansion is adiabatic, be the same as it was at 350, namely, .5032+ 80 WET AND SUPERHEATED VAPORS ART. 109 1.0533 = 1.5565. The entropy of evaporation will be found by subtracting from the total entropy of the steam the entropy of the liquid at 110, which is 0.1471, giving for the entropy of evaporation of the wet steam 1.4094. The quality of the steam may now be found by dividing the entropy of evaporation of the wet steam by that of dry and saturated steam. In this case the quality will be U) 94 77.9 per cent. From this quality the other properties of the wet steam may be determined. 109. Effect of Adiabatic Expansion on the Properties of a Vapor. When the total entropy of dry and saturated vapor decreases as the tem- perature of vaporization increases, the vapor will be partly condensed as a result of adiabatic expansion unless it is highly superheated or very wet at the beginning of the expansion. Most vapors are of this character, steam being a good example of the type. When steam expands adia- batically, a portion of it will condense so long as the initial quality of the steam is greater than about 50 per cent. On the other hand, the prop- erties of certain kinds of vapors are such that the entropy of the dry and saturated vapor increases with the temperature of vaporization. Such vapors superheat when they expand adiabatically. Ether is an example of such a vapor. If it be initially dry and saturated and be caused to expand adiabatically, it will be superheated, while if it is initially wet, it will become dryer as a result of the expansion. Vapors which condense by adiabatic expansion are dried or superheated by adiabatic compression, and those which are superheated or dried by expansion are condensed by adiabatic compression. Thus steam when very wet is condensed, and when nearly dry is dried by adiabatic compression. We may determine the adiabatic expansion line of a vapor point by point, by determining its specific volume at several pressures by the principles outlined in Art. 108. In the same way we may determine the total heat, or any other desired property, of an expanding vapor for different temperatures (or pressures). If desirable, we may derive an empirical equation which will give the relation between the property desired and the temperature or pressure of the expanding vapor. The design of turbine nozzles and of other forms of steam machinery may be greatly facilitated by employing, in such computations, a table or diagram which gives the relations between the temperature, quality, entropy, specific volume and total heat of a vapor. Peabody's temperature- entropy table is an example, giving the relation of the quality, total heat, and specific volume of steam to its temperature and entropy. Mollier's diagram, also much used for this work, gives the relations of the ART. 110 STEAM CALORIMETERS 81 quality or superheat, and the pressure of steam, to its total heat and entropy. 110. Work of Adiabatic Expansion. The quantity of work done by a mass of vapor during adiabatic expansion will depend upon the mass and the initial quality or superheat of the vapor, and upon the tem- perature or pressure limits of the expansion. It will be equal to the difference between the initial and final internal energy of the vapor. For a further development of the theory of adiabatic expansion of vapors, as applied in practice in the design of steam turbines, see Arts. 201 and 202. 111. Determination of the Quality of a Wet Vapor. In practice, all vapors which are not superheated are wet, since it is impossible by any means at our command to obtain a vapor which is exactly dry and satu- rated, just as it is impossible to obtain two points which are exactly a given distance apart. Engineering investi- gations often therefore involve the determination of the quality or super- heat of a vapor. It is not difficult to measure simultaneously the tempera- ture and pressure of a superheated vapor and thereby determine the superheat, but it is necessary to resort to indirect methods in order to deter- mine the quality of a wet vapor. The vapor whose quality engineers are most often obliged to determine is steam. An instrument for determin- ing the quality of steam is termed a steam calorimeter, and several types of such instruments are in use. 112. The Throttling Calorimeter. When the steam which is being tested contains less than 3 or 4 per cent of moisture, and the pressure is sufficiently high, it is usual to employ a type of calorimeter originally devised by Professor Peabody, which is known as a throttling calorimeter, and is shown in Fig. 19. The essential parts consist of a chamber A, usually made of pipe fittings, a valve B, which is interposed between the chamber and the source of steam, and a thermometer C, which is inserted in a thermometer well D near the center of the chamber. The steam to be tested is taken from pipe P in which it is flowing and admitted to the chamber through the valve, which is kept nearly closed, so that the a Hair Felt FIG. 19. The Peabody throttling calorimeter. 82 WET AND SUPERHEATED VAPORS ART. 113 pressure of the steam in the chamber is about that of the atmosphere. The pressure of the steam in the pipe P must be known. The total heat per pound is then given in the formula, (1) in which H w is the total heat per pound of the wet steam in the pipe P, q is the quality of the steam in the pipe, LI is the latent heat of evaporation of dry and saturated steam having the pressure of the steam in the pipe P } and hi is the heat of the liquid at the pressure of the steam in the pipe. After passing through the valve the total heat of the steam will be unal- tered, but since the total heat of dry and saturated steam as atmospheric pressure is less (in case q is sufficiently large) than the total heat H w of the wet steam, the steam in chamber A will be superheated, and the amount of its superheat may be determined by means of the thermometer. The total heat of the superheated steam in A will be given by the formula, t a ), ......... (2) in which H a is the total heat of dry and saturated steam at atmospheric pressure, t is the F. temperature registered by the thermometer, t a is the saturation temperature of steam at atmospheric pressure, and .47 is the specific heat of superheated steam at atmospheric pressure. Equating 1 and 2 we will have 9 Li+/n = # a -K47(*-* ff ) ....... (3) Solving 3 for q we will have, f q ) ~ ........ VV 113. Errors of the Throttling Calorimeter. The results given by the throttling calorimeter are affected by the following sources of error: First, loss of heat by radiation, which makes the total heat of the steam in the chamber A less than the total heat of the steam in the pipe and reduces the apparent quality of the steam; second, back pressure in the chamber A which increases the temperature registered by the thermometer and the apparent superheat in the chamber A ; third, the temperature of the blast of steam issuing from the valve is less (since part of its total heat is in the form of kinetic energy) than that of the steam in the chamber A (where the kinetic energy of the blast has been retransformed into heat), hence if this blast of steam strikes the thermometer well, the thermometer reading will be lower than it should be; fourth, the sample of steam taken from the pipe may contain a greater or less proportion of water than the ART, 113 ERRORS OF THE THROTTLING CALORIMETER S3 steam flowing in the pipe. The first source of error may be obviated by clothing the calorimeter in some non-conducting material or by arrang- ing it so that the chamber A is sur- rounded by a steam jacket, as is done in the New Hampshire calori- meter shown in Fig. 20. The second source of error may be eliminaled by obtaining the exact pressure of the steam in the calorimeter by means of a pressure gage attached to the chamber A. It is usually more convenient and quite as satis- factory to allow an ample opening for the escape of steam, so that the pressure in the calorimeter shall be only a small fraction of a pound greater than the pressure of the atmosphere. The third source of error may be eliminated by so- designing the calorimeter that the blast of steam from the reducing valve does not strike upon the walls of the thermometer well. The fourth source of error is the most difficult of all to eliminate. Steam rising through a vertical pipe is of practically uniform quality, hence a sample taken from such a pipe will represent accurately the quality of the steam. When steam flows through a horizontal pipe a quantity of water flows along the bottom of the pipe and the lower strata are wetter than the upper ones. When a sample of steam is taken from a hori- zontal pipe through an opening distant 45 from the bottom of the pipe, as shown in Fig. 21, it will represent the aver- age quality of the steam in the pipe with considerable accuracy. A sample of steam from a pipe in which the may be taken by introducing into the pipe FIG. 20. New Hampshire throttling calorimeter. FIG. 21, To C alorimeter -Sampling pipe for a horizontal steam pipe. steam is flowing downward 84 WET AND SUPERHEATED VAPORS ART. 114 WWW To Calorimeter FIG. 22. Sampling pipe for a vertical steam pipe. a small pipe in which are drilled a number of small holes in the manner shown in Fig. 22. It is preferable, when it is possible, to take steam in this manner from a vertical pipe and better to take it from a pipe in which the current of steam is rising rather than from one in which it is descending. Fortunately, the two points in a boiler plant where it is most necessary to make determinations of the quality of steam are the point where the steam issues from the boiler and the point where the steam enters the engine. In the first case, the steam is of uniform quality, and it is almost always pos- sible to take the sample from a vertical pipe. In the second case, the steam is usually passed through a separator before entering the engine, and the action of the separator is such that the steam entering the engine is uniform in quality. If any suspicion exists that the steam is not uniform in quality, great pains must be taken to insure that the sample truly represents the actual quality of the steam. 114. Other Calorimeters. In case the amount of moisture in the steam is large, the quality of the steam may be determined by condensing the steam in a known weight of water and determining the rise in temperature. A calorimeter operating on this principle is known as a barrel calorimeter. Into a known weight of water in a barrel is introduced a pipe through which steam flows. The condensation of the steam raises the temperature of the water and the heat lost by the steam is equal to the heat gained by the water. Let W be the weight of water originally contained in the barrel, and w be the gain in weight or weight of steam condensed. Let t\ be the initial temperature of the water, and t 2 be the final temperature of the water. Let hi and h 2 be the heat of the liquid (as obtained from a steam table) at the temperature t\ and t 2 respectively. Let L be the latent heat of evaporation of dry and saturated steam at the pressure of the steam which is sampled, and ^3 be the heat of the liquid at this pressure. The heat gained by the water will then be WQi^ hi) and the heat lost by the steam will be w(qL -\-hs~- h 2 ) since the steam is con- densed and the liquid reduced to the temperature corresponding to h 2 . Equating these expressions and solving for q, we will have wL The barrel calorimeter is not as accurate an instrument as the throttling calorimeter, but if properly used it will give fairly good results. The ART. 114 OTHER CALORIMETERS 85 accuracy of the calorimeter will obviously depend upon the accuracy of the thermometer readings, and of the weight obtained, upon a thorough stirring of the water in the barrel so that all parts are of the same tempera- ture, and upon the length of time which the experiment takes. The shorter the time of the experiment, other things being equal, the more accurate the results will be. The barrel calorimeter usually gives results which are too low. The separating calorimeter is an instrument which mechanically separates the water from the steam. The water is then weighed or meas- ured and the steam is weighed or estimated in some way. The weight of steam divided by the weight of water plus the weight of steam gives the quality of the steam. Carpenter's separating calorimeter, shown in Fig. 23, is an example of this class. The steam enters the instrument at the top and issues into the body of the calorimeter through the several holes in the pipe A. When the direction of motion of the steam is suddenly changed, by causing the steam to pass out of the chamber B in an upward direction, the superior inertia of the heavy particles of water carries them against the per- forated metal basket C, to which they adhere. The water so collected drips into the chamber D, where it is measured by means of the gage glass E. The dry steam following the path shown by the arrow escapes through an orifice at the bottom of the calorimeter. It may be shown experimentally that so long as the pressure in the calorimeter is more than twice that of the atmos- phere, the weight of steam escaping through this orifice in a given time is very nearly pro- portional to the absolute pressure of the steam in the calorimeter. This absolute pressure is measured by the steam gage G. The weight of dry steam discharged in a given time is then given by the formula, W = Ktp, where K is the discharge constant, t is the time (in minutes) and p is the absolute pressure in the calorimeter. K is to be determined for any particular instrument, by condensing the steam discharged at known pressure in a known time. If w be the weight of water collected in the calorimeter in time t, the quality of the steam will be W FIG. 23. Carpenter's separating calorimeter 86 WET AND SUPERHEATED VAPORS ART. 115 The errors of the separating calorimeter are those due to radiation and those due to incomplete separation of the water from the steam. These two sources of error tend to correct one another, and the latter is usually greater in amount than the former, so that the apparent quality, as obtained by the use of the separating calorimeter, is usually greater than the true quality. The separating calorimeter is a convenient instrument to use, but its discharge constant and its errors should be determined before the instrument is used. The quality of steam may be obtained by drying and superheating it by means of a measured quantity of electrical energy, as is done in the Thomas superheating calorimeter. Various types of steam calorimeters and the proper methods of using them are described in Carpenter's Exper- imental Engineering, Chapter 13. FIG. 24. FIG. 25. 115. The Steam Separator. It is usual, when steam engines are distant from the boilers supplying them with steam, or when for any reason the steam supply is likely to be wet, to interpose in the steam pipe, close to the engine, an apparatus termed a separator, whose duty it is to remove from the steam the most of the water which it contains. Sepa- rators operate on two principles. In the first type the steam passes into the separator at high velocity and its direction is suddenly changed. The wet steam consists a mixture of vapor and water. The particles of water being many hundred times heavier than the steam, their superior inertia will cause them to shoot straight ahead when the current of steam is suddenly deflected. If these particles of water encounter a wet surface, t^ey will adhere to the surface and drip to the bottom of the chamber in which it is contained. Such a separator is shown in Fig. 24. ART. 115 PROBLEMS 87 In the second type of steam separator, the steam is caused to travel in a helical path; the centrifugal force so developed, on account of the superior density of the water particles, throws them against the outside walls of the separator, upon which they collect. The water then drips to the bottom of the separator. Such a separator is illustrated in Fig. 25. A separator will usually, in case very wet steam is supplied to it, deliver steam of 98 per cent quality or better. In case the steam is fairly dry (i.e., of 96 per cent quality or better) the greater part of the moisture present will be extracted by the separator. Steam containing less than 2 per cent of moisture is usually known as commercially dry steam. Such steam may be always obtained by the use of a suitable separator. The water which collects in a separator must be drawn away at intervals, for, if the separator fills up with water, it is no longer effective. The water from a separator is usually taken care of by an automatic device termed a steam trap, which discharges the water flowing into it, at inter- vals, without permitting the escape of steam. PROBLEMS 1. How much water is contained in 8 Ibs. of wet steam whose quality is 85%? Ans. 1.2 Ibs. 2. What weight of dry and saturated steam is contained in 10 Ibs. of wet steam having 15 per cent of moisture? Ans. 8.5 Ibs. 3. What is the heat of the liquid of wet steam at a pressure of 1 atmosphere? Ans. 180 B.T.U. 4. What is the latent heat of evaporation of 1 Ib. of steam of 90 per cent quality at a pressure of 1 atmosphere? Ans. 873.4 B.T.U. 5. What is the total heat of 1 Ib. of steam of 90 per cent quality at a pressure of ] atmosphere? Ans. 1053.4 B.T.U. 6. What is the specific volume of steam of 90 per cent quality at a pressure of 1 atmosphere? Ans. 26.93 cu.ft. 7. What is the density of steam of 90 per cent quality at a pressure of 1 atmosphere? Ans. 0.0416 Ibs. per cu.ft. 8. What is the external work of evaporation of steam of 90 per cent quality at a pressure of 1 atmosphere? Ans. 65.5 B.T.U. 9. What is the internal energy of evaporation of steam of 90 per cent quality at a pressure of 1 atmosphere? Ans. 807.8 B.T.U. 10. What is the total internal energy of steam of 90 per cent quality at a pressure of 1 atmosphere? Ans. 987.8 B.T.U. 11. What is the entropy of the liquid of steam of 90 per cent quality at a pressure of 1 atmosphere? Ans. 0.3118. 12. What is the entropy of evaporation of steam of 90 per cent quality at a pressure of 1 atmosphere? Ans. 1.3003. 13. What is the total entropy of steam of 90 per cent quality at a pressure of 1 atmosphere? Ans. 1.6121. 14. The latent heat of evaporation of wet steam for a temperature of 300 is 800 B.T.U. What is its quality? Ans. 88%. 88 WET AND SUPERHEATED VAPORS ART. 115 15. The total heat of wet steam at a pressure of 100 Ibs. is 1100 B.T.U. What is its quality? Ans. 90.3%. 16. Two pounds of wet steam are contained in a volume of 12.96 cu.ft. at a temperature of 280. What is the quality? Ans. 75%. 17. Wet steam is found to weigh 0.120 Ibs. per cubic foot at a pressure of 50 Ibrf. What is its quality? Ans. 98%. 18. The entropy of evaporation of wet steam at a temperature of 180 is 1.400. What is its quality? Ans. 90.5%. 19. The total entropy of wet steam at a temperature of 330 is 1.400. What is its quality? Ans. 82.1.%. 20. Steam having a pressure of 150 Ibs. per square inch has a temperature of 408.5. What is the amount of superheat? Ans. 50. 21. Assuming the specific heat of superheated steam at atmospheric pressure to be 0.47, what will be the heat of superheat of 1 Ih. of steam at a temperature of 312 and a pressure of 1 atmosphere? Ans. 47 B.T.U. 22. What will be the total heat of this steam? Ans. 1197.4 B.T.U. 23. From a table of the properties of superheated steam find the specific volume, the total heat, and the entropy of steam of 100 Ibs. pressure and having a temperature of 427.8. Ans. 5.14 cu.ft., 1239.7 B.T.U., and 1.6658. 24. From such a table determine the temperature of steam whose pressure is 120 Ibs. and whose total heat is 1233.8 B.T.U. Ans. 421.3. 25. Determine the number of degrees of superheat of steam of 150 Ibs. pressure whose entropy is 1.6343. Ans. 100. 26. What quantity of heat is required to raise 1 Ib. of water from a temperature of 60 to a temperature of 212? Ans. 151.92 B.T.U. 27. What quantity of heat is required to evaporate 1 Ib. of water of a temperature of 60 into dry and saturated steam at a temperature of 212? Ans. 1122.3 B.T.U. 28. What quantity of heat will be required to evaporate 10 Ibs. of water having a temperature of 80 into steam of 90 per cent quality at a pressure of 100 Ibs. absolute? Ans. 10,423 B.T.U. 29. What quantity of heat will be required to evaporate 100 Ibs. of water of a temperature of 60 into steam at a pressure of 150 Ibs. and a temperature of 448.5? Ans. 121,630 B.T.U. 30. One pound of steam of a pressure of 100 Ibs. per square inch and a quality of 50 per cent is expanded isothermally until it is dry and saturated. Find the work done and the heat supplied. Ans. 31,890 ft.-lbs. and 444.0 B.T.U. 31. Steam having a volume of 2 cu.ft. and a pressure of 100 Ibs. is expanded while it remains in a dry and saturated condition to a pressure of 10 Ibs. What is its final volume? Ans. 17.33 cu.ft. 32. Dry and saturated steam at a pressure of 100 Ibs. expands adiabatically until its pressure is 10 Ibs. What is its final total entropy, entropy of evaporation, and quality? Ans. 1.6002, 1.3188, and 87.67%. 33. What will be the total heat of the steam when the expansion has proceeded to 2 Ibs. absolute? Ans. 930.0 B.T.U. 34. Steam having a quality of 10 per cent is compressed adiabatically from a pressure of 10 Ibs. absolute to a pressure of 30 Ibs. absolute. What is its quality? Ans. 4.9%. 35. At what pressure will this steam become completely transformed into water? Ans. 64.4 Ibs. 36. What quantity of work was performed in compressing this wet steam to a pressure of 64.4 Ibs.? Ans. 14.6 B.T.U. ART. 115 PROBLEMS 89 37. What quantity of work is performed by 1 Ib. of steam in expanding adiabati- cally from a temperature of 300 to a temperature of 100, the steam being initially dry and saturated? Ans. 239.1 B.T.U. 38. Steam in a throttling calorimeter has a temperature of 312 at a pressure of 1 atmosphere. What is its total heat? Ans. 1197.4 B.T.U. 39. The original pressure of this steam was 200 Ibs. per square inch. What was its quality before entering the calorimeter? Ans. 99.9%. 40. The temperature of the steam in a throttling calorimeter is 220 when the barometer indicates a pressure of 13 Ibs. per square inch. The original pressure of the steam was 87 Ibs. gage. Find the quality of the steam. Ans. 96.91%. 41. A barrel contains 400 Ibs. of water at a temperature of 75 F. After con- densing steam at a pressure of 120 Ibs. absolute, it gains 20 Ibs. in weight and 53 in temperature. Find the quality of the steam. Ans. 95.8%. CHAPTER VII MIXTURES OF GASES AND VAPORS 116. Gaseous Mixtures. When two or more sensibly perfect gases are brought into contact with one another, the particles of one tend to pass between the particles of the other. As a result, after the lapse of a sufficient length of time, the two gases will form a homogeneous mechanical mixture. This process of mixing is known as diffusion, and the mixture resulting is, in every sense except a chemical one, a perfectly homogene- ous body, and will remain so provided it undergoes no chemical action, and its component particles are not separated by enclosing the mixture within a porous vessel. 1 When such a mixture of gases occurs, all of the constituents of the mixture will come to the same temperature, and this temperature will, of course, be the temperature of the mixture. The mass of the mixture will be the sum of the masses of the several constituents. If the mixture be confined within a vessel, each of the constituents will exert upon the walls a pressure which is equal in amount to the pressure which that constituent would exert were it confined separately within the vessel, at the same temperature. Consequently, the pressure of the mixture will be the sum of the pressures of the several constituents. Were each of the constituents confined at the pressure and the temperature of the mixture, they would occupy definite volumes. The sum of these volumes will, if the constituents are all sensibly perfect gases, be the volume of the mixture. 117. The Thermal Properties of Gaseous Mixtures. The density of such a mixture, under given conditions, may be obtained by dividing the mass of the mixture by its volume, or if the masses of the several constituents are known, by dividing the sum of the products of the mass and density of each of the constituents, under the given conditions, by the mass of the mixture. From the density of the mixture the value of R for the mixture may be deduced by the method given in Art. 30. In the same way, the specific heat of such a mixture at constant pressure (or constant volume) may be found by dividing the sum of the products of the mass and specific heat at constant pressure (or constant volume) of each of the constituents, by the mass of the mixture. The value of 1 The process of separating the constituents of a gaseous mixture by the action of a porous wall is termed osmosis. For the theory of this action see Chapter XXVI. 90 ABT. 117 THE THERMAL PROPERTIES OF GASEOUS MIXTURES 91 the constant f for a mixture of gases is the ratio of the specific heats at constant pressure and constant volume, and the mixture will, during expansion or compression, behave exactly as if it were a simple gas whose thermodynamic properties are those obtained in the manner given above. We may, therefore, treat such a mixture as if it were a gas having definite and known thermodynamic properties. The mathematical statement of the properties of two or more gases may be obtained as follows : Let W and W" be the mass of the two con- stituents, R f and R" the value of the function R for these constituents, D' and D" the density of these constituents under standard conditions, K' p and K n ' p the specific heat at constant pressure, and K' v and K" v the specific heat at constant volume of the two constituents. We will then have the following relations : The mass of the mixture will be W=W'+ W" ............. (1) When the mixture is within the volume V at the temperature T, the pres- sure of the mixture will be P=^(W'R'+W"R") ........ ... (2) The density of the mixture under standard conditions will be W'D' + WD" W' + W" The specific heat of the mixture at constant volume will be K V 'W'+K V "W" For the specific heat of the mixture at constant pressure, we will have the value K P 'W'+K P "W" The ratio of these two quantities gives the value of f for the mixture, which becomes _K P 'W'+K P "W r ' K V 'W + K V "W"' The value of R for the mixture will of course be equal to R=K,-K,, ............. (7) or K P 'W'+K P "W" _ K V 'W + K 9 "W" W + W" W +W" > 92 MIXTURES OF GASES AND VAPORS ART. 119 which becomes p _ W'(K P ' - K v ') + W"(K P " - K v ") W + W" which is of course R = ^W' + + R W^~ < 10 ) An inspection of equation (6) will show that the value of f for the mixture of gases is not the weighted mean of the values of this constant for the constituents of the mixture, as might be supposed, from analogy with the other quantities. When there are more than two constituents present in the mixture, its properties may be determined by properly modifying the above equations. For instance, for a mixture of three gases the value of R becomes R'W + n"W" + R'"W" W + W" + W" 118. Mixture of a Gas with a Vapor. A mixture of a gas and a vapor becomes homogeneous through diffusion in exactly the same way as do mixtures of two or more gases. The pressure exerted by the mixture upon the walls of the containing vessel is the sum of the pressures which would be exerted by the gas and the vapor were each one contained separately in the vessel at the given temperature. If the vapor be sat- urated on account of the presence of its liquid, the pressure which it exerts will depend upon the temperature, while the pressure which the gas will exert will depend upon its volume and mass as well as on the temperature . We may then compute the pressure exerted by the gas by subtracting from the pressure of the mixture the saturation pressure of the vapor at the temperature of the mixture. In case the vapor is superheated, the pressure exerted will, as before, be the sum of the pressures of each constituent of the mixture, but the pressure of the superheated vapor depends, like that of the gas, upon the mass of the vapor and the volume in which it is confined, and the pressure of the vapor may be obtained only by the methods described in Art. 101. 119. Air a Mixture of Gases and Water Vapor. The thermal proper- ties of air, as given in Chapter II., are those of dry air, free from carbon dioxide. Outdoor air usually contains a minute percentage (.03 per cent) of carbon dioxide and a variable quantity of water vapor, so that the density, specific heat, and other thermal properties of the atmosphere are continually varying. Ordinarily, the properties of air may be assumed to be those of dry air free from carbon dioxide, without sensible error. In certain classes of engineering computations, however, it is essential to take account of the variation in the properties of air when varying quan- tities of water vapor are present. In such computations it is necessary , ART. 120 HUMIDITY OF AIR 93 to consider air as a mixture of a gas of known properties, with superheated water vapor or steam. 120. Humidity of Air. When the pressure of the water vapor present in the air is the saturation pressure of water vapor at the temperature of the air, the air is said to be saturated. If the pressure is less than this quantity, the air is said to have a certain humidity, which is expressed as a per cent and is found by dividing the actual pressure of the water vapor in the air by the saturation pressure of water vapor at the temper- ature of the air. In case the air is saturated, it contains all the moisture which it is possible for it to hold, and any reduction in temperature will precipitate some of the moisture in the form of dew or rain. In case the humidity of the air is less than 100 per cent, the water vapor present in the air is superheated, since its temperature is greater than the tem- perature corresponding to its pressure, and the air may be treated as a mixture of a gas and a superheated vapor. 121. Dew Point. If a cold metallic surface be exposed to moist air, dew will gather upon it, if its temperature is less than the saturation temperature of the water vapor present in the air. The maximum tem- perature at which .moisture will appear upon such a surface is known as the dew point. If the dew point be determined, we may, from a steam table, find the pressure of the water vapor present in the air. The dif- ference between the dew point and the air temperature is the super- heat of the water vapor present in the air. From the pressure and super- heat of this vapor we may determine its density, which will be the weight of water vapor present per cubic foot of air. 122. The Wet-bulb Hygrometer. The humidity of the air is usually determined by means of an apparatus called a wet-bulb hygrometer. This instrument consists of two thermometers both protected from the direct radiation of the sun or other objects reflecting heat. The bulb of one of these thermometers is surrounded by air. The bulb of the other is enveloped in lamp wicking which dips into a cup of water. This thermometer must be so situated that the air has free access to the wicking, but must not be exposed to wind. The water contained in the wicking, being in contact with the air, will evaporate and more will be drawn up to take its place. In evaporating, the water appropriates the sensible heat of surrounding objects and reduces the temperature of the ther- mometer bulb below that of the air. From the difference in temperature indicated by the dry bulb-thermometer, the dew-point and the relative humidity may be computed. Since the wet-bulb thermometer receives heat by radiation from surrounding objects and the pressure of the water vapor in its neighborhood, due to the continual evaporation, is higher than elsewhere, it will not indicate a temperature as low as the dew-point. It is necessary, therefore, to make use of the following empirical table in 94 MIXTURES OF GASES AND VAPORS AKT. 123 determining the humidity of the air from the indications of the wet-bulb thermometer: RELATIVE HUMIDITY , PER CENT Difference between the Dry and the Wet Thermometers, Deg. F. Dry Ther- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 >>> 23 24 26 28 30 mometer, Dee 1 F . Relative Humidity, Saturation being 100. (Barometer = 30 ins.) 32 89 7!) 69 59 49 39 30 20 11 2 40 92 83 75 68 60 52 45 37 29 23 15 7 50 93 S7 SO 74 67 61 55 49 43 38 32 27 21 16 11 5 60 94 89 83 78 73 68 63 58 53 48 43 39 34 30 26 21 17 13 9 5 1 70 95 90 8(5 81 77 72 68 64 59 55 51 48 44 40 36 33 29 25 22 19 15 12 9 6 80 96 91 87 83 79 75 72 68 64 61 57 54 50 47 44 41 38 35 32 29 26 23 20 18 12 7 90 96 92 89 85 81 78 74 71 68 65 61 58 55 52 49 47 44 41 39 36 34 31 29 26 22 17 13 100 96 93 89 86 S3 80 77 73 70 68 65 62 59 56 54 51 49 46 44 41 39 37 35 33 28 24 21 110 97 03 90 87 84 81 78 75 73 70 67 65 62 60 57 55 52 50 48 46 44 42 40 38 34 30 26 120 97 94 91 88 85 82 80 77 74 72 69 67 65 62 (50 58 55 53 51 49 47 45 43 41 38 34 31 140 97 95 92 89 87 84 82 79 77 75 73 70 68 (56 64 62 60 58 56 54 53 51 49 47 44 41 38 From Kent's " Pocket Book," 1910 Edition. 123. Normal Humidity of the Atmosphere. Except in very arid regions, the humidity of the air varies from 40 to 80 per cent, usually ranging from 60 to 70 per cent in inland districts and from 70 to 80 per cent by the sea. Consequently, air is always ready to absorb moisture, and when water is exposed to the action of the air it will be evaporated. The rate of this evaporation will depend upon the humidity and temper- ature of the air, and upon the amount of wind. By warming air, its humidity will be greatly diminished and its power to absorb moisture correspondingly increased. Drying kilns, cooling towers, and other forms of engineering apparatus depend upon these principles for their operation. 124. The Computation of the Properties of Moist Air. When the relative humidity is known, the pressure of the water vapor present in the air may be found by multiplying the saturation pressure of water vapor at the temperature of the air, as obtained from a steam table, by the relative humidity. The saturation temperature corresponding to this pressure is the dew-point. Conversely the humidity may be found by dividing the saturation pressure at the temperature of the dew-point by the saturation pressure at the temperature of the air. The density of the water vapor in the air may be found by multiplying the density of water vapor at the dew-point by the absolute temperature of the dew- ART. 124 PROBLEMS 95 point, and divided by the absolute temperature of the air. Almost exactly the same result will be obtained by multiplying the density of water vapor at the temperature of the air by the relative humidity, and since this method is both very exact and very convenient, it is proper to employ it in engineering computations. The pressure of the dry air present in the atmosphere may be found by subtracting the pressure of the water vapor from the atmospheric pressure indicated by the barometer. The density of the dry air (i.e., its weight per cubic foot) may be found from its absolute pressure and temperature by means of the characteristic equation of gases, PV= WRT. Adding together the density of the water vapor and the density of the dry air, we will have the weight of the atmosphere in pounds per cubic foot. The principles which have been developed in the preceding paragraphs with regard to the pressure, density, etc., of the constituents of the atmos- phere may be applied, with equal propriety, in the case of any mixture of gas and vapor. PROBLEMS 1. A volume of 10 cu.ft. contains 1 Ib. of hydrogen and 2 Ibs. of nitrogen at a temperature of 550 absolute. Find the pressure of the hydrogen, of the nitrogen, and of the mixture. Ans. 42,400 Ibs. per square foot, 6060 Ibs. per square foot, and 48,460 Ibs. per square foot. 2. One pound of carbon monoxide and 1 Ib. of marsh-gas are together contained in a volume of 4 cu.ft. at a pressure of 100 Ibs. per square inch. Find the pressure of each constituent. Ans. 36.3 Ibs. per square inch and 63.7 Ibs. per square inch. 3. Find the density of the mixture under standard conditions. Ans. 0.0613 Ibs. per cubic foot. 4. Find the specific heat of the mixture at constant volume. Ans. 0.3202. 5. Find the value of the constant R for the mixture. Ans. 75.79. 6. Find the value of the constant f for the mixture. Ans. 1.304. 7. A mixture of air and saturated water vapor is contained in a confined space and has a temperature of 60. The pressure of the air is 1 atmosphere. Find the pressure of the mixture. Ans. 14.952 Ibs. per square inch. 8. A mixture of air and saturated water vapor in a confined space has a tem- perature of 80 F. and a pressure of 1 Ib. per square inch absolute. Find the pressure of the air. Ans. 0.495 Ibs. per square inch. 9. If water is present and the tempreature of the mixture is increased to 200 F., what will be the pressure of the air of the water vapor, and of the mixture? Ans. 0.605 Ibs., 11.52 Ibs., and 12.125 Ibs. 10. The temperature of the air is 70, the dew-point is found by experiment to be 50, find the humidity. Ans. 49.1%. 11. What quantity of water vapor will be contained in each cubic feet of air at the above humidity? Ans. 0.000564 Ibs. 12. One thousand cubic feet of air at a temperature of 60 and a humidity of 70 per cent are compressed into a volume of 200 cu.ft. What weight of moisture did the air contain before compression? Ans. 0.58 Ibs. 96 MIXTURES OF GASES AND VAPORS ART. 124 13. What weight of moisture will the air contain at the same temperature and 100 per cent humidity after compression? Ans. 0.1656 Ibs. 14. What quantity of water will be precipitated by the compression? Ans. 0.414 Ibs. 15. A wet-bulb hygrometer gives readings of 75 and 68. What is the humidity? Ans. 70%. 16. If the pressure indicated by the barometer is 14.40 Ibs. absolute, what is the pressure of the dry air? Ans. 14.1 Ibs. per square inch. 17. If the temperature is raised to 150 and the humidity to 100 per cent, find the final volume of the air in terms of the original volume. Ans. 1.506. CHAPTER VIII THE STEAM ENGINE 125. The Mechanism of the Steam Engine. A steam-power plant consists of a boiler for the generation of steam, an engine for the partial transformation of the heat of the steam into mechanical energy, and a condenser into which the' waste steam is discharged, together with neces- sary auxiliary apparatus. The place of the condenser may be taken by the atmosphere, the steam being discharged into the air against the bar- ometric pressure. Fig. 26 shows the steam engine of such a power plant in section, the engine shown being equipped with what are termed Corliss valves. Various other types of valves are in use for the distribution of steam to the cylinder, but the action of the engine is most readily understood when the valves are of the type shown. In the figure, the steam pipe A carries steam from a boiler to the engine. In this pipe is placed the throttle valve B, which is for the purpose of shutting off steam when the engine is not running. When this valve is open, steam flows from the pipe 'into the steam chest C. Leading from the steam chests are two ports, one to each end of the cylinder D. These ports are closed by two valves e and e', which are known as the inlet valves. Within the cylinder the piston F slides back and forth, being propelled alternately in each direction by the pressure of the steam. A movement of the piston from one end of the cylinder to the other is termed a stroke. Two successive strokes make one revolution of the engine. The total distance traversed by any point in the piston during a stroke is called the length of stroke, or piston travel. The piston rod G, which is fastened to the piston, transmits the force exerted upon the piston to the cross-head H, whence it is trans- mitted by the connecting rod / to the crank J t which is keyed to the shaft K. Upon this shaft is fixed a fly-wheel, and the shaft revolves in two or more bearings. As the piston is pushed back and forth by the steam, the intermediate mechanism pushes the crank forward and pulls it back, causing the shaft to revolve. The function of the fly-wheel is to make the rate of rotation as uniform as possible by the inertia of its revolving mass, and to carry the engine over the " dead points " which occur when the crank and connecting rod are in line at either end of the stroke, at which time the force exerted by the steam has no tendency to turn the 97 98 THE STEAM ENGINE ART. 125 ART. 126 CYCLE OF OPERATIONS 99 crank. The piston is a cylindrical body, and upon the outside of this cylinder are cut grooves into which are fitted piston rings, whose function it is to expand against the side of the cylinder and prevent the escape of steam past the piston. The cross-head is restrained by the frame of, the engine and compelled to move in a direction parallel to the axis of the cylinder. A port termed an exhaust port leads from either end of the cylinder into the exhaust pipe. These ports are closed by the exhaust valves M and M' '. 126. Cycle of Operations. Assume that the various parts of the engine are each in the position shown in the drawing, the inlet valve e and the exhaust valve M' being open. Steam will enter the left-hand end (known as the head end) of the cylinder, and will exert a pressure upon the piston whose total amount is proportional to the product of the absolute steam pressure into the area of the piston. Since this pressure is greater than the pressure upon the opposite face of the piston (which is equal only to the pressure in the exhaust pipe) the piston will be forced to the right, rotating the crank in a clockwise direction. Steam from the boiler will flow into the head end of the cylinder, maintaining the pressure, and the steam con- tained in the opposite or crank end of the cylinder will escape through the exhaust port into the exhaust pipe. After the piston has moved for- ward a certain amount (usually from % to l /2 of its total travel) the inlet valve e is closed by the mechanism which operates it, the exhaust valve M f remaining open. The steam which is contained within the head end of the cylinder will now begin to expand, increasing in volume and diminish- ing in pressure, and this expansion will continue until the exhaust valve is opened at or just before the end of the stroke. At some point near the end of the stroke, which is known as the forward stroke, the exhaust valve M' is closed, and just at the end of the stroke the exhaust valve M is opened. The pressure in the head of the cylinder now drops to the same value as the pressure in the exhaust pipe, the steam escaping through valve M. The pressure in the right-hand or crank end of the cylinder begins to rise on account of the compression of the contained steam, as soon as the valve M' is closed, and at the end of the stroke, on account of the introduction of steam from the boiler through valve e', it rises to boiler pressure. The pressure upon the right-hand face of the piston now drives it to the left, causing it to make what is termed the return stroke. At the proper point of the stroke the steam supply is cut off by the closing of valve e f and the steam allowed to expand, exactly as in the head end of the cylinder. As the piston approaches the head end of the cylinder, the valve M closes, the valve M' opens, and when the crank reaches dead center (i.e., when the connecting rod and crank are in the line and the piston has reached the limit of its travel) the valve e opens. 100 THE STEAM ENGINE ART. 127 127. Efficiency of the Engine. Each succeeding revolution is a repetition of the events of the preceding one. At the beginning of each working stroke a definite amount of steam flows into one end of the cylin- der from the boiler, and during the back stroke (or exhaust stroke, as it is sometimes called) the same weight of steam escapes from that end of the cylinder into the exhaust pipe. This quantity of steam is called the cylinder feed per stroke, or simply the cylinder feed. The weight of steam contained in the cylinder and clearance space at the instant the exhaust valve closes is called the cushion steam. The working stroke of the head of the cylinder is the back stroke of the crank end, and vice versa. The heat supplied to the engine in a given time is equal to the heat imparted in the boiler to the steam which is used by the engine during that time. The heat rejected by the engine is the latent heat of the steam (which is usually quite wet) which is rejected into the exhaust pipe during the same period. The difference between these two quantities is equal to the heat radiated from the engine during this period plus the work done by the engine during the same period. The efficiency of the engine is of course equal to the work divided by the heat supplied. It is apparent that water must be supplied to the boiler to take the place of that which is evaporated by the boiler and sent to the engine. The water so supplied is termed the feed- water. This water may and should have almost the same temperature as the exhaust steam which the engine rejects, since this exhaust steam may be made to surround tubes through which the feed-water is forced on its way to the boiler, or some other method of heating the feed-water by the exhaust steam may be employed. The heat supplied by the boiler to each pound of steam is then equal to the total heat of the steam (cor- rected, if necessary, for wetness or superheat) minus the heat of each pound of the feed-water, which is at the temperature of the engine exhaust. The heat rejected per pound of steam is the latent heat of the wet steam which is rejected. The generation of steam, of course, costs money, both for the fuel which is burned, for the labor necessary in burning it and caring for the boiler, and for other necessary expenses of operating the boiler plant. It is therefore highly desirable that the engine should be as economical as possible in the use of steam, or in other words, that it should have the highest possible efficiency. 128. Types of Engines. The engine described in the preceding para- graphs is known as a simple non-condensing engine when the exhaust steam is rejected into the air. If the exhaust steam is allowed to flow into the condenser or chamber in which it is cooled and condensed, and in which a vacuum pump maintains a low absolute pressure, the engine is said to be a condensing engine. Such an engine is usually more efficient than a non-condensing engine. ART. 129 THE INDICATOR 101 It has been found that it is both more convenient and more economical to allow steam to pass through two or more cylinders in succession, in case the steam pressure is high and the engine large. The first cylinder, instead of exhausting into the air or into a condenser, exhausts into a closed space which is known as a receiver. The steam from this receiver flows into a second cylinder, in which it does work, and is finally rejected to the air, or more usually to a condenser. Sometimes it is exhausted into a second receiver and flows from this into a third cylinder and occa- FIG. 27. Section of an indicator. sionally into a third receiver, and thence to a fourth cylinder, before entering the condenser. When the steam flows through two cylinders in succession the engine is said to be compound. When it flows through three cylinders in succession, the engine is said to be triple expansion, and when it flows through four cylinders in succession, the engine is said to be quadruple expansion. 129. The Indicator. The pressure-volume diagram of the working fluid of an actual steam engine or other thermodynamic machine, is termed an indicator card. An indicator card is obtained from an engine 102 THE STEAM ENGINE ART. 129 by the use of an instrument termed an indicator. An instrument of this kind is shown in section, in Fig. 27. It consists of a hollow cylinder in which is a piston which fits rather loosely, so as to move without fric- tion. This piston is attached to one end of a small helical spring, the other end of which is fixed to the upper head of the cylinder. The pressure of the steam on the piston forces it upward against the resistance of the spring, and the amount by which the piston rises will be strictly proportional to the steam pressure producing the rise. The motion of the piston is transmitted by a rod to the parallel motion which moves FIG. 28. Indicator reducing motion. the pencil point. The motion of the pencil point will then be strictly proportional to the steam pressure exerted upon the piston. The pres- sure, in pounds per square inch required to raise the pencil point a distance of one inch, is termed the scale of the spring. This pencil point is pressed lightly against a piece of paper which is wrapped about a cylinder or drum which oscillates upon its axis in unison with the motion of the piston of the engine. This is accomplished by wrapping a cord about the drum and attaching the cord to a pantograph or other reducing motion which is in turn attached to the cross-head of the engine in the manner shown in Fig. 28. The cord is drawn back during the return stroke of the engine by the action of the drum spring. The motion of the drum will then be strictly proportional to the motion of the piston, and the distance which the ART. 130 THE THEORETICAL INDICATOR CARD 103 drum revolves during any portion of a stroke will be proportional to the volume swept by the piston during the same time. Such an apparatus will obviously draw the PV diagram of the working fluid of the engine. Usually an indicator card is taken from each end of each cylinder of an engine. 130. The Theoretical Indicator Card. The indicator card which is given by a simple engine has in theory the form shown in Fig. 29. Assume that this card represents the pressure-volume diagram of the head end of the cylinder. The line OX is "the line of zero pressure and the line OF, the line of zero volume, the two forming the axes of the diagram. The abscissa to a represents the volume of the working fluid contained in the cylinder when the piston of the engine is at the extreme left of its stroke. This volume is formed by the space included between the face of the pis- FIG. 29. Theoretical indicator card. ton and the head of the cylinder, the volume of the steam and exhaust ports, and the small volume in a space termed the counterbore. The distance between the face of the piston and the cylinder head, or plate which covers the end of the cylinder, is termed the mechanical clearance, and varies from 1 / 8 to 3 /s of an inch, according to the size and workman- ship of the engine. In order to avoid forming a shoulder in the cylinder where the piston stops at the end of its travel, the cylinder is bored out from l / 8 to l /4 of an inch larger in diameter for a short distance at either end. The space so formed is termed the counterbore. The sum of these three volumes taken together is termed the clearance volume of the engine and is usually expressed as a per cent of the swept volume of the cylinder. The swept volume of the cylinder is the product of the net piston area into the length of stroke. The area of the piston rod must be deducted for the crank end of the cylinder. The volume of the steam contained in the cylinder is never, of course, less than the clearance volume. As the piston moves to the right, steam follows into the cylinder from the 104 THE STEAM ENGINE ART. 131 boiler, maintaining the pressure constant, the increase in volume mean- while being strictly proportional to the distance which the piston travels. Point b represents the point in the stroke, and the total volume of the steam in the cylinder, at the instant that the inlet valve is shut. This is termed the point of cut-off. From this point, as the volume continues to increase with the advance of the piston, the pressure falls off, the relation between the volume and pressure being expressed very nearly, for most engines, by the equation in which K is a constant equal to the product of the absolute pressure and volume at the point of cut-off. The line be is then very nearly a FIG. 30. Actual indicator card. rectangular hyperbola, having for its asymptotes the lines 0-X and 0-Y. At the end of the stroke when the exhaust valve opens the pressure suddenly drops to d, the ordinate to d representing the pressure in the exhaust pipe. During the back stroke, the pressure continues at this value until the point e is reached, when the exhaust valve closes and compression commences. The compression of the mass of steam con- fined within the volume represented by the abscissa to e raises the pressure and also the temperature of this steam, the process of compres- sion being represented by the line ef y which is also like the expansion line be, very nearly a rectangular hyperbola. 131. The Actual Card. The actual card which would probably be made by such an engine would be represented by the dotted line which falls within the theoretical card, and is shown separately in the card drawn in Fig. 30. On this card, b is known as the point of cut-off, the lino ab is known as the steam line, the line be is known as the expansion line, c is known as the point of release, the line de is known as the back-pressure line, e is known as the point of compression, ef is known as the com- pression line, / is known as the point of admission, and fe is known as the ART. 132 POWER OF THE ENGINE 105 admission line. The steam line falls below the theoretical line, since a difference in pressure is necessary to force the steam through the valve ports at a velocity which usually ranges from 5000 to 10,000 feet per min- ute and upward. In order to clear the cylinder promptly, it is necessary to have the point of release come before the end of the stroke, as otherwise too much work would be required during the back stroke to force the steam out of the cylinder. The back-pressure line will be above the theoretical back-pressure line, on account of the difference in pressure necessary to force the steam through the exhaust ports at a velocity ranging from 3000 to 7000 feet per minute. Since the valves open and close gradually and not instantly, the card will have rounded corners at the points of cut-off, release and compression. 132. Power of the Engine. As in the case of any other pressure- volume diagram the ordinates of the indicator card are proportional to the pressure of the working fluid, the abscissae are proportional to the change in volume, and the area is proportional to the work done by the working fluid. It is usual to compute the power of the engine from the area of its indicator card. By dividing the area of the card by its length (both in inches) we will obtain the height of the mean ordinate (also in inches). The height of this mean ordinate multipHed by the " scale of the spring " will be equal to the average absolute pressure in pounds per square inch on the piston throughout the working stroke minus the average pressure during the back stroke, a quantity which is termed the mean effective pressure. If we multiply the mean effective pressure by the net area of the piston and that by the length of stroke, we will have the work done in foot-pounds per stroke. Multiplying by the number of strokes per minute, and dividing by 33,000, we obtain the indicated horse power of the engine, or the rate at which heat energy is transformed into work in the cylinder by the action of the working fluid. In the case of a double-acting engine, it is necessary, when the mean effective pressure and the net piston area of the two sides of the piston are materially different, to calculate the power for each end of the cylinder separately, and to add to the results. 133. Methods of Governing. In order that a steam engine shall be a useful source of power, it is necessary that its speed shall be very nearly constant. This means that the power generated by the expanding steam within the cylinder shall be equal to the friction losses in the engine plus the power required by the machinery which the engine drives. In order to secure this continuous adjustment of the power developed within the cylinder to the varying needs of external machinery, it is necessary to control the quantity of steam admitted to the cylinder during each stroke. We may accomplish this in two ways. We may, by causing the steam to pass through a restricted opening, reduce the 106 THE STEAM ENGINE ART. 134 FIG. 31. Theoretical cards from a throttle governed engine. pressure at which a given volume of steam is admitted to the cylinder. Or we may, by closing the inlet valve earlier in the stroke, reduce the volume of steam admitted at the cylinder at boiler pressure. The first method of controlling the speed of the engine is known as throttle governing. The second method of controlling the speed of the engine is known as cut- off governing. The effect of throttle governing upon the indicator card given by a steam engine is shown in Fig. 31. The heavy outline shows the form of the card given by the engine when the throttle valve, which controls the flow of steam to the cylinder, is wide open. The light outlines show the theoretical form of the steam and expansion lines of the card when the throttle valve is closed to a greater or less degree. In the case of an actual engine, the cards would not be of the form shown in Fig. 31, but rather of the form shown in Fig. 32. Since the speed of the piston is greatest at the middle of the stroke, the effect of the throttle valve in reducing the pressure of the steam is greatest at that point; consequently, the steam lines have in prac- tice the form shown in Fig. 32, rather than that shown in Fig. 31. 134. The Throttling Gov- ernor. The construction and operation of a throttling gov- ernor may be understood by reference to Fig. 33. In the figure, a is a steam pipe sup- plying steam to the engine to be governed and B is a balanced valve in this pipe. When the valve is at its highest position, the pipe is wide open and the steam can flow freely from pipe a into the steam chest C by the route shown by the arrow. When, however, the valve is forced down, the area of the opening through which the steam may flow is very greatly diminished, so that a large difference in pressure is required to cause the quantity of steam taken by the engine to flow through the restricted opening. Since this difference in pressure is used FIG. 32. Actual cards from a throttle governed engine. ART. 135 CUT-OFF GOVERNING 107 in forcing the steam through the throttle valve, it is not available to drive the piston of the engine, and the power of the engine is therefore reduced. The valve B is attached to the rod or stem d y which protrudes through the stuffing-box e. This rod is forced upward by the helical spring /. Two weights or balls, gg, are pivoted to the arms hh, which are caused to revolve by the gearing shown. The centrifugal force so developed causes the weights to fly outward, and to draw down the valve stem against the resistance of the spring. As the engine speeds up, centrifugal force throws the balls still further out, drawing down the stem, and closing the throttle valve. When the engine slows down, the spring forces the stem up, opening the throttle valve. Any increase above the normal speed will thus reduce the steam supply to the engine, while any decrease below the normal speed will increase this steam supply. The governor is operated by means of a belt or other form of gearing connecting it with the shaft of the engine. 135. Cut-off Governing. The variation in the form of card given by an engine governed by means of a variable cut-off governor is shown in Fig. 34. By shortening the cut-off, the quantity of steam admitted, the area of the card, and the power of the engine are all reduced. The heavy outline shows the form of card given at normal load. The light outlines show the form of card at light load, while the dotted line shows the forms of card when the. load reaches the maximum. 136. Comparison of Meth- ods of Governing. An in- spection of Fig. 35 will show that cut-off governing is preferable to throttle governing, from the standpoint of steam economy. In the figure the heavy outlines show the card given by both a throttle-governed engine, and a cut-off governed engine., at full load. Both engines take the same quantity JT IG- 33. FIG. 34. Actual cards from a cut-off governed engine. 108 THE STEAM ENGINE ART. 137 of steam, and perform the same quantity of work, and are there- fore equally efficient. The light outlines bound the cards given by the same engines at a lower load. The engines, as before, take the same quantity of steam. However, the cut-off governed engine does the work represented by the area abode, while the throttle-governed engine does the work represented by the area fgcde. The latter is less than the former by the shaded area, and the efficiency of the throttle-governed engine is correspondingly less than that of the cut-off governed engine. Con- sequently, we find that practically all first-class modern engines are governed by a variable cut off, and not by throttling. The mechanism used for producing a variable cut-off is usually much more costly and complicated than that used in throttle governing. The general types of valves used for this purpose and the mechanisms employed for moving them will be discussed in the remaining paragraphs of the FIG. 35. Comparison of throttle and cut-off governing. present chapter, in connection with the descriptions of different types of engines now in use. 137. The Common Slide Valve. The form of valve most commonly employed in the smaller sizes of steam engines is known as the slide valve. The simplest form of the slide valve is that shown in section in Fig. 36, and known as the D valve on account of its shape. In this figure, which is a longitudinal section through the cylinder and steam chest, the valve is the blackened part marked V. The valve covers the ports P and P' leading to the head and crank end of the cylinder. Steam enters the valve chest from the steam pipe, and as the valve moves to the right into the position shown, the port Pis uncovered, allowing the steam to flow into the cylinder and propel the piston to the right. At the same time the steam contained in the crank end of the cylinder escapes through the port P, into the exhaust port E, by the route shown by the arrow. The valve is caused to move back and forth by the action of an eccentric ART. 137 THE COMMON SLIDE VALVE 109 on the engine shaft. The eccentric is a disk whose diameter is much greater than that of the shaft to which it is attached, and which acts in the same manner as a crank, since its center does not coincide with the center of the shaft. As the piston continues to move to the right, the valve begins to move to the left, finally shutting off the supply of steam, and expansion begins. When the piston approaches the end of its stroke, the valve still moving to the left shuts off the port P' from the FIG. 36. The D valve and ports. exhaust port, and compression begins in the crank end of the cylinder. When the piston reaches the end of its stroke, the valve will have moved to the left sufficiently to uncover the port P' to the steam in the valve chest, and the port P to the exhaust port. During the back stroke of the engine, the same series of events occurs, except that the opposite end of the cylinder is involved in each case. FIG. 37. Steam and exhaust lap. In order to accomplish these results, it will be seen that it is necessary when the valve is in its central position, for the two ends of the valve to extend some distance beyond the inlet edges (i and i r ) of the ports, as is shown in Fig. 37. The distance A is known as the steam lap of the valve, and may be the same or may be different for each end of the cylinder. It is usual for the exhaust edges of the ports to coincide with the exhaust edges of the valve, when the valve is in the central position. Sometimes the ports are slightly uncovered as at E' , arid sometimes they are cov- 110 THE STEAM ENGINE ART. 138 ered as at E, with the valve in this position. The distance from the exhaust edge of the port to the exhaust edge of the valve is termed negative exhaust lap in the first case, and positive exhaust lap in the second. The distance which the valve moves in going from. one of its extreme positions to the other is called the travel of the valve, and is twice the eccentricity or throw of the eccentric. By changing the travel of the valve (i.e., the eccentricity of the eccen- tric) and the angular distance between the eccentric and the crank, it is possible to change the point in the stroke at which cut-off occurs. Such a change will also affect the point in the stroke at which admission, exhaust, and compression begins, but these changes will not be as great as the change in the time of cut-off. If the eccentric be connected to a governing mechanism which will automatically adjust its eccentricity and position in accordance with the power required of the engine, we may effect cut-off governing by the slide valve. An engine so governed is usually termed an automatic engine. 138. Defects of the Common Slide Valve. The D valve has the following defects: First, on account of the rather long and crooked steam passages, the clearance volume of the engine will be excessive. The result, as will appear in the next chapter is a considerable waste of steam. Second, the area of the surfaces enclosing the clearance space will be very large, which will be shown in Chapter X to result in a great waste of steam. Third, the valve opens and closes gradually instead of promptly, and the card given by the engine shows to an excessive degree the effects of wire drawing. As a result, the power given by the engine for a given weight of steam is considerably less than if the valves opened and closed promptly. Fourth, the pressure of the steam on the back of the valve forces it down upon its seat, thus causing it to wear excessively and to require a considerable amount of power to drive it. Fifth, when the plain slide valve is used in an automatic engine^ on account of the shifting of the points of compression and release, the card is greatly distorted from its proper form, except at some particular load, which reduces the power obtained from the engine for a given steam consump- tion. In order to overcome these several disadvantages, a great many types of valves have been invented. The excessive clearance and area of clearance surfaces may be reduced by lengthening the valve, so that the ports may be made short and direct. By doing so, however, we greatly increase the total pressure of the steam upon the valve, and therefore the friction and wear. In order to reduce this source of loss, the valve is usually, in the better class of engines, made of such a form that the pressure of the steam is balanced. Such a valve is termed a balanced valve. In order that the valve shall open and close promptly, it is usual in all but the smallest engines to use what ART. 139 BALANCED SLIDE VALVES 111 is termed a double-ported valve ; that is one which will admit the steam at two edges instead of at one edge only. In order to avoid the shifting of the points of release and compression, as the load upon an automatic engine varies, an auxiliary valve, whose purpose it is to regulate the point of cut-off, is sometimes employed. Such a valve is called a riding cut-off valve. 139. Balanced Slide Valves. The simplest method of balancing the slide valve is to use a valve which is cylindrical in form, instead of a flat valve. Such a valve is shown in Fig. 38. The steam is admitted at one end of the valve chest, and since the valve is hollow, it can pass from one end to the other. The action of the valve may be readily inferred from the FIG. 38. drawing, and it differs in no way from the action of the D valve. A second method of balancing the slide valve is that shown in Fig. 39, in which the valve is a perfectly flat rectangular plate covered by a second plate having in it slight recesses exactly opposite to the steam and exhaust ports, and connected to them by passages through the valve itself. Since the pressure on both sides of this valve is exactly the same, the friction resisting its motion is negligible. The objection to both these methods of balancing slide valves is that the valves leak, about 25 per cent of the FIG. 39. Straight-Line valve. steam consumption of engines using these types of valves being due to such leakage. Various other methods of balancing slide valves are in use, and the reader is referred to Halsey's " Slide Valve Gears " for a more complete treatment of the subject. 140. Multi-ported Slide Valves. The simplest form of the double- ported valve is the Allen valve illustrated in Fig. 40. The port cored in the body of the valve, permits the steam to pass into the steam ports by the two routes indicated by the arrows. A displacement of the valve of any given small amount to the right of the position shown will 112 THE STEAM ENGINE AKT. 141 increase the width of the port opening by twice the amount of the displacement. A method of double-porting a balanced slide valve is illustrated in Fig. 39, which represents the Straight-Line valve as applied to the Straight-Line engine. The path of the steam through the double ports may be inferred from the arrows, which show that the steam is admitted at two edges at the same time. Double porting the slide valve serves FIG. 40. Allen double ported valve. to reduce the friction of the valve for a given port opening, and therefore the friction and wear. The same rapidity of port opening may of course be obtained by using a common D valve with twice the travel, but it is not always advisable to give a valve such an amount of travel. 141. Riding Cut-offs. The simplest form of the riding cut-off valve is illustrated in Fig. 41, and is known as the Meyer valve. The main FIG. 41. Meyer riding cut-off valve. valve acts as a seat upon which the cut-off valve slides, the cut-off valve being driven by a separate eccentric. The cut-off valve is formed in two parts, as shown, in order that the point of cut-off may be altered by altering the distance between them. This is accomplished by threading the two halves of the valve to the valve stem with a right- and left-handed thread in order that by turning the valve stem, they may be made to approach or recede. This type of valve is much used in slow-moving engines operated without governors, such as air compressors and pumping engines. It is not, however, as satisfactory ART. 142 APPLICATION OF SLIDE-VALVE ENGINES 113 as other forms of riding cut-off, such for instance as the Buckeye valve, which may be found described in Halsey's book, to which reference has already been made. 142. Application of Slide-valve Engines. The slide-valve engine is usually built in sizes up to 300 or 400 horse-power for stationary service, and in larger powers when compact engines of high speed of rotation are desired. It is not as economical in the use of steam as are other types of engines, and is being steadily displaced by the steam turbine and by the four-valve engine. In stationary service, in the smallest sizes, a fixed eccentric and throttle governor are commonly used. In the larger sizes, the valve is made double-ported and balanced and an automatic shaft governor is used. In spite of the greater economy which it offers the riding cut-off is seldom employed. The slide-valve engine finds its principal application in high powers in connection with locomotive and the marine engines. The valve employed for high steam pressures is usually a double-ported piston valve, while for low pressures a double-ported balanced flat valve is usual. Neither locomotives nor marine engines are provided with governors, and the eccentrics are fixed. However, the point of cut-off and the power of the engine, in both cases, is controlled by means of an arrangement termed a link motion. The Stevenson link motion was formerly employed almost exclusively, but other forms, notably the Waelchert valve gear, have been found more suitable for very large powers and high steam pressures. These valve gears are manually controlled, the engineer determining the speed and power of the engine by the position of the link motion. Although slide valves have been used exclusively in locomotive and marine engine service, there is just as good reason FIG. 42. Portable engine and boiler, to believe that the employment of Engine with throttling governor, other types of valve motion would give superior results in this class of service as in any other. It is reason- able to suppose, therefore, that four-valve engines will be eventually employed in locomotive and marine service, since they are giving most excellent results in stationary service. In Fig. 42 may be seen an illustration of a plain slide-valve engine with a throttle governor mounted upon a portable boiler. This is a type of power plant often employed in agricultural service. In Fig. 43 114 THE STEAM ENGINE ART. 442 is an illustration of a single -cylinder high-speed automatic engine with a double-ported balanced valve, such as is usually employed in stationary service when the power required is small, and the engine runs non-con- densing. This engine is equipped with a shaft governor. Fig. 44 is an illustration of the cylinder and drive wheels of a locomotive equipped with a Waelschert valve gear. FIG. 43. High speed simple engine with "automatic" cut-off governor. A locomotive of this type has two cylinders of largesize, uses steam of very high pressure, and operates at very high speed, developing from 700 to 1200 horse-power in each cylinder. On account of the large number of locomotives in service, and their very great aggregate power, the matter of locomotive engine efficiency is of immense practical FIG. 44. Cylinder and drive wheels of a locomotive with Waelschert gear. importance. In Fig. 45 may be seen an illustration of a triple-expan- sion, four-cylinder marine engine, such as is commonly built for naval service. These engines are of immense power for their size and weight and run at very high speed. The high-pressure cylinders are equipped with piston valves and the low-pressure cylinders with balanced flat ABT. 442 APPLICATION OF SLIDE-VALVE ENGINES 115 116 THE STEAM ENGINE ART. 143 valves, all operated by Stevenson link motion. This link motion is not moved directly by the engineer, as is the case with the locomotive, but is operated by means of a steam cylinder, which is controlled by the engineer, the links being too large and heavy to be manually operated. The variety of slide valves in actual use is so numerous and the methods of designing them are such as to forbid an adequate treatment of the subject in a work of this kind. For a full treatment of American slide valves and the best methods of designing them the reader is referred to Halsey's " Treatise on Slide Valve Gears." 143. The Corliss Engine. The Corliss engine makes use of valves of the form shown in Fig. 26, in order to avoid the disadvantage accom- panying the use of slide valves. By the use of the Corliss valve the ports may be made short and direct. The clearance volume and clearance area are reduced to a minimum, which results in greatly increasing the steam economy. In addition the mechanism which operates the valves is so arranged that the valves are caused to open and close promptly, thus avoiding a loss of power from wire drawing. The closing of the inlet valve at the point of cut-off is effected in such a way as to leave the points of admission, release, and compression unchanged, which permits them always to occur at the proper point in the stroke. 144. The Corliss Valve Motion. The mechanism employed for operat- ing the valves of a Corliss engine is illustrated in Fig. 46. W is the wrist plate, which turns upon a pin fastened to the side of the cylinder. It is operated by the reach rod R, which is pinned at the other end to the rocker arm A, which in turn is operated by the eccentric rod, the other end of which is fastened to the eccentric strap, which embraces the eccentric E. Attached to the wrist plate are four rods termed valve rods leading to the levers which operate the four valves of the engine. The rods B and E' are pinned to the arms C and C', which in turn are keyed to short shafts termed valve stems which serve to rotate the exhaust valves. As the wrist plate is vibrated by the action of the eccentric, the valves are caused to move, opening and closing at the proper time. The action of the wrist plate is such that at the end of their travel, while they are closed, the valves are practically stationary, as will be the case with the left end or head end exhaust valve, when the wrist plate is in the posi- tion shown in Fig. 47. This allows of a rapid opening of the valve without an excessive valve travel. The valve rod D is pinned to the bell crank, or latch arm F in Fig. 48, which turns freely upon the inlet-valve stem. Pinned to the latch arm is a latch which when the arm is in the position shown, catches a block affixed to the inlet-valve arm G, and as the latch arm is drawn to the right the valve arm is caused to rotate, opening the valve. When this rotation has proceeded for a sufficient length of time to allow the ART. 143 THE CORLISS ENGINE 117 118 THE STEAM ENGINE ART. 144 desired cut-off, the latch strikes the cam H (whose position is fixed by the governor) which pushes up the latch and releases the block. The rod /, pinned to the valve arm, leads to ihe dashpot /. Within this dashpot is a piston, the raising of which creates a suction which returns the valve FIG. 47. Corliss valve motion with wrist plate in extreme position. to the closed position the instant the cam causes the latch to release the block. This piston is so arranged that just before it strikes the bot- tom of the cylinder it compresses a quantity of air, which prevents the violent blow or jar which would otherwise result. By this device, a FIG. 48. Inlet valve gear. very rapid closing of the ports is secured. A still more rapid opening and closing of the ports of a Corliss engine may be secured by the use of double-ported valves, such as are shown in section in Fig. 49. It is often desirable to use two eccentrics, operating two wrist plates, ART. 145 THE FOUR-VALVE ENGINE 119 one of which moves the exhaust valves and the other the inlet valves. This permits of a much later cut-off than is possible when one eccentric is used. When Cor- liss engines are required for rail- way or other service where the variation in load is extreme, this type of engine is preferred. When the load is fairly constant, the single eccentric type is equally as satisfactory and economical. 145. The Four- valve Engine. A type of engine known as the four-valve automatic engine is rapidly coming into favor for smaller powers (i.e., up to 300 to 500 horse-power). The exhaust valves of this type of engine are operated in the same way as are the exhaust valves of a Corliss engine. The inlet valves, however, are operated directly from the inlet- valve wrist plate, the inlet - valve rods being pinned to the valve arms, which are keyed to the valve stems. The cut-off is effected by changing the throw and angular position of the eccentric which operates the inlet-valve wrist plate. All of the advantages of the Corliss engine are realized in the four- valve automatic ^engine, excepting the prompt', closing of the inlet valve at cut-off. The form of card given by the four-valve engine is shown in Fig. 50. There is no material difference between the steam economy of the four-valve auto- matic engine and of the Cor- liss engine, but the four- valve automatic, since it may be operated at higher speeds, is Exhaust Valve FIG. 49. Sections through Corliss inlet and exhaust valves. FIG. 50. Typical card from a four valve engine. the cheaper type, and since it 120 THE STEAM ENGINE ART. 461 is simpler, it is less likely to get out of order. The governor employed with the four-valve automatic engine is a shaft governor, while that employed with the Corliss engine is usually a fly-ball governor, such as is shown in Fig. 46. 146. Gridiron Valves. Another type of valve which is used in a good many makes of steam engines is the gridiron valve, which is illustrated in FIG. 51. Section through a gridiron valve. Fig. 51. The seat upon which this valve rests contains a series of parallel slots separated by metal bridges somewhat wider than the slots, while the valve itself contains a similar set of slots. When the slots are opposite one another, the steam passes through the valve. When, however, the FIG. 52. Mclntosh-Seymour cross compound engine. bridges of the valve cover the slots in the seat, as shown in the drawing, steam cannot pass through. Various types of mechanism are employed for operating gridiron valves. The Mclntosh-Seymour engine, illustrated in Fig. 52, is fitted with gridiron valves, and is an example of a type of mechanism often employed for operating them. The engine equipped with gridiron valves is equally as economical as the Corliss engine, and was formerly equally as cheap to build. Changes in shop methods have ART. 147 POPPET-VALVE ENGINES 121 resulted in making the Corliss type the cheaper one to build, so that most large engines are now equipped with Corliss valves. 147. Poppet-valve Engines. A type of valve very much employed in European practice is known as the poppet valve. The poppet valve is of two forms, the one shown in Fig. 53 being known as a plain pop- pet valve and that shown in Fig. 54 as a balanced valve. In steam engine work the balanced poppet valve is usually employed. Poppet- valve engines are usually four-valve engines, although poppet valves are sometimes employed in pairs and some- times in connection with Corliss or other types of FIG. 53. Plain poppet exhaust valve. valves. Balanced poppet valves have the disadvan- tages of requiring a large clearance volume and of exposing a con- siderable clearance area to the action of the steam. They are, however, better adapted to the use of superheated steam, and are tighter than are other forms of valves, and are therefore much used in connection with superheated steam. A tripple-expansion pump- ing engine in which pop- pet valves are used for the exhaust valves of the intermediate cylin- der, and the inlet and exhaust valves of the low-pressure cylinder, is illustrated in Fig. 55. In FIG. 54. Balanced or double-beat poppet inlet valve, a poppet-valve engine, as in the Corliss engine, cut-off is effected by releasing the valve from the control of the opening mechanism, and allowing it to close quickly by the action of a dashpot. 122 THE STEAM ENGINE ART. 147 FIG. 55. Vertical triple-expansion pumping engine. ART. 148 SPECIAL TYPES OF ENGINES 123 Excellent results in steam economy have been obtained from poppet-valve engines, but these results are to be credited rather to the fact that highly superheated steam was employed than to any excellence inherent in the type of valve. The use of plain poppet valves in the low-pressure cylinder of a steam engine permits of greatly reducing the clearance volume and the resulting loss. By employing this type of valve, engines have been designed in which the clearance volume was only 0.35 per cent of the swept volume. In such a case, the clearance loss is exceedingly small. 148. Rotary Engines. Many attempts have been made to so design the steam engine as to avoid the use of a reciprocating piston and cross- head, applying the expansive pressure of the steam directly to rotating parts. Engines operating on this principle are usually called rotary steam engines. The rotary steam engine has not proved successful, for two reasons. First, the form of cycle which must be employed with any of the possible mechanisms is wasteful of steam, and secondly, the friction and wear of the parts are excessive. Since the mechanical efficiency of a well-designed reciprocating engine is high, there is no practical reason for the use of a rotary engine except a possible reduction in the volume and weight of the engine. This advantage, however, is outweighed in all cases by the larger steam consumption and more rapid deterioration of engines of this' type. 149. Special Forms of the Steam Engine. Many special forms of the steam engine are employed for special service. The steam himmer, for instance, is a special form of an engine with manually operated valves. Direct-acting steam pumps, the locomotive i ir pump, the steam steering- engine, the pulsometer, the steam drill nd other types are examples of highly specialized types of steam engines, adapted to work under peculiar conditions, or to perform unusual kinds of service. Such engines are usually of peculiar construction mechanically, and are almost invariably very wasteful in their use of steam, and are employed only because they offer superior advantages in the matter of cheapness, simplicity, adaptabil- ity, or ruggedness of mechanism. PROBLEMS 1. An engine takes steam of 98 per cent quality at a pressure of 100 Ibs. absolute and rejects steam at a pressure of 15 Ibs. absolute. The engine used 30 Ibs. of steam per horse-power per hour. Find the efficiency. Ans. 8.6%. 2. Find the loss due to radiation in the above problem, if the steam exhausted is of 91 per cent quality. Ans. 20 B.T.U. per pound of cylinder feed. 3. A pressure of 75 Ibs. gage raises the pencil point of an indicator 1 ins. above the atmospheric line. What is the scale of the spring? Ans. 50 Ibs. 124 THE STEAM ENGINE ART. 149 4. An indicator card has an area of 3.5 sq.ins. and a length of 3 ins.; find the mean effective pressure when the scale of the spring is 40 Ibs. Ans. 46.7 Ibs. per square inch. 5. The area of the piston of an engine is 100 sq.ins. The mean effective pressure is 40 Ibs. per square inch. The length of stroke is 2 ft. and the engine makes 150 revolutions per minute. The engine is double acting. Compute its horse-power. Ans. 72.7 H.P. CHAPTER IX STEAM CYCLES 150. The Carnot Cycle for Dry and Saturated Steam. The principal factor in the cost of steam engine operation is the efficiency of the engine, which may be denned as the ratio of the work done by the engine to the heat supplied to the engine. The efficiency of the engine depends primarily upon the .efficiency of the cycle performed by the working fluid in the engine cylinder. It is therefore in order to investigate the efficiencies of the various cycles employed in actual engines, and the methods by which these efficiencies may be increased. This chapter will not deal with those losses which are due to the imperfection of the materials or mechanism of the engine, but only with those which are due to the cycle performed by the working fluid. In theory there are. many different cycles which may be .performed by the working fluid of a steam engine. The most efficient of these is the Carnot cycle. In order to carry out the Carnot cycle in a steam engine using dry and saturated steam, the steam must be evaporated in the cylinder instead of in a separate boiler, and condensed in the cylinder, instead of being rejected to the air or to a separate condenser. The indicator card of the Carnot cycle for a steam engine is shown in Fig. 56. The volume of the water is the length of the abscissa to point a. The volume of the steam formed is the length of the abscissa to point b. As soon as FlG> 5 6 ._ Carnot cycle for dry and the water is completely evaporated, saturated steam, the steam being dry and saturated, adiabatic expansion begins, continuing to point c. During this adiabatic expansion some of the steam condenses, as was shown in Art. 109, Chapter VI. When the steam has expanded to the temperature of the cooler, the back stroke commences, and the steam is compressed and condensed at constant pressure by the action of the cooler, until point d of the diagram is reached. At this point the cooling ceases, and the mixture of steam and water is then compressed adiabatically, which increases the temperature of the mixture, and since the mixture is very wet, con- denses the remaining steam. At the end of this compression all of the 125 126 STEAM CYCLES ART. 151 steam has been condensed, and the water has the temperature of vaporiza- tion corresponding to the pressure at a. The efficiency of this cycle depends solely upon the absolute temper- ature during the isothermal expansion and compression from a to b from c to d, and was shown in Chapter IV to be E = m , in which E is the efficiency of the cycle, T\ is the absolute temperature of the steam during evaporation, and T 2 is the absolute temperature of the steam during condensation. Such a cycle is obviously imprac- ticable in the case of steam, as no mechanism can be devised which will reproduce it exactly. We may, however, reproduce it approximately by methods which will be described later. FIG. 57. Steam initially superheated. FIG. 58. Steam initially wet. 151. The Carnot Cycle for Wet or Superheated Steam. The Carnot cycle may be performed when using wet or superheated steam as a working fluid. If the steam is wet at point b, the card will be similar in form to that shown in Fig. 56, but the volume at b and at c will be less than when the steam is dry at the beginning of expansion. It may be remarked in this connection 1 hat it is not necessary that the steam be entirely condensed at point a to perform a Carnot cycle, provided only that it returns to its initial state. If the steam is highly superheated at the beginning of isothermal expansion and the temperature range of the cycle is not too great, the steam will remain superheated throughout the entire cycle and the card given by the engine be almost identical with that which would be given by a perfect gas. The form of the card is the same as that shown in Fig. 14, Chapter IV, for a gas. In case the steam is not highly superheated at the beginning of isothermal expansion it will become wet as a result of the adiabatic expansion, the isothermal compression line will also be iso- baric and the form of the card will be that shown in Fig. 57. Only a small portion of the steam may be condensed during isothermal compression, in this case, since the whole mass of steam and water must be returned to its original state by the adiabatic compression. The steam may be initially wet, and become superheated during iso- thermal expansion, in which case the card will have the form shown in Fig. 58. When ART. 152 THE RANKINE CYCLE 127 superheated steam is employed as tho working fluid in a Carnot engine, the volume of cylinder must be larger for a given weight of working fluid than when saturated steam is used. Also the work performed by a given weight of superheated steam will be very much less for the same range of temperature than would be performed by the same weight of saturated steam. The efficiency of the cycle for a given temperature range, is the same, whether wet, dry or superheated steam is employed. Neither the Carnot cycle itself nor any approximation to it is ever actually employed hi connection with superheated steam, on account of the very great cylinder volumes required to obtain very moderate amounts of power. 152. The Rankine J Cycle. A second steam cycle is one which is known as the Rankine cycle. Since this is the most efficient cycle which may be performed by steam without evaporating and condensing the working fluid within the engine cylinder, it has been adopted as the standard of efficiency with which the efficiency of all other cycles may be compared. The indicator card of this cycle is shown in Fig. 59. The engine is assumed to have no clearance, and the walls of the cylinder to be non- conductors of heat. Steam is admitted from a boiler from point a to point b, the expansion being isothermal (and isobaric) and the boiler and steam pipe being a part of the expansion chamber. FIG. 59. Watt diagram of the At b cut-off occurs, and the steam Rankine cycle contained in the cylinder expands adiabatically to the pressure of the exhaust pipe, as shown by line 6-c, some of it condensing during the process. At the. end of this expansion the steam is discharged into the exhaust pipe at a constant back pres- sure, line c-d representing this process of isothermal compression. Line d-a represents the rise in temperature and pressure without change in volume which results when the inlet valve opens. The efficiency of the Rankine cycle may be found in the following manner: During the period of admission the work done by each pound of steam is equal to the external work of evaporation of steam of the temperature of admission multiplied by the quality of the steam admitted. During the adiabatic expansion the steam loses intrinsic energy, and the work done during expansion is equal to the difference between the intrinsic energy of the steam at the beginning and at the end of the expansion. The work done in forcing the steam out of the cylinder against the back pressure is equal to the external work of evaporation of steam at the temperature of exhaust, multiplied by the quality of the steam exhausted. The work done during the cycle per pound of steam will then be equal 1 Often termed the Clausius Cycle. 128 STEAM CYCLES ART. 152 to the sum of the external work of evaporation and the intrinsic energy of the steam admitted, less the sum of the external work of evaporation and the intrinsic energy of the steam exhausted, which is, of course, equal to the difference between the total heat of the steam admitted and the total heat of the steam exhausted. If we know the pressure (or temperature) and quality of the steam admitted, we may compute its total heat and its entropy. The entropy of the steam exhausted is the same as that of the steam admitted, since the expansion is adiabatic. From the known entropy and temperature of the steam exhausted, we may compute its quality and its total heat. The difference between the total heats is the work done per pound of steam admitted. The heat supplied in the boiler to each pound of steam is equal to the total heat of the steam admitted, less the heat of the liquid at the temperature of exhaust. We may therefore express the efficiency of this cycle by the formula F = ^JLTj^J? H 1 -h 2 ' in which HI is the total heat of the steam admitted, H 2 is the total heat of the wet steam discharged, and h 2 is the heat of the liquid at the tem- perature of exhaust. It may be shown that the efficiency of the Rankine cycle, like that of the Carnot cycle, is increased by increasing the temperature range of the working fluid. Referring to the formula for the efficiency of the Rankine cycle given in the preceding paragraph, it will be seen that an increase in the initial total heat of the steam will result in an increase of the efficiency of the cycle, since both the numerator and denominator of the fraction will be increased by the same amount, while the total heat of the steam rejected will be diminished, on account of the greater range of expansion. Since the total heat of the steam increases with the pres- sure, it will be seen that an increase in the initial pressure of the steam must result in an increase in the efficiency of the cycle. An investiga- tion of the properties of steam will show that when it expands adiabat- ically, between any two temperatures, the decrease in the total heat is greater than the decrease in the heat of the liquid. Consequently, a downward extension of the temperature range of the Rankine cycle will add to the numerator of the fraction expressing the efficienc}^ a larger quantity than it will add to the denominator, and the efficiency of the cycle will be increased by a reduction of the terminal pressure. In case superheated steam is used in the Rankine cycle, the form of card will be exactly the same as that shown in Fig. 59, except that the form of expansion line will slightly change when the expanding steam reaches the saturation point. The efficiency of the cycle will, of course, ART. 154 THE MODIFIED EANKINE CYCLE 129 be expressed by the formula already given, but the value of HI, instead of being the value for the total heat of wet steam, will be the value for the total heat of superheated steam of the given pressure and temperature An investigation of the properties of superheated steam will show that the greater the superheat of the steam, the greater will be the efficiency of the cycle. Since it is practicable to use superheated steam of a much higher temperature than saturated steam, this is a matter of importance in the theory of the economy of the steam engine. 153. The Modified Rankine Cycle. The Rankine cycle described in the preceding paragraph cannot be reproduced in a steam engine, since no engine. can be constructed without clearance, or of materials which are perfect non-conductors of heat. However, it would be possible in a non-conducting cyclinder to produce a cycle which is the thermo- dynamic equivalent of this cycle by the method shown in Fig. 60, which is the theoretical indicator card from an engine operating on a modified Rankine cycle. The engine has the clearance volume represented by the distance from OP to point a. Cut-off occurs at 6, adiabatic expansion occurs from b to c to the pressure of the exhaust, the exhaust is discharged at this pres- sure from c to d, and at d com- FlG 60. Modified Rankine cycle. pression begins. The volume at point d is so chosen that by adiabatic compression of the entrapped steam, it will be raised to its initial pressure, temperature and quality, in passing from state d to state a. An engine operating on this cycle has exactly the same efficiency as an engine operating on the Rankine cycle, since the cushion steam does the same work during expansion as is done upon it during compression. However, the volume of its cylinder must be somewhat larger than that of an engine operating on the Rankine cycle, since the volume from c to d in each diagram must be the same in order for the two engines to develop the same power per stroke. 154. Computation of a Rankine Cycle. The following example will serve to make clear the method of computing the efficiency of the Rankine cycle for a given range of temperature and pressure. Assume that one pound of steam of a pressure of 150 pounds absolute and a quality of 90 per cent performs a Rankine cycle, being exhausted at a pressure of 2 pounds absolute. The total heat of the steam will be h + qL = 330. 2 + 90X863. 2 = 1107.1 = HI. The entropy of the entering steam will be n + ^~ = 130 STEAM CYCLES ART. 154 .5142 + . 90X1.0550=1.4637 = ^. The entropy of the exhaust steam will be the same as that of the entering steam and the entropy of evapora- tion will be #2-^2 = 1.4637-0.1749=1.2888. The quality of the steam exhausted will be 1.2888 1:7431= 74.0 per cent. The total heat of the steam exhausted will be 94.0 + .74 X 1021.0 = 850 = H 2 . The heat of the liquid, h< 2 is from the tables 94.0 B.T.U. The efficiency of the cycle is therefore 1107.1-850.0 Q I . o 20 >> .3? 1C) 25 75 100 125 150 Initial Absolute Pressure 175 200 225 250 FIG. 61. Relation between the efficiency of the Rankine cycle and the initial steam pressure. Curve I is for 15 Ibs. back pressure. Curve II, is for 2 Ibs. back pressure. In order to illustrate the effect of changing the temperature or pres- sure range upon the efficiency of the Rankine cycle, the curves shown in Figs. 61 and 62 are drawn. The curves in Fig. 61 show the effect of varying the initial pressure for various constant back pressures, while those in Fig. 62 show the effect of varying the back pressure for various constant initial pressures. It may be noted in connection with the efficiency of this cycle, that the cycle is most efficient when dry steam is used and that when wet steam is used the efficiency gradually falls off, ART. 155 THE RANKINE JACKETED CYCLE 131 as is shown by the curve in Fig. 63. The effect of increasing the super- heat is shown in the same figure. That part of the diagram lying to the left of the heavy vertical line is the region of wet steam, while that lying to the right is the region of superheated steam. 155. The Rankine Jacketed Cycle. In order to minimize the loss resulting from cylinder condensation, it is often found advisable to heat the walls of the steam engine cylin- der by surrounding them with a jacket or steam space, con- taining steam at boiler pressure. Wet steam readily ab- sorbs heat both by conduction and ra- diation, while dry steam does not ab- sorb heat readily. As the steam in the engine cylinder ex- pands, it tends to condense and its temperature falls. The wet steam in the cylinder con- sequently tends to absorb heat from the cylinder walls, which in turn ab- ,1 ,, ,, 2 4 6 8 10 12 U 16 18 sorb heat irom the Absolute Back Pressure, steam jacket, so FIG. 62. Relation between the efficiency of the Rankine that the steam in cycle and the back pressure, the engine cylinder is maintained in practically a dry condition throughout the whole range of expansion, but is not, at any time, appreciably superheated. In consequence of these facts, when a steam cylinder is thoroughly jacketed, the steam within the cylinder performs a cycle, usually termed the jacketed cycle, throughout which it is assumed to remain in a dry and saturated condition. The theoretical indicator card given by an engine operating on the jacketed cycle, with complete expansion, is shown in Fig. 64. Dry steam is admitted from a to b. During expansion the steam remains in a dry and saturated condition 132 STEAM CYCLES ART. 155 30 15 10 and line c-d is therefore, a line of constant steam weight. The heat necessary to main- tain the steam in this condition is supplied from the jacket by the lique- faction of the steam contained therein. At the end of expan- sion dry and satura- ted steam is rejected to the exhaust. The efficiency of the Rankine jacket- ed cycle with com- plete expansion is less than that of the uiijacketed cycle, as may be shown in the following manner. Referring; to Fig. 65, a-b-d-c is the pres- sure volume diagram of the Rankine un- jacketed cycle for 1 pound of steam, and a-e-f-d is the dia- gram of the Rankine uiijacketed cycle, 10 20 30 40 50 60 70 80 90 100 g Quality % ^ &I& , Superheat in Degrees. FIG. 63. Relation between the efficiency of the Rankine cycle and the quality of the steam. when the quantity of steam taken is such that the amount of dry steam in the cylinder at the end of expansion is 1 pound, b e f c is then the FIG. 64. Card for a Rankine jacketed cycle. FIG. 65. Showing the efficiency of the jacketed cycle. ART. 156 EFFICIENCY OF JACKETED CYCLE WITH WET STEAM 133 equivalent of a Rankine cycle whose efficiency will be the same as the efficiency of either of the other two cycles. The line b-f is the line of constant steam weight, or the expansion line of the Rankine jacketed cycle for 1 pound of steam. The quantity of heat supplied by the jacket is equal to that represented by the area b-f-c plus the heat rejected by the Rankine cycle b-e-f-c. If we represent the heat rejected by R } the heat equivalent of the area b-f-c by J and of the area b-e-f-c by U, we will have for the efficiency of the heat supplied by the jacket, J + R' wh'le the efficiency of the heat supplied in the cylinder feed of an unjack- eted cycle will be represented by the formula U_ = U~+ R' Since U is much larger than J, it will be seen that the efficiency of the heat supplied by the jacket is much less than if this heat had been supplied in the cylinder feed. Consequently, the efficiency of the jacketed cycle will be less than the efficiency of the unjacketed cycle. The quantity of work done during the jacketed cycle may be determined by writing an empirical equation which expresses the relation between the pressure and volume of dry and saturated steam for the range of expansion of the cycle, and so obtaining the work done under the expan- sion line. The total work done during the cycle will be the work done under the expansion line plus the external work of evaporation of steam at the initial pressure, less the external work of evaporation of steam at the exhaust pressure. The heat rejected per pound of working fluid will be the latent heat of evaporation of the steam at the exhaust pressure. The heat supplied will be the sum of the heat rejected and the work done. The heat supplied from the cylinder feed will be equal to the total heat of steam at the initial pressure less the heat of the liquid at exhaust pressure. The heat supplied by the jacket will be equal to the total heat supplied less the heat supplied in the cylinder feed. The number of pounds of jacket feed per pound of cylinder feed will be found by dividing the latent heat of evaporation at the initial pressure by the heat supplied by the jacket per pound of cylinder feed. 156. Efficiency of the Jacketed Cycle with Wet Steam. In case the steam sup- plied to a jacketed engine is wet, the efficiency of the cycle will be seriously reduced, since the wet steam will be evaporated during the expansion period and will not perform the work which it would otherwise do. A jacketed engine in theory always rejects dry and saturated steam. Practically the steam contains a very small percentage of moisture. No theory can be developed for the jacketed cycle on the assumption 134 STEAM CYCLES ART. 157 that the steam is initially wet, unless the form of expansion line is also assumed. In the case of an actual engine, it may be assumed that the expansion line has the form PV n =K, and the value of the index n may be determined from the indicator card. The theory of the cycle may then be developed after finding the initial and final quality of the steam from the known cylinder volume and cylinder feed. 157. The Imperfect Cycle without Clearance. In the actual steam engine it is not practicable to expand the steam completely (i.e., to expand it till its pressure equals the back pressure) for several reasons. In the first place, it is necessary, in order to govern the speed of the engine, to have a variable terminal pressure when the load, or quantity of power developed by the engine, varies. In the next place, it will be found that the friction of the engine will be very greatly increased if the cylinder is made large enough to allow of complete expansion. In addition, there are certain losses which are increased by increasing the ratio of expansion of the steam. In order to minimize these losses, the cycle adopted in practical work is of the form already described in Fig. 29. The effect of introducing terminal drop (i.e., a difference between the terminal and exhaust pressure), is of course to reduce the quantity of work performed by a given weight of steam. This may be shown graphically by the theoretical card in Fig. 66, which is the card of an engine expanding steam adiabatically from an initial pressure of 100 pounds per square inch to a final pressure of 16 pounds per square inch. The lines a a, b-b, c-c, and d-d represent the drop in pressure at the end of the stroke, w r hen the ratio of expansion is one, two, three, and four. The area included within the lines repre- sents the quantity of work performed by the steam. The quantity of steam FIG. 66. Card showing the loss due . , . ,, to incomplete expansion. required is the same in each case, but it will be seen that the greater the ratio of expansion, the greater the quantity of work which this steam will perform. The effect of introducing terminal drop is therefore to increase the thermodynamic loss of the cycle, and to reduce the other losses in the engine. That terminal drop is chosen which makes the sum of the practical losses and the theoretical loss a minimum. It may be noted that when the steam expands to a pressure lower than the exhaust pressure, not only are the actual losses still further increased, but the efficiency of the cycle is reduced. Fig. 67 is the indicator card for such a cycle. When the exhaust valve opens at point d } air or steam will rush into the cylinder from the exhaust pipe, increasing the pres- sure to e. This air or steam must be expelled against the back pressure. ART. 157 THE IMPERFECT CYCLE WITHOUT CLEARANCE 135 It does no work while it is entering the cylinder, but in expelling it from the cylinder, work is done upon it represented by the area cde. It will therefore be seen that power was lost as a result of the expansion below the back pressure. The work done during a cycle in which there is terminal drop, but no clearance, may be found by treating the cycle as though it consisted of two parts, a Rankine cycle (area abcf in Fig. 68) whose back pres- sure is equal to the terminal pressure, and a second cycle (area cde-f) in which the work done is equal to the product of the difference between the terminal pressure and exhaust pressure in pounds per square foot into the terminal volume in cubic feet. The terminal volume per pound of cylinder feed may be discovered by multiplying the specific volume of steam at the terminal pressure by the quality of the steam at FIG. 67. Loss due to extreme expansion. FIG. 68. Work done during a Rankine cycle. the end of expansion. The quality may of course be obtained from the known initial and final conditions. Designating the total heat of the steam at admission by HI, at the terminal pressure by H tj the terminal volume in cubic feet by V t , the terminal pressure in pounds per square foot by P t , the exhaust pressure by P 2 , and the heat of the liquid at the temperature of exhaust by h 2 , we will have for the work in foot pounds during the imperfect cycle without clearance U = J(H!-H t ) + (P t -'P 2 )V t . For the efficiency of the cycle, we will have U E = J(H 1 -h 2 y In Fig. 69 will be found curves showing the relation between the terminal pressure and the efficiency for different rondrtions of initial and exhaust pressure. 136 STEAM CYCLES ART. 158 158. The Effect of Clearance. It has already been shown that in case expansion and compression are complete, the efficiency of the cycle 30 25 15 10 20 60 140 160 180 300 80 1UO 130 Terminal Drop FIG. 69. Relation between the efficiency of the imperfect cycle and the terminal drop in Ibs. per sq.in. Curve I. For 100 Ibs. initial and 15 Ibs. back pressure. Curve II. For 100 Ibs. initial and 2 Ibs. back pressure. Curve III. For 190 Ibs. initial and 1 Ib. back pressure. is not altered by clearance. Usually, however, the efficiency of the cycle is reduced by clearance, as may be seen from the following considerations: The two simplest cases of loss from clearance are first, when the compres- sion is complete and the expansion is incomplete, and secondly, when the expansion is complete and there is no compression. In Fig. 70 is the card of an engine having com- plete compression, but incomplete expansion. Every portion of the steam contained in the cylinder during expansion performs work in propor- tion to its mass. Consequently, the net work performed by the steam in the clearance space during expansion During its compression, the net work FIG 70. Showing clearance loss with incomplete expansion. is represented by the area a-f-g-h. ART. 159 THE PRACTICAL CYCLE 137 FIG. 71. Card showing the effect of incom- plete compression. expended upon it is represented by the area a-e-h. Consequently, the net loss due to the clearance is represented by the area f-e-g. The loss occurring in the second case may be understood by referring to Fig. 71, which is an indicator card for 1 pound of steam expanding to back pressure. Every portion of this steam performs work during the cycle in proportion to its mass. Assume that the engine has a clearance represented by the ab- scissa to point 6 on the diagram. The steam contained in the clear- ance space at the end of compres- sion, if compressed adiabatically, would return by the path f-a to its initial condition. The quantity of steam introduced during admission period is represented by the volume a-c. All of this steam does work during expansion, but that portion of it represented by the volume a 6 does no work during admission, except to adiabatically compress the steam already in the clearance space at point /. Consequently, the area a-b-f represents the work lost on account of clearance. 159. The Practical Cycle. In the practical cycle expansion is incom- plete and we have both clearance and incomplete compression. It is therefore in order to determine the effect of these various elements on the efficiency of the cycle. Referring to Fig. 72, it may be seen that if the steam contained in the clearance space at point /, which is the point of compression, were compressed adiabatically to the initial pressure, it would have the volume represented by the abscissa to point a. The quality of the steam at / is, in theory, the quality which the steam would have after expanding adiabati- incom- cally from its initial to its terminal pressure, since the steam which re- mains in the cylinder expels by its adiabatic expansion the steam which escapes from the cylinder at the instant of release. Consequently, steam compressed adiabatically from point / to the initial pressure would have the initial quality, which, however, would not be the quality of the cylinder feed. Were this steam compressed adiabatically, it would do the same work during complete expansion as was expended upon it during compression. o FIG. 72. Clearance loss with plete expansion and compression. 138 STEAM CYCLES ART. ir,0 However, the cushion steam expands only to the pomt h, whose pressure is the terminal pressure, and therefore the quantity of work expended in compressing the cushion steam exceeds the work it per- forms per cycle by the area f-h-4. The cylinder feed, which has the volume a-c, if working in a cylinder without clearance, would perform work represented by the area acdef. However, it actually performs work represented by the area bcdefg, and area a-bg represents the loss on account of clearance. The sum of the areas a-b-g and h-J-i represent the total loss occurring in this cycle on account of clearance. It will be seen that the area h-J-i increases as the terminal pressure rises, and is proportional to the quantity of cushion steam. By increasing the quantity of cushion steam, we will reduce the loss represented by the area a-bg, but we will also increase the loss represented by the area hf-i. In theory, the best results with a given clearance are obtained when the point of compression is made such that the sum of these two losses is a minimum for the given ratio of expansion. This usually occurs when the compression is nearly complete. In practice, it is found that high compression decreases the actual efficiency of the engine, on account of its effect upon other losses. 160. Efficiency of the Practical Cycle. The determination of the theoretical efficiency of the practical cycle, on the assumption that the expansion and compression of the steam are adiabatic, is a matter of some complication. The method of computing this efficiency may be understood by referring to the card for such a cycle for 1 pound of steam, illustrated in Fig. 73. In this computation the following notation will be used : F is the weight of the cylin- der feed in pounds, C is the weight of cushion steam in pounds, Hb is the total heat of the steam at point />, H c the total heat of the steam at point c, V c the terminal volume in cubic feet, P c the terminal pressure 73.-Work done by an imperfect in P Unds P 6 ' B .l uare f Ot ' P tlle cyc j e exhaust pressure in pounds per square foot, P is the pressure at point / in pounds per square foot, P a is the initial pressure in pounds per square foot, H e is the total heat of the exhaust steam per pound, H f the total heat of the cushion steam per pound at point/, and /^the heat of the liquid at the temperature of exhaust. The. weight of the working fluid, which is F + C, is 1 pound. The quality of the steam at point e is the quality which the steam would have in expanding adiabatically from the initial pressure and quality to the back pressure. The weight of cushion steam may be found from the known pressure, volume, and quality of the steam AIIT. 160 PROBLEMS 139 at point e. The total heat and other properties of the steam at point c, e and / may be computed, since the entropy of the steam is the same at these points as at b. The card may now be divided into four areas. Area g-b-c-i is a Rankine cycle for 1 pound of steam and the work done during this cycle in foot-pounds is J(H b H c ). Area i-c d-j is a rectangle and the work done is V C (P C Pd). Area h-f-e-j is a Rankine cycle performed by the cushion steam, and the work done in foot-pounds is / C (Hf H c ) . Area gafh is a rectangle and the work done is equal to V a (P b Pf). The quantity of heat supplied during the cycle is equal to H b C Hf F h 2 . The efficiency of the cycle is found by divid- ing the heat equivalent of the work done per cycle by the heat supplied. In case it is desired to work out the cycle for any other quantity of work- ing fluid than one pound, the procedure will be exactly the same except that the total heats at points b and c will be the total heats of the actual weight of working fluid. Since all of the heat is supplied in the cylinder feed, the quality of the cylinder feed may be determined from its weight and the quantity of heat supplied. In case the quality of the cylinder feed, and its weight, and the weight of the cushion steam, are known, the total heat at c and consequently the volume and other properties of the working fluid at different points of the cycle, maybe determined from the fact that H b = C Hf-\-F H a in which FH a is the total heat of the cylinder feed. In case the volumes at 6, c, and e are known and the quality of the cylinder feed is known, the weight of the cushion steam and the properties of the work- ing fluid at different points of the cycle may be computed by successive approximation . PROBLEMS 1. Steam operated on a Carnot cycle between pressures of 150 Ibs. per square inch and 2 Ibs. per square inch absolute will give what efficiency? Ans. 28.4%. 2. What will be the efficiency of steam initially dry and saturated when worked through the same pressure range in a Rankine cycle engine? Ans. 25.7%. 3. By what percent must the total cylinder volume in Problem 2 be increased for the engine, to operate on a modified Rankine cycle and give the same power, if the clearance is 30 per cent of the total volume at cut-off? Ans. 43%. 4. Find the efficiency of a Rankine cycle engine taking steam at 90 per cent quality at a pressure of 150 Ibs. absolute and rejecting it at a pressure of 2 Ibs. absolute. Ans. 24.9%. 5. Find the efficiency of a Rankine cycle engine taking steam at 150 Ibs. absolute and 200 superheat and rejecting it at a pressure of 2 Ibs. absolute. Ans. 33.4%. 6. A jacketed engine without clearance and with complete expansion takes dry and saturated steam at 100 Ibs. absolute, and rejects dry and saturated steam at 16 Ibs. absolute. Find the index of the expansion line. Ans. 1.152. 7. Find the constant of the above curve for 1 lb. of steam. Ans. K=4S7 when p is in pounds per square inch and V in cubic feet. 140 STEAM CYCLES ART. 160 8. Find the work done during expansion by 1 Ib. of steam. Ans. 104,200 ft.lbs. 9. Find the heat added during expansion. Ans. 108.1 B.T.U. 10. Find the work of the cycle. Ans. 110,800 ft.lbs. 11. Find the efficiency of the cycle. Ans. 12.80%. 12. Find the efficiency of a Rankine cycle engine working dry and saturated steam through the same pressure range. Ans. 13.4%. 13. An engine without clearance takes 1 Ib. of steam of 90 per cent quality and 100 Ibs. pressure, and expands it adiabatically to 25 Ibs. pressure. Find the terminal volume. Ans. 14.96 cu.ft. 14. The back pressure in the above problem is 2 Ibs. Find the work done during the cycle. Ans. 148,060 ft.lbs. 15. Find the efficiency of the cycle. Ans. 19.0%. 16. If the clearance space in the above engine is made equal to 50 per cent of the swept volume to the point of cut-off, and compression is complete, what will be the swept volume for 1 Ib. of cylinder feed? Ans. 20.23 cu.ft. 17. What will be the work done per pound of steam supplied? Ans. 120,290 ft.lbs. 18. What will be the efficiency of this cycle? Ans. 14.4%. 19. An engine takes steam of 100 Ibs. pressure. The steam is dry and saturated at cut-off, and has a volume of 4.429 cu.ft. It expands adiabatically to 30 Ibs. pres- sure. The back pressure is 15 Ibs. per square inch. The volume of the cushion steam at the point of compression is 4 cu.ft. The pressure at the end of compression is 60 Ibs. What is the clearance volume? Ans. 1.185 cu.ft. 20. What is the volume at release? Ans. 12.74 cu.ft. 21. What is the weight of the cushion steam? Ans. .171 Ib. 22. What is the work done during the cycle? Ans. 78,720 ft.lbs. 23. What is the weight of the cylinder feed? Ans. .829 Ib. 24. What is the total heat of the cylinder feed? Ans. 990.3 B.T.U. 25. What is the heat supplied in the boiler to each pound of cylinder feed? Ans. 1016 B.T.U. 26. What is the efficiency of the cycle? Ans. 12.0%. CHAPTER X i LOSSES IN THE STEAM ENGINE 161. Classification. The losses which occur in the steam engine mo be classified under nine heads, as follows: 1. Unavoidable thermodynamic loss. 2. Losses due to the imperfection of the cycle employed. 3. Losses due to the imperfection of the condensing machinery employed. 4. Losses due to wire drawing and fluid friction. 5. Losses due to cylinder condensation. 6. Losses due to valve and piston leakage. 7. Losses due to the conduction and radiation of heat. 8. Losses due to clearance. 9. Losses due to mechanical friction. 162. Loss when a Perfect Cycle is Employed. The first of these losses cannot be reduced by any method whatever, without changing the temper- ature range through which it is possible for the working fluid to operate. It is the thermodynamic loss of the Carnot cycle. Expressed as a frac- T tion of the total heat supplied this loss is equal to ^, in which r l\ is equal to the absolute temperature of the steam supplied to the engine, and T 2 is the temperature of the circulating water discharged from the con- denser. In the case of an engine using saturated steam, the unavoidable thermodynamic loss is fixed on the one hand by the highest steam pres- sure which it is safe and profitable to carry, and on the other hand by the quantity and temperature of the condensing water available. In case superheated steam is employed, the upper limit of temperature may be considerably raised. 163. The Practical Limits of Pressure and Superheat. The upper limit of steam pressure is usually found to be between 200 and 250 pounds per square inch, the corresponding temperature being from 380 to 400 F. Engines operating at higher pressures than this usually give trouble ; difficulties are encountered in properly constructing and maintaining the boilers and pipe lines, and the increased dangers and expense of opera- tion more than overbalance the resulting gain in thermodynamic efficiency. We may therefore place the upper limit of the temperature range at 400 F. or 860 absolute in the case of engines using saturated steam. 141 142 LOSSES IN THE STEAM ENGINE ART. 164 When superheated steam is employed, the upper limit of the tem- perature range may be raised to about 600 F. At higher temperature than this, lubrication of the cylinders and valves of a reciprocating engine becomes impossible, and on account of excessive expansion and weaken- ing of 1 materials of construction, difficulties begin to be encountered in steam turbine operation. The upper limit of temperature with super- heated steam is therefore about 1060 absolute. 164. Lowest Practicable Temperature of Condensation. In practice the final temperature of the condensing water depends on the quantity of condensing water available, and on its initial temperature. It is, however, practically impossible to secure a final temperature lower than 70 F., except in winter, or when a large supply of cool condensing water is available. In summer, and especially in the tropics, the final temper- ature of the condensing water will rise to 100 or 110 F. The lower limit of temperature range is therefore about 530 to 570 absolute. 165. The Per Cent of Unavoidable Loss. Since the extreme tem- perature range practicable for steam engines is from 1060 absolute to 530 absolute, the unavoidable thermodynamic loss can never be less than 50 per cent. Except under the most favorable conditions it is, extremely difficult to realize a temperature range greater than from 960 to 560 absolute, under which conditions 41.6 per cent of the heat sup- plied is available for transformation into work and 58.4 per cent is unavoid- ably lost. In case saturated steam is used, the extreme range will rarely be greater than from 860 to 560 absolute, in which case 35 per cent of the heat is available, and 65 per cent is unavoidably lost. When the engine is run non-condensing with a steam pressure of 100 pounds absolute, only about 14.7 per cent of the heat supplied is available, and the unavoidable thermodynamic loss is 85.3 per cent. Compound con- densing engines are usually operated under such conditions that only about 15 to 25 per cent of the heat supplied is available. It will thus be seen that of the heat supplied to a steam engine, from 50 to 85 per cent is unavoidably lost, even when the engine is ideally perfect in every detail. 166. Loss Due to Imperfection of Cycle. The efficiencies of the cycles commonly employed in steam engine work have already been discussed at length in Chapter IX. The loss due to the imperfection of the cycle employed, expressed as a per cent of the total heat supplied, is equal to the difference between the efficiency of the perfect cycle and that of the imperfect cycle actually employed. It is better, however, to express this loss as a per cent of the available heat. We may do so by dividing the difference between the efficiency of the perfect cycle and the imperfect cycle, by the efficiency of the perfect cycle. This loss is minimized by adopting the most efficient cycle possible. ART. 168 EFFECT OF IMPERFECT CONDENSER ACTION 143 167. Effect of Imperfect Condenser Action. The effect of the third source of loss is to raise the temperature and pressure of the steam enter- ing the condenser. If it were possible to bring the condensing water and the steam together in such a way that they would attain a common temperature, and at the same time not introduce air into the condenser, the action of the condenser would be perfect. However, in order to condense the steam, it is necessary that the final temperature of the circulating water" be somewhat less than that of the condensing steam. The required temperature difference is variable, amounting sometimes to over 20. In addition, air is present in the condenser, and its presence prevents the pressure of the steam in the exhaust pipe from reaching the pressure, and therefore the temperature, of the steam in the condenser itself. On account of the presence of air and the imperfect cooling of the steam, the temperature range of the working fluid, and therefore the efficiency of the engine, is reduced. The loss from this source depends upon the efficiency of the cycle employed, becoming greater as the efficiency of the cycle increases, hence the importance of good condensing machinery in connection with steam engines and turbines of high efficiency. The amount of this loss may be determined by computing the theoretical efficiency of the cycle employed, at the observed back pressure (call this efficiency E ), and at the back pressure corresponding to the tem- perature of the discharged circulating water (call this efficiency E t ) } and taking their difference (which is E t E ). The result will be the amount of this loss expressed as a per cent of the heat supplied. It would be more proper, however, to express it as a per cent of the total heat trans- formable into work by the cycle employed, which may be done by divid- ing the difference found above by the quantity E t . 168. Loss from Wire Drawing and Steam Friction. The fourth source of loss in the steam engine arises from the fact that a difference of pressure is necessary in order to force the steam through the port openings and steam passages of the engine at the necessary velocity. The loss in pressure incurred in forcing steam through a restricted port opening at high velocity is said to be due to wire drawing. The loss in pressure incurred on account of the roughness and crookedness of the steam passages is said to be due to fluid friction. In each case the loss in pressure is approximately proportional to the square of the velocity of the steam. When these openings and passages are of ample area, so that the maximum velocity of the steam does not exceed 6000 to 8000 feet per minute, the loss of pressure is very small. When, however, the passages are restricted, and the valves do not open and close promptly, the pressure difference becomes considerable and the area of the card actually given by the engine is materially less than that of the theoretical card which would be given by the engine in case its ports were ample, 144 LOSSES IN THE STEAM ENGINE ART. 169 and its valves opened and closed instantly. The ratio of the area of the actual card to the area of the theoretical card is termed the card factor of the engine, and is usually expressed as a per cent. The loss due to fluid friction and wire drawing, expressed as a per cent of the work represented by the area of the theoretical card, is found by subtracting the card factor from 100 per cent. 169. Values of the Card Factor. The card factor for locomotives is usually from 75 to 85 per cent. For ordinary high speed engines with ample ports the card factor will range from 85 to 95 per cent. The card factor for a good Corliss engine is about 95 to 98 per cent, while for slow- moving pumping engines equipped with Corliss valves the card factor is practically 100 per cent. It will be seen that this loss varies from about 25 per cent to less than 1 per cent. It may be reduced by making the steam and exhaust ports short and direct, and of ample area, and so operating the valves that they open and close promptly. 170. The Design of Engine Ports. The ports of steam engines are usually designed by making the cross-sectional area of the inlet passages such that the nominal velocity of the steam through them is from 5000 to 9000 feet per minute, and the area of the exhaust passages such that the nominal velocity of the steam through them is from 4000 to 7000 feet per minute. The nominal velocity of the steam is found by dividing the piston area by the port area and multiplying the quotient by the mean piston speed. Consequently, the formula for the design of ports will be S_A V ' in which P is the port area ; A is the piston area ; S is the mean piston speed ; V is the nominal steam velocity. Since the actual piston speed is variable, and since some of the steam supplied condenses in the cylinder during admission, the actual velocit}' of the steam in the inlet and exhaust passages is from 50 to 75 per cent higher than the nominal velocity, during some parts of the stroke. Most types of valves open and close gradually and therefore greatly restrict the port openings during a considerable portion of the stroke. The effect of this restriction is to very greatly increase the loss due to wire drawing. It is impossible to estimate the loss from this source, except by making comparisons with engines in which this loss has been measured. 171. Cylinder Condensation. The most important source of loss in the steam engine is due to the condensation of steam upon the cylinder ART. 171 CYLINDER CONDENSATION 145 wall during the admission period, and its subsequent evaporation during the period of expansion and exhaust. The cause of this loss will oecome apparent when we consider the phenomena which occurred in the cylin- der while the engine is in operation. The wall which encloses the work- ing fluid is of cast iron or steel, and is therefore a good conductor of heat. It has been shown both from theory and by actual measurement that the surface of this wall, at the instant of admission, is somewhat cooler than the entering steam. On account of this difference in temperature, at the instant of admission some of the steam immediately condenses upon the wall surface, 1 raising its temperature. Since the wall is a good conductor, heat begins to flow from the surface into the wall. Were it not for this flow of heat the temperature of the surface would be instantly raised to that of the entering steam, and condensation would cease as soon as it began. On account of this flow of heat, the temperature of the surface cannot be raised instantly to that of the steam in contact with it, and the condensation goes on at a gradually decreasing rate throughout the period of admission. When expansion begins, the temperature of the steam begins to fall, and finally it becomes equal to the temperature of the wall surface. At this instant condensation ceases. After this point is passed, the tem- perature of the wall surface is greater than that of the expanding steam, and the moisture which has condensed upon it begins to evaporate, the heat now flowing to the surface from the interior of the wall. As the steam pressure continues to fall, the evaporation becomes so rapid as to be almost explosive in character. In consequence of this the steam evaporated from the wall during the latter part of the expansion period is quite wet. If the steam is not all evaporated by the end of the expan- sion period, and probably it usually is not, the remainder of the water is blown off in the form of spray at the instant that the exhaust valve opens and terminal drop occurs. During the exhaust stroke the wall surface is much hotter than the steam contained in the cylinder, and therefore the steam is dried by the heat radiated to it from the wall. At the beginning of compression the layer of steam in immediate contact with the wall is superheated. However, since superheated steam absorbs heat with difficulty, the radiant heat from the wall is unable to superheat the main body of cushion steam to any appreciable extent, and this steam is, at the beginning of compression, practically dry and saturated. 1 It is on this account that it is necessary to open the inlet valve before the engine begins its working stroke. If the valve is not so opened, the pressure in the cylinder will not begin to rise until the piston has completed a portion of the working stroke, and there will be a considerable loss in power without any change in the steam con- sumption of the engine. 146 LOSSES IN THE STEAM ENGINE ART. 172 After the closing of the exhaust valve, as a result of adiabatic com- pression the whole of the cushion steam is superheated, and its temperature raised above the temperature of the cylinder walls. As soon as its pressure becomes that corresponding to the temperature of the walls, this super- heated steam begins to condense, exactly as moisture from the air con- denses upon the surface of a cold object whose temperature is below the dew-point. In a great many engines, compression is not carried to this point, but in high speed engines with light load, the com- pression is often sufficient to show FIG. 74. Card showing cylinder conden- F sation during compression. thls phenomenon by a sudden change in the direction of the com- pression line on the indicator card. This effect may be noted at a in Fig. 74, where there is a decrease in the volume of the cushion steam without a corresponding change in pressure. 172. The Amount of Heat Interchanged. Since the steam alternately imparts heat to, and extracts it from, the cylinder wall, the temperature of the wall surface, and consequently of every point within the wall, undergoes periodic variation. This temperature variation is a maximum at the wall surface, and grows rapidly less as the distance from the parti- cle to the wall surface is increased. The amount of the temperature variation is shown by Professor Cotterill 1 to be given by the equation (1) in which R is the temperature range of any particle, R s is the temperature range at the wall surface, x is the distance of the particle from the surface, and m is determined by the thermal properties of the material of the wall and the periodicity of the cycle. Its value is given by the equation Nws m- In which N is the number of cycles per second, w is the density of the metal in pounds per cubic foot, s is the specific heat of the metal, and / is the specific conductivity of the metal in B.T.U. per second per cubic foot, per degree difference in temperature. As a result of the periodic variation in temperature of the wall sur- face, a definite quantity of heat is imparted to each square foot of the 1 See Chapter X of Cotterill's work, " The Steam Engine." ART. 174 PRACTICAL ASPECTS OP CYLINDER CONDENSATION 147 wall by the steam, and again rejected by the wall to the steam, during each revolution of the engine. This quantity of heat may be shown to be Q = KR,^^, (3) in which Q is the number of B.T.U. surrendered by the steam to each square foot of the wall surface per cycle, K is a constant depending upon the form of the temperature cycle of the wall surface, R s is the temperature range of the wall surface, and w s f and N are as in the preceding para- graph. The value of the constant K is unity in case the temperature cycle of the wall surface is harmonic, and is very nearly unity for other probable forms of the cycle. 173. The Practical Aspects of Cylinder Condensation. It might be thought that the loss due to cylinder condensation could be deduced directly from equation (3) in the preceding article. This would be true if the temperature range of the wall surface were known. However, the temperature range depends on the form of the indicator card, the pressure range of the steam, the quality of the steam entering the cylinder and the rotational speed of the engine, and it is obviously impossible to determine it with any accuracy. Hence we can make only a rough estimate of the probable 'amount of cylinder condensation in the case of any particular engine, operating under given conditions. We may, however, readily determine what changes are necessary in the operating conditions in order to minimize the cylinder condensation. An inspec- tion of the equation will make it apparent that the loss may be reduced: first, by reducing the temperature range of the wall surface; second, by increasing the rotational speed of the engine; third, by reducing the area of the wall surface enclosing the clearance space; and fourth, by making the wall of non-conducting material. 174. Methods of Reducing the Temperature Range of the Wall Surface. Five methods are available for reducing the temperature range of the wall surface : first, by increasing the rotational speed of the engine ; second, by supplying the engine with dry or superheated steam; third, by decreas- ing the ratio of expansion ; fourth, by reducing the temperature range of the steam in the cylinder ; and fifth, by jacketing the cylinder with steam of boiler pressure. The effect of increasing the rotational speed of the engine is to increase the rate at which the pressure falls during expansion, to increase the rapidity of evaporation, and consequently the wetness of the steam evaporated during the expansion period, to reduce the heat loss from the wall due to this re-evaporation, and therefore to reduce the temperature range of the wall surface. The effect of supplying an engine with wet steam is to increase the quantity of water deposited upon the wall surface by a given heat transfer, 148 LOSSES IN THE STEAM ENGINE ART. 175 to increase the loss of heat due to the subsequent re -evaporation of this water, and therefore to increase the temperature range of the wall surface . By -supplying the engine with dry or superheated steam, the heat loss from the wall caused by the re -evaporation of the deposited moisture is greatly diminished, and the temperature range of the wall surface cor- respondingly reduced. The greater the superheat of the steam supplied the less the loss from re-evaporation, and therefore the less the temperature range of the wall surface. Decreasing the ratio of expansion reduces the heat loss during the expansion period by shortening this portion of the cycle. It also reduces the heat loss by increasing the terminal drop and so removing the moisture more completely at the instant of release, by its explosive evaporation. Other things being equal, it is apparent that the temperature range of the wall surface must be proportional to the temperature range of the steam in the cylinder. We may reduce the temperature range of the steam in the cylinder and also the ratio of expansion, by using a multiple expansion engine. In the case of a compound engine, the temperature range of the steam is reduced to one-half, and in the case of a triple expan- sion engine to one-third of its value for a simple engine of the same pres- sure range. The cylinder condensation is reduced by a still larger amount, since the ratio of expansion is also reduced. The effect of a steam jacket is .to raise the mean temperature of the cylinder wall and therefore to reduce the initial condensation. Since less steam is condensed, less heat will be lost by its re-evaporation, and the effect of the jacket is therefore to greatly reduce the temperature range of the wall surface. A steam jacket properly applied always increases the efficiency of an engine, since the thermodynamic loss due to the use of the jacket is always less than the reduction effected by the jacket in the loss from cylinder condensation. However, the effect of the jacket in increasing the economy of large engines of high piston speed is insignifi- cant, and the cost of applying the jacket to such engines does not war- rant the slight saving resulting from its use. Jackets are therefore not usually applied to engines having a rotational speed of more than GO to 75 revolutions per minute, unless they are desirable for operating reasons, as, for instance, to enable the engineer to quickly warm up the engine when starting. 175. Effect of Increasing the Speed of Rotation. It has already been shown that increasing the rotational speed of the engine affects the amount of cylinder condensation indirectly by reducing the temperature range of the wall surface. An inspection of Equation (3) Art. 172, will show also that it affects this loss directly, the amount of the loss for a given tem- perature range being inversely proportional to the square root of the number of revolutions per minute. On both of these accounts it is AET. 178 REDUCING THE CLEARANCE AREA 149 desirable that an engine should be operated at a high rotational speed. The general design of high speed engines, however, is usually such as to make them very wasteful of steam on account of the type of valve employed, the large clearance volume, the heavy compression, and the great area of clearance surface. In practice the greatest steam economy is obtained from an engine of long stroke and high piston speed, but of comparatively low rotational speed. 176. Reducing the Clearance Area. The area of the wall surface upon which cylinder condensation occurs may be reduced by making the steam and exhaust ports short and direct and by giving the engine a high piston speed. The high speed automatic engine usually has long and crooked ports, and being of very short stroke has a low mean piston speed. Consequently, the loss from cylinder condensation is greater in such engines than it is in long-stroke four-valve engines of equal power, which have short, direct ports and high piston speed. It must be borne in mind that it is not the cylinder condensation per cycle which the designer should seek to minimize, but rather the cylinder condensation per pound of steam supplied. Increasing the rota- tional speed of an engine by shortening the stroke, and without changing the piston speed, will reduce the weight of cylinder feed per revolution in greater ratio than it reduces the weight of cylinder condensation per revolution, and will therefore increase the loss from condensation. For mechanical reasons it is advisable to limit the mean piston speed to 1000, or at the utmost 1200 feet per minute, while speeds of 600 to 900 feet are usually employed. The length of stroke is determined by financial considerations, long-stroke engines being more expensive for a given power than short -stroke engines. In practice the stroke is usually limited to three times the diameter of the high pressure cylinder, and is rarely greater than 6 feet. 177. The Use of a Non-Conducting Wall. The application of non- conducting materials to those parts of the clearance surface that are not subject to wear has often been advocated. However, actual tests of engines in which the clearance surfaces have been covered with porcelain, glass, slate or other non-conducting materials, have not usually shown sufficient gain in economy to warrant the use of this method of reduc- ing cylinder condensation. In general, such tests have shown but little increase in economy, although Thurston has reported a reduction of 60 per cent in the amount of cylinder condensation from the use of this method. It is highly probable, however, that the steam jacket is a more efficient and practical method of reducing the loss. 178. Weight of Steam Condensed Per Revolution. It is apparent from the foregoing discussion of cylinder condensation that it is impossible to derive a rational formula which will give accurately the amount of 150 LOSSES IN THE STEAM ENGINE ART. I7fi steam condensed per revolution when the dimensions of the engine, the conditions of operation, and the form of indicator card are known. However, a large number of empirical equations have been developed by which this quantity may be determined with more or less accuracy. An investigation of a large number of engine tests serves to show that the amount of cylinder condensation may be determined approximately by the equation in which C is the number of pounds of steam condensed per revolution, A is the number of square feet of wall surface exposed per revolu- tion to the action of the steam at cut-off, R x is the temperature range of the steam during the expansion period in degrees Fahrenheit, R is the total temperature range of the steam, and N is the number of revolutions per minute. The application of this formula will be readily understood from the following example: An engine having a 12"X36" high pressure cylinder takes steam at 160 pounds absolute. The ratio of expansion is 3 and the back pressure is 30 pounds absolute. The area of wall surface exposed to the action of steam at cut-off is 16 square feet. The number of revolutions per minute is 125. Required the weight of steam condensed per revolution. [ Assuming hyperbolic expansion, the pressure at release will be one- third the initial absolute pressure, or 53 pounds per square inch. The temperature of the steam at admission is 364, at release 285 and at the back pressure 250. The temperature range during expansion is 79 and the entire temperature range is 114. Substituting in the formula we will have 779 4- 1 14 \ C= .00033 X 16 (123.688 ) = - 069 lbs - The weight of steam condensed per stroke is therefore about .035 pound. By adding this quantity to the cylinder feed per stroke shown by the card, the probable weight of steam consumed per stroke of the engine may be computed. In computing the area of the wall surface exposed to the action of the steam per revolution at cut-off, it is necessary to divide this surface into three parts. The first part is the area of the cylinder head and the piston. The second part is the area of the walls enclosing the ports and steam passages, together with the valve faces. The third part is the surface of the cylinder ban-el up to the point of cut-off. The first and third parts may be computed from the generp] dimensions of the engine, ART. ISO VALVE AND PISTON LEAKAGE 151 while the second part must be computed from the detail drawings of the engine cylinder. The areas must be computed for both the head and crank end of the cylinder and their sum taken, when the steam condensed per revolution is desired. 179. Valve and Piston Leakage. The importance of the sixth source of loss in the steam engine will depend upon the design, the workmanship and the method of operation of the engine. The leakage past the piston of .a steam engine ought to be very slight, in practice, if the piston is properly made and provided with properly fitted packing rings. It is usual to make the piston from .005 to .015 inch smaller in diameter than the cylinder, and then to provide the piston with two elastic packing rings which expand and prevent the escape of steam. In case these rings are broken, or lose their elasticity, the loss from piston leakage may become a considerable quantity, but this rarely happens when the engine receives proper care. A valve which is forced down upon its seat by an unbalanced steam pressure will be steam tight after it has worn to a good bearing. When such a valve is new, however, although the surfaces of the valve and seat may be scraped to an exact plane while cold, the valve will not necessarily be tight when it is hot. The heat and the pressure of the steam upon the back of the valve invariably tend to distort these surfaces. The high spots soon wear down, however, and the valve becomes tight. A Corliss valve, like a slide valve, tends to wear tight. It will be seen, therefore, that a plain slide valve, a Corliss valve, and a properly fitted poppet valve, will not leak under service conditions. Piston valves and balanced slide valves, on the other hand, are prac- tically certain to leak. In order that the valve shall slide freely, it is necessary that the distance between the balance plate and the valve seat shall exceed the thickness of the valve by from 0.003 inch to 0.005 inch. In the case of a piston valve, a similar difference is required between the diameter of the valve and the valve seat. In consequence of this fact, when such a balanced valve is reciprocated, there is a very considerable space through' which steam and water may find their way directly from the steam chest to the exhaust port. No definite value can be set for the amount of this loss, since it will depend on the clearance of the valve, on the value of the steam and exhaust pressure, on the lap of the valve, and on the kind and amount of lubricant used on the valve. The amount of this leakage per revolution is often equal to or greater than the amount of cylinder condensation per revolution. 180. Effects of Leakage upon the Indicator Card. The effect of valve and piston leakage upon the indicator card of a steam engine is exactly the same as that of cylinder condensation. A leak past the piston, or from the cylinder into the exhaust, during the admission period, 152 LOSSES IN THE STEAM ENGINE ART. 181 gives exactly the same effect as does initial condensation. A leak from the steam chest into the cylinder during the expansion period gives the same effect as re-evaporation. There is no way by which the effects of cylinder condensation and re-evaporation may be separated from those of leakage in the case of an engine test, or by which the amount of either may be determined, and they must therefore be considered together in *an analysis of such a test. However, since the two kinds of losses arise from entirely different causes, it is necessary to consider them separately when attempting to reduce them by correct methods of engine design. It may be pointed out in this connection that while it is possible to measure the amount of leakage while an engine is blocked in a given position, it is impossible to measure or to estimate the leakage which occurs in that engine under operating conditions. If an engine is blocked in position and steam is turned on, it will usually be found that no important leak takes place either through the valves or past the piston. If the valves of this engine be then made to move without uncovering the ports, they will be found to leak. If the ports of a slide valve engine be blocked by some means, for instance by filling them with lead, arid the valve be made to move in the normal manner, a considerable leak will usually be discovered from the steam chest into the exhaust port. A part of this is steam leakage, while a part is due to condensation and subsequent evaporation of the steam upon the valve surface, the ports, etcetera. Measuring the leakage under these conditions will not, however, deter- mine the leakage under normal operating conditions, since the quality and amount of steam passing through the valve ports is radically different. It will be seen that the automatic engine with a balanced slide valve is essentially wasteful, on account of this source of loss. This is one reason for its rapid displacement of late years by the four-valve automatic engine, in which this source of loss is greatly reduced, if not entirely obviated. There is no possible way by which the loss due to leakage in a Corliss or other four-valve engine can be measured, but it is probable that this loss under running conditions is not materially greater than it is when the engine is blocked and the valves are closed. 181. Conduction and Radiation. The seventh source of loss, namely the conduction and radiation of heat from the steam cylinder, has the effect of increasing the cylinder condensation by reducing the mean tem- perature of the cylinder wall and thereby increasing the temperature range of the wall surface. Its amount in the case of a jacketed engine may be measured by determining the quantity of steam condensed in the jacket when the engine is not running. In the case of un jacketed engines the amount of this loss cannot be determined, and the extent of its effect upon cylinder condensation is impossible of estimation. This ART. 183 LOSSES DUE TO CLEARANCE 153 source of loss may be very largely eliminated by covering the exterior surface of the cylinder with some non-conducting material, such as mineral wool, asbestos sponge, or magnesia. This non-conducting coating is usually covered by a lagging of cast iron or sheet steel for the purpose of protecting it from mechanical injury and improving the appearance of the engine. 182. Losses Due to Clearance. It has already been shown in the preceding chapter that, when an ideal engine has clearance no thermo- dynamic loss results if the expansion and the compression are complete. In the case of a practical engine, there is always a loss due to clearance, even though both the expansion and compression are complete. The work of compressing the cushion steam in such an engine is much greater than the work done by the cushion steam during expansion, since the steam is practically dry and saturated at the beginning of compression, while it is quite wet at the beginning of expansion, on account of initial condensation. It will be seen that the amount of this loss depends on the weight of the cushion steam and can be reduced only by reducing the clearance volume and the compression pressure to a minimum. In case no compression is employed the theoretical efficiency of the cycle will be reduced. It is therefore advisable from the standpoint of efficiency to adopt that degree of compression which will make the sum of the theoretical and the practical losses a minimum. The greater the amount of cylinder condensation the greater will be the relative importance of the practical loss and the less the degree of compression which may be profit- ably employed. It will, therefore, be found in practice that compression is undesirable when the amount of cylinder condensation is large. With some types of engines, it is unadvisable for mechanical reasons to do away with compression, or even to reduce it very much. This is the case with all high-speed engines. A considerable amount of com- pression and a large clearance space is necessary in order that such engines shall operate smoothly, and without excessive depreciation. The pur- pose of the cushion steam is to take up the shock which would otherwise be experienced as a result of the rapid reversal of the heavy reciprocat- ing parts at the end of the stroke. High speed engines are necessarily made with large clearance, in order that there shall be sufficient cushion steam to serve this purpose. It will therefore be seen that the clearance losses are high in this type of engine, and it is partly on this account that the slow-moving long-stroke engine with its small clearance will usually be found to be more efficient. 183. Friction Losses. Usually from 6 to 14 per cent of the power developed in the cylinder of an engine at rated load is lost in overcoming the friction of the moving parts. The amount of this loss varies with the speed of the engine, but is practically independent of the load. Con- 154 LOSSES IN THE STEAM ENGINE ART. 183 sequently, the indicated power developed when the engine is running- idle measures the amount of this loss. This loss may be minimized by the proper design and lubrication of the bearings and by careful attention to their adjustment arid alignment. The amount of the loss depends upon the weight of the moving parts, the relative velocity of the rubbing sur- faces, the quality of the lubricant, the method of introducing the lubricant, the fit -of the bearings, and the ratio of the maximum to the mean effective pressure. Heavy moving parts, by increasing the pressure on the bearings, increase the friction loss. When the shafts and pins are larger in diameter than is necessary for proper strength and stiffness, the friction loss is increased on account of the higher velocity of rubbing. When a copious supply of good lubricant is furnished in such a manner that it completely lubricates the rubbing surfaces, the loss is reduced. The most efficient method of accomplishing this is to furnish an excess of the lubricant at the points where the bearing pressure is the greatest, by means of a force pump, so that the shaft is practically floated on oil. When the sup- FIG. 75 a. FIG. 75 6. Showing the effect of excessive running clearance. ply of oil is insufficient the lubricating film between the rubbing surfaces is thin. The amount of friction loss varies inversely with trie thickness of this film, hence the desirability of an ample supply of lubricant. The difference between the diameter of the shaft or pin, and of the box in which it rotates, is an important matter. If the difference is too small, the lubricating film is necessarily thin, and the friction loss high. If the difference is too great, the shaft will be supported in the manner shown in Fig. 75 a, instead of that shown in Fig. 75 6, and the lubricating film will be easily destroyed on account of the excessive pressure along the narrow surface of contact at c. When the ratio of the maximum to the mean effective pressure is high, not only must the moving parts be heavy in order to resist the excessive stresses imposed at certain parts of the stroke, but the pres- sure transmitted from the piston to the bearings will be large in comparison with the power actually developed. A low ratio of expansion is there- fore favorable to high mechanical efficiency. The mechanical efficiency of a compound engine will be higher than that of a simple engine having ART. 184 REDUCING THE LOSSES BY PROPER DESIGN 155 the same total expansion, since the expansion is divided between two cylinders in the case of a compound engine, and the ratio of the maximum to the mean effective pressure is greatly reduced. By increasing the number of cylinders acting upon a shaft, the turning moment is made more even, and the weight of the fly-wheel may be reduced. A cross compound engine in which two cylinders act on crank pins set at right angles is therefore more efficient mechanically than a single cylinder engine or a tandem compound engine of the same power and speed. Since the fly-wheel and other moving parts of a high speed engine are usually much lighter than those of a long stroke engine of the same power, and since the ratio of expansion is greater in the case of a long stroke engine, a high speed engine is usually mechanically more efficient than a long stroke engine. A few tests are on record which indicate an exceedingly small loss from mechanical friction in high speed engines, sometimes as low as 2 per cent of the indicated horse-power of the engine, but it is doubtful whether these unusual results were realized, or whether the tests were inaccurate. 184. Reducing the Losses by Proper Design. It will be noted that some of these losses are of such a nature that when one is decreased, another one is increased. It slhould be the aim of the engine designer to reduce the sum of the losses to a minimum, which involves balancing these losses one against another. For instance, increasing the ratio of expansion reduces the loss due to the imperfection of the cycle and increases that due to cylin- der condensation. For some 10 particular ratio of expan- sion, the sum of these two losses will be a minimum, and that ratio of expansion will be the one chosen. The design of an engine, however, is not an exact process in which the various losses are exactly estimated and balanced one against another, and certain dimen- sions accurately determined which will make the sum of these losses a minimum. On the contrary, a considerable latitude may be allowed in fixing upon the principal dimensions of an engine without affecting its efficiency to any noticable degree. In Fig. 76 will be found a curve giving the relation of the ratio of expansion occurring in an actual engine to the efficiency of the engine. It will be seen that 456 Ratio of Expansion FIG. 76. Effect of changing the ratio of expan- sion on the efficiency of an engine. 156 LOSSES IN THE STEAM ENGINE ART. 184 as the ratio of expansion is increased the efficiency rises and then falls off, and that for the ratio of expansion between 2f and 4, the efficiency is practically constant. Similar effects may be noticed in regard to changes in almost every one of the principal dimensions of an engine. Not all of the sources of loss are of this character, however. Increasing the clearance volume of an engine, for instance, always reduces the efficiency of the engine. Increasing the clearance area invariably has the same effect. In cases of this kind, it should be the aim of the designer to adopt every expedient which will reduce such losses to a minimum. PROBLEMS 1. What per cent of the heat supplied is unavoidably lost with the perfect cycle when steam is supplied at 100 Ibs., absolute and exhausted at a pressure of one atmosphere? . Ans. 15 per cent. 2. What per cent is unavoidably lost when steam is supplied at 180 Ibs. absolute and a superheat of 200 and the final temperature of the condensing water is 90 F.? Ans. 53.2 per cent. 3. If the theoretical efficiency of the cycle employed in the first case is 10 per cent, what per cent of the available heat is lost? Ans. 33 per cent. 4. A Rankine cycle is employed in Problem 2. What per cent of the available heat is lost? Ans. 33.4 per cent. 5. If the back pressure in the engine in Problem 4 be 1.5 Ibs. instead of that cor- responding to the temperature of the discharged condensing water, what per cent of power will be lost, assuming a Rankine cycle to be employed between the new pressure limits? Ans. 8 per cent. 6. The mean effective pressure of an actual indicator card is 45 Ibs. The theoretical mean effective pressure for the same ratio of expansion, back pressure, and amount of compression,. is 48 Ibs. What is the card factor of the engine? Ans. 94 per cent. 7. The mean effective pressure obtained from the theoretical indicator card for a locomotive is 126 Ibs. What will be probable actual mean effective pressure? Ans. 94 to 106 Ibs. 8. An engine cylinder is 10 in. in diameter and the area of the ports is 8 sq. ins. The mean piston speed is 600 ft. per minute. What is the nominal velocity of the steam? Ans. 5,850 ft. per minute. 9. An engine having a cylinder 18 ins. in diameter and a 3-ft. stroke, makes 125 revolutions per minute. Assuming a nonrnal steam velocity of 5,000 ft. per minute, what will be the area of the exhaust ports? Ans. 38 sq. in. 10. A non-condensing engine takes steam at a pressure of 100 Ibs. absolute and has a ratio of expansion of 3. The area of wall surface exposed to the action of the steam per revolution at cut-off is 10 sq. ft. and the number of revolutions per minute is 200. Find the weight of steam condensed per revolution. Ans. 1.0276 Ibs. 11. The low pressure piston of a triple expansion engine is provided with poppet valves, so that the area of wall surface exposed to the action of steam at cut-off is that of the cylinder head, piston, and the barrel. The initial pressure is 14 Ibs. absolute and the condenser pressure 1 Ib. absolute. The cylinder is 80 ins. in diameter and 5 ft. stroke. The engine makes 30 revolutions per minute. The ratio of expansion is 2. Find the weight of steam condensed per revolution in per cert of the cylinder feed per revolution, assuming no clearance volume. Ans. 35 per cent. ART. 184 PROBLEMS 157 12. Construct an indicator card for an engine taking steam at 100 Ibs. absolute and discharging it at 16 Ibs. absolute with a ratio of expansion of 3, having 10 per cent clearance and complete compression, assuming all compression and expansion lines to be hyperbolic, and that the quality of the steam in the cylinder at cut-off is 50 per cent and at compression 100 per cent. Find the work done per pound of working fluid. 13. Find the work done per pound of steam supplied. 14. Assume the same conditions as before except that there is no compression, and find the work done per pound of working fluid. 15. Find the work done per pound of steam supplied. (Note the effect of com- pression on the efficiency.) 16. A friction card is taken from an engine and its area found to be 0.16 sq. in. The card at full load of the same length has an area of 1.55 sq. ins. What is the mechanical efficiency of the engine? Ans. 89.7 per cent. CHAPTER XI NOTES ON THE DESIGN AND TESTING OF STEAM ENGINES 185. Choice of Type of Engine. In designing a steam engine, it is first necessary to settle upon the type of engine and the range of .steam pressure to be employed. The type chosen will depend upon the power required, and upon the use to which the engine is to be put, and is settled primarily by financial and not by purely thermodynamic considerations. It is desirable that the cost of operation of the power plant shall be a minimum. This cost of operation includes three principal elements, the first being the cost of fuel, the second the cost of attendance, and the third the interest and other fixed charges on the first cost of the plant. An engine which is highly economical in the use of fuel usually will be costly, and hence the fixed charges will be large. If an engine is to be operated for a large part of the time, or if fuel is expensive, the cost of the fuel becomes the most important element in the cost of operation, and a highly efficient type of engine will be chosen, in spite of its first cost. If the engine is to be used only a small part of the time, or if it is small in size, or if the fuel is cheap, the fixed charges become the largest item in the cost of operation. In such a case the cheapest engine will be chosen in spite of its low efficiency. In this connection it should be remembered that it is not the cost of the engine alone, but the cost of the whole plant which we desire to reduce. The more efficient the engine, the smaller the boiler which will be required to operate it. If a cheap engine is very inefficient, the boiler required may become so large and costly that the total cost of the plant will be greater than it would be if a more costly, but more efficient engine had been chosen. Hence, when comparing the cost of operation of two engines, it is necessary to take account of the size and cost of the boiler plant required to operate each of them. It is not often, however, that the designer of an engine is called upon to fix the type and horse-power of the engine, or the range of steam pressure to be employed. That is usually the work of the consulting- engineer who designs the power plant. While large engines are almost always built to order, they are usually built from standard drawings and patterns, which have been prepared in anticipation of the probable require- ments of power plant engineers. When a number of such designs have 158 ART. 186 MULTIPLE EXPANSION ENGINES 159 been submitted to him, together with the prices of the engines, it is the duty of the consulting engineer to choose the particular one which will give the lowest plant operating cost. The type and size of engine which a manufacturer will attempt to build will depend on the facilities of his plant, and the apparent demands of the market. Having originated a series of sizes, he will then, by making minor changes in his designs and patterns, seek to adapt them in the best manner possible to the needs of each particular case, as they are outlined by the consulting engineer. 186. Cylinder Arrangements for Multiple Expansion Engines. The multiple expansion engine is an engine in which the steam performs work in two or more cylinders in succession, in the manner already described in Chapter VIII, Art. 128. Many different cylinder arrangements are used for such engines. In the case of compound engines, the two cylin- ders may be in line with one another with the two pistons upon a com- mon piston rod as in Fig. 77 a. The first cylinder into which the steam enters is called the high pressure cylinder, while the second is called the low pressure cylinder. They are indicated by the letters H.P. and L.P. in the diagram. Rec. is the receiver placed between the cylinders. This arrangement is termed a tandem compound engine. A second arrange- ment is shown in Fig. 77 fr, and is known as a cross compound engine. The two cylinders are side by side, each one acting upon a separate crank, which is keyed to a common shaft. In order to obtain a more even turn- ing moment the two cranks are placed at right angles to one another, so that when one of the cylinders is at dead center, the other one will be at mid-stroke. A compound engine may have two L.P. cylinders, in which case it is called a three-cylinder compound. The cylinders are then usually arranged side by side, and act upon three separate cranks set at 120 to each other, all keyed to a common shaft as shown in Fig. 77 c. A fourth arrangement is that known as the angle compound engine shown in Fig. 77 d, in which one cylinder (usually the H.P.) is horizontal, and the other is vertical. Both act on a common crank pin, and since one cylinder is at dead center while the other is at mid-stroke, the same uniform turning moment is obtained as is gotten from a cross compound engine. A fifth arrangement is that termed the duplex compound, in which the H.P. and L.P. cylinders both act on a common cross-head, as shown in Fig. 77 e. A sixth arrangement, which permits the designer to dis- pense with the receiver, is termed a Wolff compound, and is illustrated in Fig. 77 /. The two cross-heads are linked to opposite ends of a walk- ing-beam, so that the two pistons move in opposite directions. Admis- sion to the L.P. cylinder occurs directly through the exhaust valve of the H.P. cylinder, and continues for almost the entire stroke. Various 160 NOTES ON DESIGN AND TESTING OF STEAM ENGINES ART. 186 ART. 186 MULTIPLE EXPANSION ENGINES 161 other cylinder arrangements are occasionally used in practice, but the ones given are the most common. The triple expansion engine usually has three cylinders, termed respect- ively the high pressure, the intermediate, and the low pressure cylinders. The two receivers are known as the first and second receivers. The three cylinders are usually placed side by side and act on three cranks keyed to a common shaft and placed at angles of 120 with one another, as shown in Fig. 78 a. Four cylinder triple expansion engines are often built, H.P. I.P. L.P. v 1 IL FIG. 78 a n FIG. 78 6 FIG. 78. Cylinder arrangements for triple expansion engines. having two low pressure cylinders. They are arranged as shown in Fig. 78 6. Quadruple expansion engines are seldom built except for merchant marine service, and often have 5 or 6 cylinders, acting on as many cranks keyed to a common shaft. The introduction of the steam jturbine which is capable of utilizing low pressure steam to better advantage than the steam engine has tended to minimize the importance of triple and quad- ruple expansion engines. Greater economy can be obtained by utilizing 162 NOTES ON DESIGN AND TESTING OF STEAM ENGINES ART. 187 the steam from a compound engine in a low pressure steam turbine than by further expanding it in additional cylinders. 187. Advantages of Multiple Expansion. The multiple expansion engine offers several advantages over a single engine having the same ratio of expansion. They are: First, reduced cylinder condensation, on account of the reduction in the temperature range and ratio of expansion per cylinder. Second, reduced leakage loss, on account of a reduction in the pres- sure difference which causes the leakage. Third, higher mechanical efficiency, since the ratio of the maximum to the mean effective pressure in each of the cylinders is greatly reduced, being usually from 40 to 70 per cent of what it would be were the same total ratio of expansion employed in a single cylinder engine. Fourth, the principal parts of the engine are less heavy and costly, since the maximum total steam pressure on each of the pistons is only from 20 to 30 per cent of what it would be were a single cylinder engine employed having the same total ratio of expansion. Fifth, by causing two or more cylinders to operate on separate cranks on the same shaft, as is done in the cross compound engine, a more even turning moment may be secured, which is a matter of very great importance in the case of engines operating alternating current generators in parallel, and is desirable in many other cases. 188. Action of the Steam in a Compound Engine. In order to make clear the action of the steam in the cylinders of a compound engine, the simplest possible case will be considered. Assume a compound engine in which the weight of cushion steam is the same per stroke for each cylinder; the H.P. cylinder is without compression, and the L.P. cylinder has complete compression. The weight of cylinder feed per stroke will of course be the same for each cylinder, since all of the steam leaving the high pressure cylinder must pass through the low pressure cylinder before it is finally discharged from the engine. Assume that the receiver is of very large volume, so that no change of pressure results when the H.P. cylnder is discharged into it or the L.P. cylinder takes steam from it. If there is no loss from wire drawing the pressure of the steam entering the L.P. cylinder will be the same as that exhausted from the H.P. cyl- inder. If the volume of the steam taken per stroke by the L.P. cylinder is the same as the volume of the steam discharged by the H.P. cylinder, the H.P. cylinder will have complete expansion and the form of its card will be that bounded by the lines ab c din Fig. 79. The L.P. cylinder will take the same volume of steam from the receiver as was discharged into it by the H.P. cylinder, and its card will be that bounded by the lines dcefg in the same figure. An inspection of the two cards will serve ART. 189 DETERMINATION OF CYLINDER DIMENSIONS 163 G F FIG. 79. Theoretical card for a com- pound engine. to show that they are simply the theoretical card of an engine having a large ratio of expansion. The work done by the steam in passing through the engine is the same as the work which that steam would do in the L.P. cylinder of the engine, if the steam were admitted to the cylinder at boiler pressure, and a sufficiently short cut-off were used to get the same ratio of expansion in the L.P. cylinder as actually occurs in the entire engine. The addition of the high pressure cylinder does not increase the power of the engine, but it does result in gaining the advantages already enumerated in the preceding article. On this ac- count, when the range of steam pressure available is great enough to make a large ratio of expansion desirable, a compound engine is almost always chosen, rather than a simple engine of the same power. It is not often, however, that the clearance volumes and points of compression in the high and low pressure cylinders of an engine are so adjusted that the weight of cushion steam contained in each cylinder is the same. Furthermore, the receiver is never of sufficiently large volume to eliminate pressure changes due to the discharge of steam by the H.P. cylinder and draft of steam by the L.P. cylinder. On this account, the usual behavior of the steam in the cylinders of a multiple expansion engine is not quite the simple matter that has been outlined. However, the error introduced by estimating the power of a multiple expansion engine from the area of the theoretical card already described and the volume of its low pressure cylinder, is so small that it may be neglected in designing such an engine. It is customary in design work to fix the size of the low pressure cylinder of a multiple expansion engine by assum- ing that steam is admitted to that cylinder at boiler pressure, and that the total range of expansion occurs there. 189. Determination of Cylinder Dimensions. When the size and type of engine and range of steam pressure have been settled, either to meet a given set of operating conditions or to meet the probable require- ments of the market, it is next in order to determine the probable mean effective pressure and the size of cylinder (or in the case of a multiple expansion engine, the size of L.P. cylinder) required to develop the power. In order to do this, it is usual to lay out to scale the theoretical card for the pressure range and ratio of expansion which it has been decided to adopt. Having drawn the theoretical card, the designer 164 NOTES ON DESIGN AND TESTING OF STEAM ENGINES ART. 189 measures or calculates its area and from its area and length the mean ordinate of the card is obtained. Multiplying together the height of the mean ordinate, and the pressure scale of the drawing, the theoretical mean effective pressure is obtained. The theoretical mean effective pressure should then be multiplied by the proper card factor in order to obtain the actual mean effective pressure at the rated load of the engine. The area of the piston of the engine is now obtained by the formula A =33,000, in which A is the area of the piston in square inches, HP is the indicated horse-power of the engine at rated load, S is the mean piston speed in feet per minute, and P is the mean effective pressure in pounds per square inch. The mean piston speed is of course equal to twice the length of the stroke in feet times the number of revolutions per minute. The area so obtained will of course, be the area of the low pressure piston in the case of a multiple expansion engine. In case the engine has two or more L.P. cylinders, it is the combined area of all the L.P. pistons. If the engine is to be a compound or triple expansion engine, the theoretical card is now divided by horizontal lines into two or three por- tions as nearly equal in area as may be. This is done in order that the amount of work developed in each of the cylinders shall be the same. Fig. SO represents such a card as would be laid out in designing a com- pound engine. The horizontal line e f divides the card into two portions of nearly equal area. The high pressure card which is the upper of the two areas is now modified by giving a certain amount of terminal drop as shown by the line c d. The reasons for giving this terminal drop are that it reduces the size of the high pressure cylinder, increases FIG. 80. Card used in designing a the mechanical efficiency of the compound engine. engine, and reduces the loss due to cylinder condensation. The length e d will now represent the swept volume of the H.P. cylinder while the length i h will represent the swept volume of the low pressure cylinder. If both cylinders are of the same length of stroke, the ratio of e d to i h also represents the ratio of the piston areas of the two cylinders. Having determined the area of the low pressure piston by the rule already given, the area of the high pressure piston may bo determined by this ratio. The length of stroke may next be chosen, ART. 190 THE DESIGN OF RECEIVERS 165 and the number of revolutions per minute be determined by twice the length of stroke in feet. 190. The Design of Receivers. In order that the low pressure cylin- der may receive its supply of steam without too much variation in pres- sure, and that the high pressure cylinder may exhaust its steam, while the low pressure inlet valves are closed, a receiver of considerable vol- ume is interposed between the high and low pressure cylinders. The volume of the receiver is usually made from 2 to 6 times the volume of the high pressure cylinder. The larger the volume of this receiver, the higher the card factor of the engine, and the less the loss due to over- lapping of the cards. However, if the receiver is made too large, the loss due to radiation will overcome the advantage of an improved card factor, so that the limits given represented the practical range in varia- tion of receiver volume. In the case of a triple expansion engine, the volume of the second receiver, interposed between the intermediate and low pressure cylinders, is from 1^ to 4 times that of the intermediate cylinders. It may be shown that the relative position of the cranks of an engine has an important effect on the range of pressure variation in the receiver. The cranks should be so placed that this pressure varia- tion will be a minimum. On account of its adiabatic expansion and the loss of heat by radia- tion, the steam which enters the receiver will be wet. If this wet steam is permitted to enter the low pressure cylinder, the cylinder condensa- tion will be greatly increased on account of the excessive wetness of the steam. To avoid this it is customary to heat the steam in the receiver by means of a coil of pipe called a reheater. The reheater is supplied with steam of a higher pressure than that in the receiver, and on account of its high temperature it evaporates the water, thus supplying the second cylinder with dry steam. However, this action is accompanied by a thermodynamic loss and is practically the equivalent of operating the engine on a jacketed cycle. A preferable method is to so form the receiver - that it becones a separator, mechanically removing the moisture con- tained in the entering steam, and supplying the second cylinder with steam that is practically dry. A reheater may be used to advantage in connection with a separating receiver, but the amount of heat supplied by the reheater will then be very small. The use of the reheater will give almost absolutely dry steam to the following cylinder, with a result- ing decrease in the loss from cylinder condensation. The amount of reheater surface used varies greatly in different types of engines, and is dependent very largely on the judgment of the designer. Good practice sanctions the use of from 0.02 to 0.05 square feet of reheat- ing surface per pound of steam per hour. In case a separating receiver is used, the area of reheating surface may, of course, be greatly diminished. 166 NOTES ON DESIGN AND TESTING OF STEAM ENGINES ART. 19' 191. Design of Jackets. In the case of very slow-moving engines, as for instance long stroke pumping engines, the cylinders should be jacketed. It is customary, when practicable, to jacket both the barrel and the heads of the cylinder. It is equally advisable to jacket the piston although this is seldom attempted on account of the difficulty of intn; v ducing steam and carrying away the drip through the piston rod. When jacketing an engine, care must be taken that the jackets are drained, so that water will not accumulate in them, since a jacket filled with water tends to increase rather than diminish the loss due to cylinder condensa- tion. It is not difficult to drain the jackets of the cylinder barrel, but oft- times considerable ingenuity must be used in order to drain the jackets of the heads, when the valves are placed in the heads, as they are usually in the case of slow speed vertical engines. The reheating coils in the receivers must also be so arranged that they can be drained. The jacket drain should lead to a trap which will discharge the accumulated water without permitting the escape of steam. In the case of a high pressure cylinder, this trap should discharge into the receiver, as should also the drip from the reheating coil, in order that the sensible heat of the water may be utilized in evaporating a portion of its weight into steam, which will do work in the low pressure cylinder. In a triple expansion engine, the drips from the intermediate cylinder and the reheater coil of the second receiver in like manner may discharge into the second receiver. When a highly efficient multiple expansion engine is desired, an approximation to the Carnot cycle may be obtained by pumping the feed- water from the hot well (i.e., the chamber into which the air-pump dis- charges the condensed steam) through heating coils surrounded by steam from the receivers. The steam used to heat the feed- water has already done work in one or more cylinders, and the feed-water is finally sup- plied to the boiler at practically the temperature of the steam in the first receiver. While this method makes an engine highly economical, the economy of the plant will be lower than if an economizer were used. Although this method has been employed in practice, it was used, not in order to secure a high plant economy, but in order to earn a bonus for a high engine economy. Having settled upon the areas of the pistons, the length of stroke, the number of revolutions per minute of the engine, the volume of the receivers and the amount of reheating surface, the areas of the ports may be computed by the rules given in Art. 170. The remainder of the design of the engine becomes a problem in machine design in which the principles of thermodynamics play no part. 192. Theoretical Indicator Cards for Multiple Expansion Engines. Iri order to construct accurately the theoretical indicator cards for a multiple expansion engine, it is necessary to take account of the volume of the receivers, and the pressure VRT. 192 INDICATOR CARDS FOR MULTIPLE EXPANSION ENGINES 167 variations which take place within them. It is customary to compute the form of the cards for such engines on the assumption that the product of the pressure and the volume of a given weight of steam is a constant quantity. This is not exactly true, but is a sufficient approximation in estimating the power and proportioning the cylin- ders of such engines. Having designed the cylinders and the receivers of a multiple xpansion engine, and, from the design, computed the clearance volume of each of the cylinders, we are in position to draw the theoretical indicator cards of the several cylinders. In order to illustrate the method of constructing such cards, a cross com- pound engine will be assumed. In such an engine steam is admitted at boiler pressure to the H.P. cylinder up to the point of cut-off. After the H.P. inlet valve is closed, the steam in that cylinder expands until the end of the stroke, when the exhaust valve opens. If, as is usually the case, the receiver pressure is less than the terminal pressure of the H.P. cylinder, there will be a sudden drop in pressure in the H.P. cylinder, and a sudden rise in the pressure in the receiver, at the instant of release. The H.P. piston will now begin to return, compressing the exhaust steam into the receiver and consequently raising the pressure, both in the receiver and in the H.P. cylinder. When the H.P. piston reaches mid-stroke, the L.P. piston arrives at the end of its stroke and the L.P. inlet valve opens. Unless compression is complete in the L.P. cylinder, steam will rush into this cylinder from the receiver, and the receiver pressure will drop. During the remainder of the back stroke of the H.P. piston, the L.P. piston is moving forward, and the L.P. cylinder is taking steam at a faster rate than it is discharged by the H.P. cylinder. Since the steam is increasing in volume, its pressure will fall until the L.P. inlet valve closes. If this occurs before the H.P. exhaust valve closes, the pressure in the receiver and the H.P. cylinder will again begin to rise. If it occurs after the H.P. exhaust valve closes, the pressure in the receiver will not rise and the pressure in the H.P. cylinder will rise only an account of compression. Fig. 81 is an illustration of the theoretical card given by such an engine; a^b is the steam line of the H.P. cylinder; 6-c is the expansion line of the H.P. cylinder; c-d is the terminal drop of this cylinder; d-e is the period during which the H.P. exhaust is being compressed into the receiver before the L.P. inlet valve opens; e-f represents the drop in pressure in the H.P. cylinder when the L.P. inlet valve opens; f-g represents the period during which the H.P. exhaust and the L.P. inlet valves are both open ; g-h is the compres- sion period in the H.P. cylinder; f'-g' is the admission period of the L.P. cylinder up to the time when the H.P. exhaust valve closes; g'-i' is the remainder of the admission period, which occurs while the H.P. exhaust is closed; i'-j' is the expansion period of the L.P. cylinder, j'-k' represents the L.P. terminal drop, k'-l' the L.P. exhaust; l'-e' repre- sents the L.P. compression period, and e'-f represents the rise in pressure in the L.P. cylinder at the point of admission which is coincident with the fall in pressure, p.-f, in the H.P. cylinder and the receiver. In computing the card for such an engine, it is necessary to know the pressure and volume at L.P. release, (/')> and the initial and back pressure (i.e., at ab, and k'-l'). FIG. 81. Computed card for a cross compound engine. 168 NOTES ON DESIGN AND TESTING OF STEAM ENGINES ART. 192 It is also necessary to know the receiver volume (which we will designate by the symbol R) and the volumes of the high and low pressure cylinders at points h, b, c, e, g, e f , g', i', j f , and I'. These may be determined graphically when the clearance volumes, and the points of cut off and compression are known for each cylinder. In order to illus- trate the method of computing the card the following example will be assumed: The initial steam pressure is 150 pounds, the L.P. terminal pressure 10 pounds, and the back pressure 2 pounds per square inch absolute. The swept volume of the H.P. cylinder is 4 cubic feet and of the L.P. cylinder 15 cubic feet. The H.P. clearance volume is 0.4 cubic feet (i.e., 10 per cent) and the L.P. clearance volume 0.6 cubic feet (i.e., 4 per cent). The receiver volume is 12 cubic feet. The point of compression is 10 per cent from the end of the stroke for each cylinder, and L.P. cut-off occurs at 40 per cent of the stroke. We will now have F/-15.6 cu.ft. Vi'= 6.6 " y e '= 2.1 " V a - -4 " y= 4.4 " In order to find the volume of the L.P. cylinder at point g', we may make the con- struction shown in Fig. 82, in which points H and L represent the simultaneous positions of the H.P. and the L.P. cranks at the point of compression in the H.P. cylinder, distance a b represents the distance of the point of compression from the end of the stroke of the H.P. cylinder, and a c the distance of the point g' from the end of the stroke of the L.P. cylinder. From such a construction we find the distance a c to be 20 per cent of the stroke, and the volume Ty = 3.6'cu.ft. The product of the pressure and volume of the steam in the L.P. cylinder at release is Vj' Pj' = 15.6X10 = 156. The product of the pressure and volume at cut-off is the same, and the pressure FIG. 82. The pressure in the receiver at this point is the same. Consequently the product of the pressure and volume of the steam in the L.P. cylinder and receiver together at this point is 156 + 23.7X12=440. ART. 192 INDICATOR CARDS FOR MULTIPLE EXPANSION ENGINES 169 The volume of the steam in the receiver and L.P. cylinder at point g' is 12 + 3.6 = 15.6cu.ft. The pressure The product of the pressure and volume of the steam in the H.P. cylinder, the receiver, and the L.P. cylinder at the instant H.P. Compression begins is therefore 440 + 28.2X0.8-462.6. The volume of the steam contained in the H.P. cylinder, the receiver, and the L.P. cylinder at L.P. admission is 2.4 + 12 + 0.6 = 15cu.ft. We will therefore have for the pressure p/ ' = P/ = 46 1- 6 = 30.8 Ibs. The product of the pressure and volume of the steam contained in the L.P. cylin- der during compression is 2X2.1=4.2. The product of the pressure and volume of the steam in the low pressure cylinder at point /' is 30.8X0.6 = 18.5. The product of the pressure and volume of the steam in the H.P. cylinder and the receiver at point e is therefore 462.6-4.2=458.4. The product at point / is 462.6-18.5=444.1. Since the volume of the steam at both points is 12+2.4 = 1.44 cu.ft., the pressure at e is .. 14.4 The volume of this steam at d is 12+4.4 = 16.4 cu.ft., and its pressure is The pressure of the steam in the receiver at H.P. release is P/ = 23.7, and the product of its pressure and volume is therefore 23.7X12=284. The product of the pressure and volume of the steam in the H.P. cylinder at release is therefore 458.4-284 = 174.4. The pressure at release was therefore ~~ =39.7 Ibs. 4.4 170 NOTES ON DESIGN AND TESTING OF STEAM ENGINES ART. 103 The volume at H.P. cut-off was 17/1/1 1.162 cu.ft. and cut-off occurs at 19 per cent of the stroke. The pressure at e' is the pressure at h is gXF g _28.2X0.8 = f) The volume of the cylinder feed is 174.4-28.2X8 150 1.01 cu.ft. The indicated steam consumption per stroke is 1.01X0.338 = 0.342 Ibs. The actual steam consumption per stroke may be estimated by adding to the indicated steam consumption the estimated weight of the steam condensed per stroke, and an allowance for leakage. The power of the engine may be estimated by finding the power of each cylinder shown by the cards obtained, after making proper reduction for wire drawing and steam friction. ' 193. Combined Cards for Multi-Cylinder Engines. The combined card of a steam engine is obtained by placing together the H.P. card and L.P. card, using the same scale of pressures and the same scale of volumes and setting off the admission line of the two cards at such distance from the zero volume line is as indicated by the clearance of the respective cylinders. As has already been shown , when the same weight of cushion steam is con- tained in each cylinder, and the compression in the L.P. cylinder is complete and there is no compression in the H.P. cylinder, the com- bined card (except for over- lapping wire drawing, and H.P. terminal drop) is the same as would be given in a single cylinder engine FIG. S3. Theoretical combined cards. having the volume of the L.P. cylinder and the same total ratio of expansion. If the same weight of cushion steam is con- tained in each cylinder, but the conditions of compression are different, from those given, the card will be that which would be given by a cylinder of different swept volume, as may be seen in Fig. 83, in which the length A ART. 194 TESTING STEAM ENGINES 171 represents the swept volume of the theoretical cylinder required to develop the power shown by the card, and length B represents the swept volume of the actual low pressure cylinder. The swept volume plus the clear- ance volume for the two cylinders, however, will be the same. When the weight of cushion steam contained in the two cylinders is different, it will be impossible to draw correctly a combined card which will represent the action of the steam, since the weight of steam represented by the H.P. card will be different from that represented by the L.P. card. In such cases, it is customary to refer the two cards to the same pressure and volume scales. The theoretical expansion line for the two cards will not, however, be the same. 194. Testing Steam Engines. In making a test of a steam engine it is usual to obtain the following data: First, the pressure of the steam supplied to the engine. Second, the quality of steam supplied to the engine. Third, the weight of wet steam rejected by the engine. Fourth, the pressure of the steam in the condenser. Fifth, the temperature of the water entering and leaving the condenser. Sixth, the weight of the drip from each of the jackets. Seventh, the number of revolutions per minute made by the engine. Eighth, indicator cards are taken from each end of each cylinder. Ninth, the brake horse-power of the engine is obtained. The precautions which must be observed in making such a test to insure that these data are properly taken have been outlined by a com- mittee of the American Society of Mechanical Engineers, in their standard methods of testing steam engines. 1 The method of testing here outlined involves the use of a surface condenser. When any other type of con- denser is employed, the weight of water fed to the boiler and not the weight of steam rejected by the engine, must be taken as the measure of the steam supplied. An engine test should last several hours and the conditions of load, steam pressure, vacuum, etc., should be kept as nearly constant as possible. Any considerable variation in these quantities during the test will invalidate the results. The readings are taken at frequent intervals, usually every ten minutes. 195. Graphical Analysis of an Engine Test. It is instructive in working up the results of an engine test to superimpose the indicator cards of the engine upon the theoretical diagram of the cycle in order to determine the magnitude and distribution of the losses which occur. In order to do this, it is necessary to construct a mean card for each of the cylinders, which will represent the average con- ditions for both the head and crank ends of that cylinder for the entire test. After computing the average mean effective pressure developed during the entire 1 See the Transactions of the A.S.M.E. for 1902. The rules are also published by the Society in pamphlet form. 172 NOTES ON DESIGN AND TESTING OF STEAM ENGINES ART. 195 test in the head and crank end of each cylinder, that set of indicator cards is chosen in which the mean effective pressures are nearest to the average. These cards are, f course, the best representative cards for the test. Each of the cards may then be ruled with a number of equidistant vertical lines, as shown in Fig. 84. Upon the paper on which the mean card is to be constructed for any cylinder, rule a horizontal line, for the atmospheric line, making its length represent the swept volume of both ends of the cylinder, to any suitable scale. Upon it erect the same number of equi- distant vertical lines as has already been drawn upon each of the indicator cards. Head End Card Crank End Card \ \ \ \ \l a' Mean Card FIG. 84. Construction of a mean card. Upon the first vertical line of the head end card, measure the distance from the atmospheric line to a point on the outline of the card, as a-b. Add to this distance the corresponding distance c-d measured upon the crank end card, and lay off upon the first vertical line of the mean card the sum of the distances a-b and c-d, at a'd'. In like manner lay off all the other points and so draw a card which is the mean of the head and crank end cards for the cylinder. The zero pressure line may now be drawn parallel with the atmospheric line, the distance between the lines being determined by the atmospheric pressure at the time of the test, as computed from the barometer reading. The zero volume line is drawn perpendicularly to the atmospheric line at such a distance from the end of the mean card as represents the sum of vhe head and ART. 195 GRAPHICAL ANALYSIS OF AN ENGINE TEST 173 crank end clearance volumes. The theoretical indicator card for a Rankine cycle with complete compression is now constructed, the weight of cushion steam and the weight of working fluid being the same for the Rankine cycle as it is for the cylinder in question. The quality of the steam at cut-off and at the beginning of compression, in the Rankine cycle, is assumed to be the same as that of the cylinder feed, as deter- mined during the engine test. The pressure limits of the Rankine cycle are, in the case of the H.P. cylinder of a multiple expansion engine, the pressure of the steam at the throttle valve and that of the steam in the receiver. In the case of an intermediate cylinder, the pressure limits of the Rankine cycle are the pressures of the steam in the preceding and following receivers. In the case of the L.P. cylinder of a multiple expan- sion engine, they are the pressure of the steam in the preceding receiver and the pres- f N FIG. 85. Actual card superimposed upon a Rankine cycle card to show the losses. sure corresponding to the temperature of the discharged condensing water. In the case of a simple non-condensing engine, the pressure limits are the pressure of the steam at the throttle and the pressure of the atmosphere. Fig. 85 shows the construction for the L.P. cylinder of a compound engine, the heavy outline being the actual indicator card, while the light outline is the theoretical card for the Rankine cycle. Since terminal drop is employed, the toe of the Rankine cycle, bounded by the lines cdN, will be lost. This loss is due to the imperfection of the cycle employed. A line g-h drawn parallel with the line f-d (which represents the pressure corresponding to the temperature of the discharged condensing water) and tangent to the actual card, marks off the area ghfN is which represents the loss due to the imperfection of the condensing apparatus. The expansion line FIG. 86. Card from a non-condensing engine superimposed on a Rankine cycle card. of the steam may now be completed, and is represented by the line je. The area j-b-c-e will then represent the loss of power due to cylinder condensation. The shaded area minus the dotted area represents the loss of power due to the combined effects of steam friction, wire drawing, and overlapping. The smaller the volume of the receiver, the larger will be the amount of this loss. The area a-K-L represents the loss due to clearance. There is a further loss due to clearance included in the area c-d-f on account of the incomplete expansion of the steam compressed in the clearance spaces. If an adiabatic expansion line j-i be constructed from point /, the area e-j-i will be the work restored by the re-evaporation of the steam initially condensed. A part of this work so restored is, of course, lost from other causes. The area in the lower left- 174 NOTES ON DESIGN AND TESTING OF STEAM ENGINES ART. 196 hand corner, bounded by the compression line and by the line L-h, is the work lost on account of the compression of dry and saturated steam which results from the heat- ing of the exhaust by the cylinder walls. Fig. 86 represents a card similarly treated for a simple non-condensing engine. The losses may be traced out by the reader. 196. Other Methods of Analyzing Engine Tests. A method formerly much in use in analyzing the results of an engine test is that known as Hirn's analysis. In this method, the heat transferred to or from the steam contained in the cylinder is determined for each portion of the cycle. It is assumed in Hirn's analysis that all heat transfers not otherwise accounted for are due to cylinder condensation or re- evaporation. This is not true, since such heat transfers are often due to leakage. The computations involved in Hirn's analysis are rather laborious, as may be seen by reference to Art. 55 of the second volume of Zeuner's Technical Thermodynamics, in which the theory of Hirn's analysis is fully developed. Hirn's method of analysis emphasizes unduly the losses due to cylinder condensation, and does not separate or analyze other sources of loss. On this account, Hirn's method of analysis is not much used at the present time in determining the amount and distribution of the losses in the steam engine. Another method of determining the losses in a steam engine is to draw the tem- perature-entropy diagram of the fluid contained in the cylinder and then to superimpose this diagram upon the theoretical temperature-entropy diagram of the cycle in the manner shown in Chapter XXV. The temperature-entropy diagram has the advantage of illustrating more clearly the heat transfer to and from the cylinder walls, but it is more difficult to employ than the methods described in Art. 195, which are, on the whole, the most satisfactory methods of analyzing the results of an engine test. 197. Methods of Comparing Engine Efficiencies. Many methods are in use for stating the efficiencies of steam engines. One of the com- monest is to determine the number of pounds of dry steam supplied per hour to the engine per indicated horse-power developed. This is usually known as the water rate of the engine. While, in general, a low water rate means a highly efficient engine, the water rates of different types of engines are not proportional to their true economy. Accordingly, a second method has been suggested in which the efficiency of the engine is expressed in terms of its heat rate (i.e., in terms of the number of B.T.U. supplied to the engine per indicated horse-power per hour). The heat rate may be derived from the water rate by subtracting from the total heat of the dry steam supplied, the heat of the liquid at the temperature of exhaust, and multiplying by the water rate. Sometimes the number of B.T.U. supplied per brake horse-power is given. In the case of direct connected units, the efficiency of the combined unit is often expressed by the number of B.T.U. supplied per kilowatt hour output of the gen- erator. Occasionally the number of B.T.U. per minute is made the basis of the statement of efficiency. The efficiency is often expressed as a per cent of the theoretical efficiency of the Rankine cycle. The effi- ciency referred to the Rankine cycle may be obtained by dividing the ART. 198 RELATION BETWEEN LOAD AND EFFICIENCY 175 heat rate of the Rankine cycle for the given temperature range by the heat rate of the actual engine for the same temperature range. The total efficiency of an engine is sometimes given ; which is the per cent of the total heat supplied which is actually transformed into useful work. In the table given in Art. 210, will be found recent figures for the best efficiencies of steam engines and turbines, in which the efficiencies are stated in the different ways most commonly employed. 198. Effect of Variation in the Load on the Efficiency. The power developed by an engine is not a fixed quantity, but is usually automatically varied by the governor in such a manner as to keep the speed of the engine .Hi 10 IbO 200 60 80 100 130 140 Load in per cent of the Bated Load . FIG. 87. Load curve of a steam engine. constant. The governor accomplishes this by increasing or diminishing the quantity of steam per stroke taken by the engine. As a result of the action of the governor, the form of the steam cycle and the conditions of operation vary as the load on the engine is varied. In consequence of these changes the losses vary, being usually less at low loads than at high loads. If the sum of the losses were always proportional to the power developed, the efficiency of the engine would be constant at all loads. Since such is not the case, it follows that at some particular load the heat rate of the engine will be a minimum (i.e., its efficiency will be a maximum) and at all other loads the heat rate will be increased. The rated power (i.e. the nominal horse-power) of a steam engine is usually the indicated horse-power at which it gives the minimum heat 176 NOTES ON DESIGN AND TESTING OF STEAM ENGINES ART. 198 consumption per brake horse-power per hour. In the case of other types of heat engines (e.g., steam turbines and gas engines) this is not true, since such engines give the greatest economy at the maximum possible load, and if rated at their most economical load they would have no overload capacity. The efficiency of a steam engine falls off rapidly at low loads, as may be seen by referring to the " load curve " shown in Fig. 87, and it is therefore desirable to operate such an engine at or above its rated load. Consequently when a plant is to furnish a variable amount of power, several engines should be installed, and such a number of them should be operated at any time as will make the load on each one as nearly as possible equal to its rated load. Furthermore, in comparing the efficiency of different engines, it is necessary to compare their efficiencies at their most economical loads, since comparison on any other basis would be misleading. A statement of the results of an engine test should therefore always include a state- ment of the actual and of the rated load of the engine, in order that it may be known whether the conditions of operation were such as to make reasonable economy possible. In the case of an engine with a throttling governor, the total steam consumption of the engine is given approximately by y the formula O A 20 40 60 80 100 120 HO Indicated Horse Power in Terms of the Rated Load FIG. 88. Curve of total steam consumptign. in which S is the total steam consumption, A and K are constants, and H.P. is the brake horse-power developed by the engine. This is known as Willan's Law. It does not hold for cut-off governed engines, for which we may write an approximate mula of the form for- in which n is greater than one. The general form of the curve of total steam consumption for such an engine is shown in Fig. 88. In this figure the segment A is equal to the friction horse-power. A line through tangent to the curve of total steam consumption will obviously touch it at the point where the water rate per indicated horse-power is a minimum. In like manner, a tangent through A will touch it at the point where the water rate per brake horse-power is a minimum. ART 198 PROBLEMS 177 A flat load curve is a desirable characteristic in an engine, and when two engines of equal efficiency are compared, that one is the better which has the flatter load curve. PROBLEMS 1. A steam turbine plant costs $60.00 per kilowatt, while a steam engine plant costs $80.00 per kilowatt. If the fixed charges are 15 per cent per annum in each case, and the plant operates 15 hours per day, for 300 days per year, what will be the costs per kilowatt hour due to fixed charges on the plant? Ans. 0.200 cents and 0.267 cents. 2. The steam turbine plant requires 2 Ibs. of coal per kilowatt hour, and the steam engine plant 1.8 Ibs. per kilowatt hour. Coal costs $2.00 per ton. What is the cost per kilowatt hour in each case? Ans. 0.10 cents and 0.09 cents. 3. Which of the two plants will operate at the least total cost per kilowatt hour, disregarding all other costs except those given? Ans. The turbine plant will operate at 0.300 cents and the engine plant at 0.357 cents per kilowatt hour. 4. Construct a combined card for a compound engine taking steam at 150 Ibs. gage and discharging it at 2 Ibs. absolute. The clearance of the low pressure cylinder is 5 per cent and the pressure at the end of compression Ibs. absolute. The ratio of expansion is 16- Assume hyperbolic expansion and compression. 5. Divide the above card into two parts so that the areas of the two parts are equal. 6. Give sufficient terminal drop to the H.P. card so that the total steam load on the H.P. piston will be equal to that on L.P. piston, at the instant when the load is a maximum in each cylinder. (The total steam load is equal to the area of the piston times the difference in steam pressure at inlet and exhaust.) Assume that the lengths of stroke are equal for the two cylinders and that the areas of the cylinders are proportional to the volumes. 7. Find the mean effective pressure of the above card referred to the L.P. cylinder, assuming a card factor of 90 per cent. 8. What must be the diameter of the L.P. cylinder of an engine, in order that it shall develop 500 indicated horse-power at 600 ft. per minute piston' speed, with the M.E.P. found in Problem 7. 9. Find the proper volume for the receiver for the above engine, assuming that it is to be a cross compound engine. 10. An engine uses 10,000 Ibs. of steam of 98 per cent quality in a 2-hour test. The indicated horse-power is 250. What is the water rate of the engine? Ans. 19.6 Ibs. per hour. 11. If the steam is supplied at 125 Ibs. gage pressure and the condenser pressure is 3 Ibs. absolute, what is the heat rate of the above engine? Ans. 21,310 B.T.U. 12. If the mechanical efficiency of the engine is 92 per cent, what is the heat rate per brake horse-power per hour? Ans. 22070 B.T.U. 13. What is the heat rate of the Rankine cycle for the same temperature range? Ans. 10,810 B.T.U. 14. What is the brake efficiency of the above engine expressed as a percent of the efficiency of the Rankine cycle? Ans. 49% 15. What is the total efficiency of tluj above engine? Ans. 11.5% CHAPTER XII THE STEAM TURBINE 199. Impulse and Reaction Turbines. The steam turbine is a heat engine which makes use either of the impulse or of the reaction of a jet of steam, in order to transform the energy of this steam into work. If the turbine operates by utilizing the impact of the steam jet, it is known as an impulse turbine. If it makes use of the reaction of the steam jet, it is known as a reaction turbine. Turbines which combine both prin- ciples are sometimes used and are known as impulse-reaction turbines. The impulse turbine is sometimes termed the velocity turbine, and the reaction turbine is sometimes termed the pressure turbine. 200. The Theory of the Turbine Nozzle. If steam be supplied under pressure to a properly shaped nozzle, it will flow from the nozzle with a very high velocity in the form of a jet. If this jet be permitted to strike upon a suit- ably formed surface so that its direction of motion is changed, as in Fig. 89, the impact of the jet upon the surface will tend to force the surface backwards, and if the surface be permitted to move, work will be performed. The Kerr turbine, illustrated, in Fig. 90, is of this type. If the nozzle itself be permitted to move, the reaction of the escap- ing steam will force it backward, and work will be performed. This is the principle of the reaction turbine. The Avery turbine, illustrated in Fig. 91, is of this type. It will be seen that the proper operation of a steam turbine will depend upon the form of the nozzles used. It is therefore a matter of primary importance in steam turbine design to make the nozzles of the proper form and size for the work which they are to do. The following paragraphs will serve to make 178 FIG. 89. Impact of steam jet upon a properly formed vane surface. ART. 200 THE THEORY OF THE TURBINE NOZZLE 170 clear the action of turbine nozzles and the methods of designing them. When steam flows through a nozzle each particle will be found to expand in volume and increase in velocity as it passes from the region of high pressure to that of low pressure. In passing through the nozzle, the steam will neither gain nor lose heat. This being the case, the kinetic energy of each pound of steam as it passes a given cross-section of the nozzle, plus the work done by this steam in displacing the steam in the region into which it rushes, must be equal to the loss of internal energy of this pound of steam, plus the work done upon it by the advancing FIG. 90. Section of a Kerr turbine. mass of steam which takes its place in the region from which it flows. A consideration of Fig. 92 will make this apparent. In the figure A is a cylinder and B a nozzle. The cross-section of the nozzle is very small in comparison with that of the cylinder, so that the velocity of the steam in the cylinder may be neglected. The steam flowing from the nozzle passes into the tube (7, whose cross-section is the same as that of the nozzle at the point where the nozzle terminates. Assume that cylinder A is filled to the point d with a steam having a pressure PI and entropy N, and that tube C is filled to the point E with steam having a pressure P 2 . Since the steam neither gains nor loses heat in passing through a frictionless nozzle, the entropy in tube C will be the same as in cylinder A, and the expansion is adiabatic. At E in the tube and at D in the cylinder are pistons which' exert upon the 180 THE STEAM TURBINE ART. 200 steam a pressure equal to that exerted upon them by the steam. The pressure in tube C being less than that in cylinder A, the steam will flow from AtoC through the nozzle, and if the pres- sures are to remain constant, the pistons must both move to the right. Assume that the pro- portions of the nozzle are such that 1 pound of steam flows per second, then the work done upon the steam per second by piston D will be the external work of evaporation of 1 pound of steam of pressure PI and entropy N. The work done by the steam upon piston E will be equal to the external work of evaporation of 1 pound of steam at pressure P^ and of entropy N. The kinetic energy of the pound of steam flow- ing in the tube C will then be equal to the work of expansion (which is the difference between the internal energy of a pound of steam when in cylinder A and in the tube C) plus the work done by piston Z), minus the work done upon piston E. This is of course equal to the difference between the total heat of the pound of steam at pressure PI and entropy Nj and its total heat at the same entropy and at the pressure P 2 , a quantity which we will designate by the symbol AH, and which is usually termed the heat drop. The kinetic energy of a body having a mass of 1 pound is of course FIG. 91. Diagram illus- trating the principle of the A very turbine. e C FIG. 92. Ideal apparatus illustrating the flow of steam through a nozzle, We have already seen that whence 7 2 64.34 777.5 JH. (2) (3) ART. 201 FORM OF THE TURBINE NOZZLE 181 Solving for V, the velocity of the steam leaving the nozzle, 7=^61.34X777.8 AH = 223.6 V/IH. ... (4) 201. Form of the Turbine Nozzle. As the steam flows through the nozzle H increases in velocity and volume and diminishes in pressure. The area at any section is directly proportional to the specific volume of the steam and inversely proportional to its velocity. If the cross-sec- tional areas at a series of points in the nozzle be computed it will be found that the areas diminish at first until the pressure in the nozzle becomes about 58 per cent of the initial absolute pressure of the steam, and from that point onward the areas again begin to increase. The point of minimum section is known as the throat of the nozzle. The quantity of steam discharged by the nozzle obviously depends on the area of the throat or minimum section provided the steam is discharged into a region in which the pressure is less than 58 per cent of the initial steam pressure. In order to have a nozzle discharge steam with a minimum of tur- bulence and friction, it is advisable that the acceleration of the body of steam contained within it shall be constant. Such a constant accelera- tion requires of course that the amount of heat energy transformed into work between any two cross-sections shall be proportional to the dis- tance between these sections. A nozzle of the proper form may therefore be computed in the following manner: First, having given the initial pressure and quality of the steam, its entropy should be found. Second, choose a series of pressures whose saturation temperatures differ by an approximately constant amount. Third, from the known entropy of steam during its adiabatic expansion, compute the total heat and specific volume of the steam at these several pressures. Fourth, compute the heat drop (i.e., the quantity JH) for each of the several pressures. Fifth, compute the resulting velocity at each of the several pressures. Sixth, from the velocity and specific volume of the steam at each of the several pressures, determine the proper cross-sectional area of the nozzle. Seventh, compute the diameter of the section for each of these several areas. Eighth, make the distance of each section from the inlet end of the nozzle proportional to the heat drop. These computations may be made from Marks and Davis's Steam Tables or may be approximately determined from the total heat entropy diagram. It is usually more convenient, however, to make them by means of Peabody's temperature-entropy table. The method of per- forming the computations may be seen from the following example. Required to design a turbine nozzle to discharge 10,000 pounds of steam per hour, the initial pressure of the steam being 175 pounds absolute and the initial superheat 96. The nozzle discharges into a pressure 182 THE STEAM TURBINE AttT. 201 of 20 pounds absolute. Assume that the entering velocity of the steam at the mouth of the nozzle is 100 feet per second. From Peabody's temperature -entropy table, the nearest pressure is 175.3 pounds and the nearest superheat is 95. 7. The entropy is 1,62. The work can be most easily performed by tabulating it in the manner shown in Table X. TABLE X p H AH U Vel. Sp. V. A, A D L 175.3 1251.2 0.2 100 3.018 0.03018 12.07 3.93 0.0 169.0 1247.6 3.6 3.8 435 3.102 0.00714 2.856 1.91 0.126 162.8 1244.0 7.2 7.4 608 3.190 0.00525 2.100 1.64 0.259 156.8 1241.4 10.8 11.0 741 3.280 0.00442 1.768 1.501 0.378 152.9 1238.0 13.2 13.4 818 3.343 0.00409 1.636 1.443 0.469 134 . 5 1226.3 24.9 25.1 1120 3.605 0.00329 1.316 1.296 0.872 117.9 1214.7 36.5 36.7 1354 4.079 0.00301 1.204 1.340 1.278 101.6 1201.8 49.4 49.6 1574 4.566 0.00290 1.160 1.217 1.730 89.6 1191.2 60.0 60.2 1735 5.018 0.00290 1.160 1.217 2.10 77.6 1179.4 71.8 72.0 1896 5.610 0.00296 1.184 1.230 2.52 67.0 1167.7 83.5 83.7 2042 6.384 0.00312 1.248 1.251 2 92 57.5 1155.9 95.3 95.5 2183 7.290 0.00334 1.336 1.304 3.34 49.19 1143.9 107.3 107.5 2316 8.368 0.00362 1.448 1.360 3.76 41.84 1131.6 120.6 120.8 2458 9.639 0.00392 1.568 1.415 4.22 35.32 1119.4 131.8 132.0 2567 11.16 0.00435 1.740 1.490 4.61 29.82 1106.9 144.3 144.5 2687 12.99 0.00482 1.928 1.570 5.05 24.97 1094.3 156.9 157.1 2800 15.18 0.00543 2.172 1.665 5.49 20.02 1079.0 172.2 172.4 2935 18.46 0.00629 2.516 1.792 6.02 In the first column, headed P, will be found the successive pressures for which the dimensions of the nozzle are to be computed. In the column headed H will be found the total heat of the steam at the given pressure, and entropy 1.62, as obtained from the temperature-entropy table. In the column headed AH will be found the difference between the initial total heat and the total heat at the pressure given. In the column headed U will be found the heat drop plus the initial kinetic energy of the steam in B.T.U. In the column headed Vel. will be found the velocity of the steam. In the column headed Sp.V. will be found the specific volume of the steam as taken from the steam tables. In the column headed AI will be found the area of a nozzle in square feet, per pound of steam flowing per second. In the column headed A will be found the actual area of the nozzle in square inches to pass 10,000 pounds of steam per hour. In the column headed D will be found the diameter of the nozzle in inches, and in the column headed L, the length in inches from the inlet end of the nozzle to the section having the diameter given. The following formulae will be used in making the various computa- tions : ART. 202 FORM OF THE TURBINE NOZZLE 183 Vel. = 223.6V 7 'U, Sp.V. 1 VeL ' 10000 3600 ' L = K AH, in which K is a constant so chosen as to make the nozzle of reasonable length. The form of the nozzle so computed is illustrated in Fig 93. FIG. 93. Form of turbine nozzle giving constant steam acceleration. 202. Alternate Methods of Designing a Turbine Nozzle. It will be seen that the work of computing the exact form of a nozzle which will give constant acceleration to the steam becomes laborious when a tem- perature-entropy table is not available. Consequently, steam turbine nozzles are usually designed by finding the area of the throat and of the mouth of the nozzle and making the nozzle of the form shown in Fig. 94. The radius of the entering portion should be made equal to the diameter of the throat in case a circular nozzle is employed. The divergent portion of the nozzle is a frustrum of a cone, the elements of which make an angle of about 5 with the axis. Sometimes the throat is made straight for a distance equal to one-half its diameter as shown 184 THE STEAM TURBINE ART. 202 in Fig. 95. Either of these forms gives a nozzle of high efficiency, although it is not reasonable to suppose that the efficiency would be as high as in the case of a nozzle designed to give constant acceleration to the steam. The work of designing a nozzle like that in Fig. 94 may be seen from the FIG. 94. Turbine nozzle of the usual form. following example, in which quantities from Mark's and Davis' Steam Tables are used : Design a nozzle taking dry and saturated steam at 100 pounds and discharging 1 pound per second, against a pressure of 20 pounds absolute. FIG. 95. Another form of turbine nozzle, having a cylindrical throat. The entropy of steam of 100 pounds pressure is 1.6020. Since the expan- sion in the nozzle is adiabatic, the entropy of the steam coming from the nozzle will be the same. The entropy of the liquid at 20 pounds absolute is 0.3355. The difference, or 1.2665, is the entropy of vaporization of the wet steam coming from the nozzle. The quality of the steam coming ART. 202 ALTERNATE METHODS OF DESIGNING A TURBINE NOZZLE 185 from the nozzle may be found by dividing this quantity by the entropy of vaporization of dry steam of 20 pounds pressure and is 90.8 per cent. The total heat of steam of 100 pounds pressure is 1186.3 B.T.U. The total heat of the wet steam at 20 pounds pressure is found by the formula H 2 = h + qL and is 196.1 + 90.8X960.0=1068.1 B.T.U. The difference, or 118.2 B.T.U. is the quantity of heat transformed into kinetic energy in the nozzle, a quantity previously designated by the symbol AH. Substituting in the formula we will have 2435 feet per second for the velocity of the steam issuing from the nozzle. The specific volume of the steam may be found from its quality and will be 20.08X0.908= 18.23. Dividing this by the velocity of the steam, we will have for the area of the mouth of the nozzle required to discharge 1 pound of steam per second, 0.0075 square feet or 1.08 square inches. The pressure of the steam in the throat of this nozzle will be 58 pounds. We may by the process already employed, find the area of the throat of the nozzle when it is required to discharge 1 pound of steam per second. The entropy of the liquid at 58 pounds is 0.4242. The entropy of vaporization will be 1.1178. The quality of steam will be Il== 96.4 per cent. The total heat will be 259.8 + 916.5X96.4-1143.3. The heat drop will be 1183.3-1143.3 = 40 B.T.U. The velocity of the jet at the throat will be 223.6V J#= 1413 ft. per sec. The specific volume of the steam passing the throat of the nozzle will be 96.4X7.45 = 7.13. The area of the throat will be . 186 THE STEAM TURBINE ART. 203 203. Efficiency of Turbine Nozzles. The efficiency of a turbine nozzle is found by dividing the kinetic energy actually realized by the energy theoretically developed from the given pressure drop. On account of the friction of the steam against the walls of the nozzle, and also on account of the eddying produced when the nozzle is of improper form, the velocity of the issuing steam, the quantity of steam discharged and the efficiency of the nozzles are reduced. An improperly designed nozzle may give an efficiency as low as 90 per cent and a velocity and quantity of discharge of about 95 per cent of the theoretical value. A properly designed nozzle expanding steam between the pressure limits for which it was designed, ought to give an efficiency of more than 97 per cent, and such an efficiency has been realized by a nozzle of the form shown in Fig. 95. 204. The Design of Turbine Vanes. After the steam has been expanded in the nozzle, it is necessary to extract its kinetic energy by causing it FIG. 96. Properly and improperly formed vane surfaces. to strike upon a moving surface. Its energy is usually utilized by causing it to strike upon a series of vanes (also termed blades and buckets) fixed upon the rim of a revolving disk or drum (which is often termed a rotor). The form and motion of the surface upon which the jet strikes should be such that the steam will be taken up smoothly and brought to some lower velocity without shock or eddying. This result will be achieved if the surface of the vane is suitably curved, and the steam enters the vane in such a manner that the direction of its motion relative to the vane is tangent to the curved surface of the vane at the entering edge, as shown in Fig. 96 a. If, however, the vane is not properly curved, or if the jet strikes obliquely upon its surface, there will be more or less ART. 205 CLASSIFICATION OF UMPULSE TURBINES 187 eddying of the steam at the point of impact and some of the kinetic energy developed in the nozzle will be lost by being re transformed into heat. The effect of such oblique impact may be seen in Fig. 96 b. Since the vanes are moving as the steam enters them, the effect of this motion must be considered. Referring to Fig. 97, line a-b represents by its length and direction the absolute velocity and direction of motion of the entering jet of steam. Line c-d represents by its length and direction the velocity and direction of motion of the moving vanes. The velocity of the jet of steam relative to any point in the vanes will therefore be represented by the line FIG. 97. Velocity diagram. ae, which is the third side of the triangle whose second side, b-e, is parallel and equal to c-d. If the surface of the vane has the form shown by the curve /- l> ^ l>- t^COO^ 1 !> ^rt^CO COCOCOOO O-^^OT 1 T IT (O5O T IC^CIO O *W3fc 000 C Ill |S|| || | ^ IO CO CO CO CO CO CO CO CO O CO OO 00 O5 ^ 1 1 T-i r-t T-H T-^ * ino HVIiri J9d ureajg spunoj OOGOOO COOOO5O5 O5C5O5T 1 OO i IT 1 i 1 GO Jn H AV X J8d uiuajg spunoj T-^ C^l C^ C^l CO CO CO ^ CO ^ CO CO CO >O t^* CO a;n[0t>'qy 'ainssajj jprag '^'OO'O OO'OCOOO CD^OCOO Tfi iO Ol T i OO ooo do^o OO'T-HO o i-J ci ci d jeauaadng CD -^ 1C T-I O r O5 I-H o c i 1 T-I (M (M C^ IOOCM OOCOrJHO COOC1O O 5THTJH OCOi-Ht-~ .OO5 lOC-lO'O OOOT-HO O C^ O CO O O- PQ^PQ^ x IH* * cS BINES icitats Gasellschaft ' S-i ' ' ' ... : H : : : : GQ ! M j: | 1 TUR Parsons Erste Brunner. . , Allgemeine Electr Bersman. . > u = i N v g ' 6 % > : K-^ .S ' M ' co g 3 i3 2-C03 $ t3 2 r9 fJO 034) a! -tj503 Oi)-3 "^i ^ i^j : ^s^ js'i 22 S8^^ : ^S S 3 ? g^ "" o I- g S ge ndi rbine rate p Q 0) O ^ -2 s -g ^^ ^ 5 TJ O If I II =- ned e y a mbi fficien sumpt ratio On Thi rat 198 THE STEAM TURBINE ART. 210 PROBLEMS 1. Dry and saturated steam enters a turbine nozzle at a pressure of 100 Ibs. per square inch. The nozzle discharges into a pressure of 2 Ibs. per square inch. Find the theoretical velocity of the steam discharged. Ans. 3560 ft. per sec. 2. Dry and saturated steam at 150 Ibs. enters a turbine nozzle. Find the pressure and velocity of the steam in the throat of the nozzle. Ans. 87 Ibs. and 1470 ft. per sec. 3. Design a turbine nozzle taking dry and saturated steam at 20 Ibs. pressure and discharging it at 2 Ibs. pressure. The entering velocity of the steam is 100 ft. per second. Use Peabody's temperature-entropy table if available and design a nozzle having constant acceleration. 4. Design a nozzle for the conditions in the preceding problem, making it of the form shown in Fig. 94, using the methods outlined in Art. 202. 5. A four-stage turbine takes steam at 150 Ibs. pressure and 110 superheat. The back pressure is 1 Ib. absolute. Find the proper pressure in each of the four stages, assuming that the efficiency of the turbine is 75 per cent. Ans. 150 Ibs., 54.5 Ibs., 16.9 Ibs., and 4.5 Ibs. CHAPTER XIII CONDENSING MACHINERY 211. Classification of Condensers. There are in use with the steam engine two classes of condensers. In the first class of condensers the steam is brought into contact with a metallic surface, which is continu- ally cooled by the application of cold water to the opposite side of the metal, and the condensed steam and the air which is mingled with the vapor in the condenser are removed by some form of pump, termed the air-pump. In the second class of condensers the condensing water and the steam are brought into direct contact, and it is necessary for the air- pump to remove not only the condensed steam and the air which it has brought over, but also the water of condensation and its entrained air. Condensers of the first class are known as surface condensers. Con- densers of the second class are divided into jet condensers, barometric condensers, and ejector condensers. 212. Surface Condensers. In the surface condenser the cooling water is usually caused to flow through thin-walled metal tubes by means of a pump termed the circulating pump. These tubes may be made of any suitable kind of metal, such as copper, iron or brass, but tinned brass tubes are most usual. These tubes are placed within a metal shell, usually made of cast iron, into which the steam enters from the exhaust pipe of the engine. Every particle of steam coming in contact with one of these tubes is immediately condensed, and were no air present, the pressure of the steam would be that corresponding to the temperature of the outside of the condenser tubes, since as soon as each bit of steam is condensed by contact with a cold tube, it will leave about the tube a vacuum into which other steam will rush/ so causing the condensation to be continuous. Since, however, the steam contains some air, as was explained in Art. 167, these tubes are surrounded by a rarefied atmosphere, through which the steam makes its way with some difficulty, so that the temperature of the steam in the condenser is higher than that of the surface of the condenser tubes. One of the fundamental points of surface condenser design is to so arrange the condensing surfaces that the blast of steam which sweeps over them from the exhaust pipe will clear away the air surrounding them, and by the continual stirring up of the vaporous contents of the 199 200 CONDENSING MACHINERY ART. 213 condenser, bring every particle of steam as quickly as possible into contact with the condensing surfaces. Since the steam which is condensed is continually bringing into the condenser quantities of air, it follows that if this air is not removed, the pressure within the condenser will continually increase and the efficiency and power of the engine will be correspondingly reduced, until finally no advantage will be obtained from the condenser, since the pressure in the condenser will be as great as the pressure of the atmosphere. In order to avoid this difficulty, the air must be removed from the con- denser as fast as it is introduced. The pump which removes the air is called the air-pump. In case it removes air alone, and the water of condensation is removed by a separate pump, it is called a dry-vacuum pump. A condenser should be so arranged that as the steam flows through it, the air should be removed from that point of the condenser most distant from the entrance, since this will result in the removal of the max- imum quantity of air in a given quantity of vapor. It will be understood that the air-pump not only removes air, but also the vapor or steam present in the condenser, and it is therefore desirable to have the air- pump draw its charge from that portion of the condenser which con- tains the largest proportion of air in the vapor. 213. Arrangement of Cooling Surface and Air-Pump. The tubes of a condenser are usually about l / 2 to 1 inch in diameter, and the water flows through them from one end to the other. Condensers are com- monly made in the manner shown in Fig. 106, which is a diagrammatic cross-section of a condenser. The steam enters from the exhaust pipe at A and as it enters, it encounters the cool tubes, where it is condensed. The current of steam passes to the left along the tubes and then back on the other side of the plate B, where the steam and condensed water is drawn by the air pump through the outlet C. The water enters the chamber D from the circulating pump and flows to the left through the tubes until it reaches the chamber E, from which it returns through the upper rows of tubes into the chamber F separated by the partition G from the chamber D and leaves by the outlet shown. It will be noted that the current of cooling water is opposite in direction to the current of steam. The effect of this is to increase the efficiency of the con- denser, as will appear from the following. The steam which enters the condenser at A carries with it some air. This comes in part by leakage through joints in the exhaust pipes and passages, in part by leakage around the piston rod and valve stems of the low pressure cylinder, and in part from air dissolved or intrained in the feed water. Since the condenser is open from end to end, there is only a very slight difference in pressure between the inlet and the outlet. The amount of air present in each unit of volume is much ART. 214 THEORY OF THE SURFACE CONDENSER 201 greater, however, near the outlet than it is near the inlet, since the con- densation of the steam occurs at all points through the condenser and is particularly rapid near the inlet. Since the pressure of the air is greater near the outlet on account of the greater amount of air present, the pres- sure of the steam and therefore its temperature, must be less near the outlet. In order to extract the heat most effectually from such a mixture of steam and air it is necessary to bring the coldest vapor into contact with the coldest condensing water and the hottest condensing water into contact with the hottest vapor. Hence, the most efficient surface condenser will be that in which the steam is admitted to the condenser at the point where the condensing water is discharged and the conden- sing water introduced at the point where the air pump takes its suction. FIG. 106. Section of a surface condenser. 214. Theory of the Surface Condenser. The following theory of the surface condenser is based on the assumption, which is not quite fulfilled in practice, that the air pressure in a condenser is infinitesimal, and the steam in all parts of the condenser is at the same temperature. When water passes through a tube surrounded by steam of a given temperature, the steam condenses upon the outside of the tube (provided the water is colder than the steam) and the water receives heat by the process, consequently increasing in temperature. Assuming a tube having a diameter c in feet, a length L, in feet, and through which water is flowing with the velocity V, in feet per second, we will have the water warmed at a rate depending upon the rate of heat absorption. It is known that the amount of heat transferred from steam to water under these con- ditions depends upon the difference in temperature between the steam and water. Let this difference in temperature be T t a variable, let T 8 202 CONDENSING MACHINERY AKT 214 be the temperature of the steam and T w be the initial temperature of the water. Then the number of B.T.U. transferred from the steam to the water through each square foot of tube surface per second is equal to K T, where K is a constant to be determined experimentally. Let us assume that we have within the tube a small volume of water whose length is dL and whose area is that of the cross-section of the tube. The weight of this small quantity of water will be 4 0.7854 c 2 dLx 62.5 = 49. 1 c 2 rfL Ibs (1) If its temperature in a given short increment of time be increased by dT, and its specific heat is assumed to be unity, the amount of heat absorbed will be 49.1 dT dL c2 = the heat absorbed (2) The heat absorbed through the tube in the given increment of time, dt, will be equal to 3.1416 cXdL K T dt=the heat transferred. . . . (3) The heat transferred will, of course, equal the heat absorbed by the water, and we may so write them, or 3.1416 cdLKT d* = 49.1 dT dL c 2 (4) Clearing, we have dT K -^ = 0.064 dt (5) Integrating these expressions we have rr j log e T = 0.064 + C (6) In order to find C, we may put t equal to zero, in which case the difference in temperature between the steam and the water will be (T S ~T W }, since the water has received no addition of heat. From this we deduce that C = log e (T 8 -T w ), (7) and (8) ART. 215 RATE OF HEAT TRANSMISSION IN SURFACE CONDENSERS 203 It may be noted that since the difference in temperature T is contin- ually diminishing as the time, t, increases, the expression dT is essen- tially negative, which throws the equation into the form given when properly written. In order to find the temperature to which the water will be raised in a condenser or feed-water heater, we may write ^ for t, which gives the length of time required for the water to traverse the given length of the tube. Substituting this value for t we obtain the temperature differ- ence between the water and the steam after the water has traversed the condenser tube, and from this the rise in temperature and the quantity of heat absorbed by the water in traversing the tube. 215. Rate of Heat Transmission in Surface Condensers. Experi- ments by various engineers, according to Kent, give for the rate of trans- mission of heat through clean metal surfaces, from 0.09 to 0.18 B.T.U. per square foot per second. In the case of ordinary metal surfaces fouled by cylinder and saline deposits, the conductivity is about % that for clean metal surfaces. If we substitute the value given above for K we will find that the equation reduces to the form log c T = log e (T 8 -T W ) - 0.004 ~- ..... (1) V This equation, for the purposes of computation, may be reduced to the form log T --= log (7 7 S - T w ) - 0.02 -- (2) or to the form logT = log (7 7 S -7^)- 0.02 ~, (3) in which T is the difference in temperature between the water and steam at any instant, t is the length of time during which the water has been ; flowing through the condenser in seconds, d is the diameter of the con- denser tubes in inches, L is the length of the condenser tube in feet. V is the velocity in feet per second for the water flowing in the tubes, T 8 is the temperature of the steam and T w is the initial temperature of the water. The constant given above is that which is proper for brass condenser tubes under average condition. In the case of iron tubes the constant would be slightly less, and in the case of copper tubes slightly greater than 0.02. 204 CONDENSING MACHINERY ART. 21n If we plot from this equation the relation between the temperature of the water flowing in the condenser tubes and the length of time during which it has been flowing through the condenser, as is done in Fig. 107, we will find that the water starts at the temperature T w and rapidly increases in temperature at first. As t increases, however, this rate of temperature increase becomes less and less, and the temperature finally approaches, but never reaches, T s . Hence, no matter how much we may increase the area of the condensing surface, we cannot bring the temperature of the condensing water to the temperature of the steam. From this same figure it will also be seen that if the amount of water flowing through a condenser be diminished, the final temperature of 10(1 r 70 60 H lit 40 50 60 70 Time in Seconds. 90 100 FIG. 107. Relation between the temperature of the cooling water and the time it occupies in passing through the condenser. the water will be increased. However, since this increase in tempera- ture is not proportional to the decrease in the quantity of water flowing, the capacity of the condenser will be diminished. Fig. 108 shows the relation between the capacity of the condenser, in pounds of steam per square foot of cooling surface per hour, and the condensing water sup- plied per square foot of cooling surface per hour, at temperatures 60 and 30 below the steam temperature. An inspection of these curves shows that by increasing the quantity of water flowing, we can increase the quantity of steam which may be condensed without changing the size of the condenser, but doubling the quantity of .circulating water will not double the quantity of steam condensed, although it will very largely increase it. 216. The Jet Condenser. In the case of the jet condenser which is illustrated in Fig. 109, steam is introduced into a receiver (which is ART. 216 THE JET CONDENSER 205 usually pear shaped in form) at the top. Into this receiver there is sprayed, usually by the suction created by the air-pump, a supply of water. This water being introduced in the form of fine spray exposes a large surface upon which the steam in the condenser quickly condenses. The mingled water of condensation and condensed steam are then with- drawn, together with the air which has been brought in by the steam, ii 10 300 300 400 500 600 700 800 Lbs. oi.' Cooling Water per sq. ft. per Hr. 900 1000 FIG. 108. Relation between the water circulated and the capacity of the condenser. CURVE 1. For an initial temperature difference of 30 between the steam and cooling water. CURVE II. For an initial temperature difference of 60 between the steam and the cooling water. and that given up by the condensing water under the combined influence of heat and vacuum. In the case of the jet condenser, the air-pump must be very much larger than in the case of the surface condenser, in order to attain the same vacuum. No circulating pump is required ordinarily with a jet condenser, the air-pump performing that service. The amount of air to be drawn away in a given time, in the case of a jet condenser 206 CONDENSING MACHINERY ART. 217 is several times that which must be drawn away in the case of a surface condenser of the same capacity, since a considerable proportion of the air in the jet condenser is that which is brought in by the condensing water. Where a high vacuum is to be maintained other forms of conden- sing apparatus are usually preferable to the jet condenser. This is also true in those cases where it is desirable to use the condensed steam as boiler feed, as for instance in marine work, and stationary power plant work when steam turbines are used. In the latter case, since the steam turbines do not require internal lubrication as do steam engines, the exhaust steam carries n6 oil and the con- densate is suitable for boiler feed. In the case of the ordinary reciprocating engine, however, the cylinder oil in the exhaust steam is difficult to extract, and unless it is extracted, the water of condensation is not suitable for boiler feed. 217. The Ejector Condenser. The ejector condenser is a type of condensing apparatus which depends upon the velocity of the stream of condensing water to carry away the air in the condenser. Such an appa- ratus is illustrated in Fig. 110. The steam enters the condenser through the pipe A. The condensing water is forced into the condenser under considerable pressure through the pipe B, and flows into the body of the apparatus at high velocity in the form of a hollow cone, the steam condensing upon its surface. The. air associated with the steam is swallowed up in this stream of water and carried past the throat of the condenser in the form of innumerable bubbles. As the stream of con- densing water and condensed steam descends through the tail pipe F, these bubbles are carried through, since the velocity of the water in the tail pipe is higher than the velocity at which the bubbles ascend. The condensing water, the condensed steam and the entrained air are finally discharged into a well at the bottom of the tail pipe. Many arrange- ments are in use for exposing a greater area of the condensing water to the action of the steam and for regulating the quantity of water used when the condenser is not operated at its capacity. It is not necessary that the condenser should be set up at an elevation in the manner shown, since the placing of a pump, preferably a centrifugal pump, in the tail pipe, will permit this type of condenser to be used when head room is limited. FIG. 109. Section of denser. con- ART. 218 THE BAROMETRIC CONDENSER 207 218. The Barometric Condenser. The barometric condenser shown in Fig. Ill differs from the ejector condenser in that it does not depend upon the velocity of the condensing water to eject the air, and from the jet condenser in that the condensing water is not removed by the air- pump. The air is removed by a separate pump known as a dry vacuum pump, through the air pipe A. A tail pipe F, shown "in the drawing, is "Water FIG. 110. Diagram of an ejector condenser. FIG. 111. Section of a barometric condenser. of use only to carry away the condensing water. The water rises to such a height in the tail pipe that it will flow out of the condenser against the pressure of the atmosphere. 219. Importance of Good Vacuum. With the advent of the steam turbine, the matter of high vacuum and good condensing apparatus has very greatly increased in importance. While the power of a compound 208 CONDENSING MACHINERY ART. 220 engine of the ordinary type will be increased only about four and one- half per cent, by increasing the vacuum from 26 to 28 inches, the power of a steam turbine for a given steam consumption will be increased in most eases by about 12^ per cent. Increasing the vacuum from 28 inches to 29 inches will increase the power of steam turbine almost 10 per cent. Since the excellence of the vacuum obtained depends upon the efficiency of cooling and upon the efficiency of the air pump, it will be seen that the proper design of condensers and air pumps is a matter of very great economic importance in turbine installations. 220. Air in the Condenser. Water usually contains about 3 per cent of air, by volume, at ordinary temperatures, the volume of the air being estimated as free air (i.e., at atmospheric pressure and tempera- ture). It may also contain a larger proportion by volume of carbon dioxide or ammonia, although it very seldom does. These gases may be dissolved in water, or 4 they may be entrained (i.e., suspended in the water in the form of fine bubbles). All of these gases may be expelled by heating the water to boiling at atmospheric pressure in an open feed-water heater. Under the conditions ordinarily encountered in condenser practice, we may expect to have introduced into the sur- face condenser from the feed water about 1 cubic foot of free air for every 30 to 100 cubic feet of feed-water. The amount of air which enters the condenser on account of leakage when the exhaust piping and the rod packings are in good ordfer, will be from 50 per cent to 150 per cent of that normally entering with the feed-water. The air-pump must therefore be designed to handle 1 cubic foot of free air for every 10 to 50 cubic feet of feed-water when it serves a surface condenser, or 1 cubic foot of free air for every 30 to 150 cubic feet of condensing water when it serves a jet or barometric condenser. The pressure of the air in a surface condenser is usually about .30 to .50 pound per square inch absolute, when a first-class air-pump of usual proportions is employed. Since the pressure of the atmosphere is 14.7 pounds per square inch, it will be seen that the volume of the air in the condenser will be about 30 to 50 times its volume at atmos- pheric pressure. Consequently, if the usual percentage of air is asso- ciated with the feed- water, the volume of the air to be removed from a surface condenser will be roughly equal to the volume of the feed- water, and the air-pump must be proportioned accordingly. The pres- sure in the condenser will be equal to the pressure of the water vapor, which is determined by its temperature, plus the pressure of the air. It will be seen then, that if the pressure in the condenser is to be reduced, and a higher vacuum attained, we may do so either by reducing the temperature of the vapor by furnishing a larger quantity of cooling water, or else we may increase the capacity of the air-pump and so AKT. 221 THE AIR-PUMP 209 reduce the pressure of the air. The pressure of the air is approximately inversely proportional to the capacity of the air pump. In the case of a jet or barometric condenser, the volume of the air removed is about one-half the volume of the condensing water. Since, however, a condenser requires about 20 pounds of condensing water per pound of feed-water it will be seen that a jet or barometric condenser will need a much larger air-pump than will a surface condenser, to maintain the same vacuum. It is possible by careful workmanship and proper design of the piping system, to make the exhaust pipe leading from the engine or turbine to the condenser, air tight. In the case of a properly designed turbine it is also possible to eliminate entirely all air leakage, although there will be some air leakage in the case of the best steam engines, around the valve stems and piston rods. In the case of a steam turbine plant it is possible, since no lubricating oil is carried into the condenser by the steam, to pump the condensed steam back into the boiler and use it over and over again. The feed-water obtained in this manner will, of course, be free from air, so that it is practicable in & first-class steam turbine plant to maintain a very high vacuum with a comparatively small air-pump when a surface con- denser is used. When a jet condenser is used, the vacuum will not, of course, be as good as it would be with a surface condenser, unless the supply of condensing water is very limited. In case the supply of condensing water is limited, it will be found that a jet condenser will give a better vacuum, since in the case of the jet condenser, the condensing water is raised to the temperature of the vapor in the condenser, while in the case of a surface condenser there will necessarily be a differ- ence between the temperature of the vapor and that of the discharged condensing water. 221. The Air-pump. Air-pumps Fia i 12 ._S e ction of a wet air pump, are of two classes, wet and dry pumps. The wet air pump removes the condensed steam or condensing water and the air together. A section of such a pump is shown in Fig. 112. Since the valves of the pump are so arranged that they are always 210 CONDENSING MACHINERY ART. 221 covered with water and the clearance space of the pump cylinder is filled with water at the end of the stroke, it will be seen that there will be no air in the clearance space when the suction stroke begins. This is a matter of great importance in air-pump design. If the clearance space of the air-pump is filled or partially filled with air at the end of the stroke, this air, if it is to be expelled at all, must be at atmospheric pressure. Consequently, during the suction stroke of the pump, this air will expand and prevent the pump from taking suction from the condenser during the greater part of the stroke, which will very greatly reduce the capacity of the pump for a given size of cylinder. By designing the pump so as to avoid the presence of air in the clearance space at the end of the stroke, this difficulty is avoided. When a dry vacuum pump is used and the water is removed by a separate pump, it will be seen that it will be impossible to use this scheme in avoiding the presence of air in the clearance space. A dry vacuum pump may, how- ever, be constructed with very little clearance, much less than is practicable in the case of a wet air pump. It may also run at a high speed, which greatly in- creases the capacity of a given size of cylinder. Dif- ferent methods are adopted by different makers in order to avoid the reduction in capacity incident upon the clearance of the cylinder. One method is to use two cylinders, the larger one of which takes its suction from the condenser, and discharges into a receiver, while the second one takes its suction from this receiver and discharges into the air. It will be seen that the vacuum obtainable by this system of operation with pump cylinders of given clearance, is much greater than can be obtained by the use of a single cylinder of the same clearance, as may be seen from the following consideration. Assume a clearance of 5 per cent. Then with a single cylinder air-pump, the lowest pressure which can be reached will be about 1 /2o of an atmosphere when the quantity of air entering the condenser is negligible. This will be the lowest air pressure reached in the condenser in the case of a FIG. 113. Section of a dry vacuum pump. ART. 221 THE AIR-PUMP 211 FIG. 114. Card from the dry vacuum pump, shown in Fig. 113. single cylinder air-pump, or in the receiver in the case of the com- pound air-pump. The extra cylinder of the compound air-pump will reduce the pressure in the condenser to l / 2 o of the pressure in the receiver, or y 40 o of an atmosphere. If the quantity of air entering the condenser is appreciable, the air pressure will of course be greater in both cases than the amounts given. A second method sometimes used is to connect the clearance space of the two ends of a double-acting cylinder by means of a valve which is opened for an instant after the contents of one end of the cylinder have been discharged against atmospheric pres- sure. A device of this kind is shown in Fig. 113. The port P connects the two ends of the cylinder during the instant just following the discharge of the contents of one end, and previous to the beginning of the compression of the contents of the other end. By this means, the pressure of the air in the clearance space is caused to fall to that of the opposite end of the cylinder, so that the card given by the air-pump has the form shown in full lines in Fig. 114, instead of that shown in dotted lines in the same figure, which would be the form of card given by the pump if it did not have the auxiliary port. The capacity of the pump without this auxiliary port would be proportional to the distance a-d. By means of this auxiliary port, the capacity is increased until it is proportional to the distance a-c. The efficiency of the pump when measured by the ratio between the work actually supplied to it and the work theoretically required to remove the air is less with the auxiliary port than without it. However, the advantage of very greatly increasing the capacity of the pump, without increasing the size of the cylinder, makes this a desirable principle of con- struction. A third method of increasing the vacuum obtained by the use of a given air-pump is to force the air from the main condenser into a small auxiliary condenser by a blast of steam as shown in Fig. 115. In this figure A is the main condenser, R is a so-called augmentor condenser, and C is an aspirator operated by a steam blast. The purpose of the aspirator is to draw the air out of the main condenser, and to force it into the augmentor condenser in which its pressure will be materially greater than in the main condenser. The difficulty of removing the air from the augmentor condenser, will of course be very much less than of removing it from the main condenser in which the absolute pressure will be considerably lower. The steam used for the blast may be low 212 CONDENSING MACHINERY ART. 221 pressure steam, which has already been used in an engine or turbine and which has surrendered the most of its potential work. FIG. 115. Section of a surface condenser equipped with an augmenter condenser. PROBLEMS 1. Cooling water enters a surface condenser at a temperature of 56. The tem- perature of the steam in the condenser is 90. It takes four seconds for the water to pass through the condenser. The diameter of the condenser tubes is 1 in. What is the final temperature of the condensing water? Ans. 61.7 F. 2. A condenser having tubes 8 ft. long is arranged with four passes (i.e., so arranged that the water passes through the condenser four times, making its total travel 32 ft.). The tubes are f in. diameter and the velocity of the water is H ft. per second. The temperature of the steam is 110 and of the entering water 80. Find the temperature of the water discharged from the condenser. Ans. 101.92 F. 3. What quantity of cooling water enters each tube per second in problem 2? Ans. 0.288 Ibs. 4. What quantity of heat is imparted by the condensing steam to this quantity of water? Ans. 6.31 B.T.U. 5. The condenser in Problem 2 is required to condense 30,000 Ibs. of steam per hour, having a quality of 85 per cent. What quantity of heat must be absorbed by the cooling water? Ans. 26,250,000 B.T.U. per hr. 6. How many pounds of circulating water will be required to absorb this quantity of heat with the given rise in temperature? Ans. 333 Ibs. per sec. 7. How many tubes will be required in each pass in order that this quantity of water may be circulated under the conditions in Problem 2? Ans. 1155. 8. What total area of cooling surface will the above number of tubes furnish? Ans. 7250 sq.ft. 9. How many pounds of wet steam will be condensed per square foot of cooling sur- face per hour? Ans. 4.14 Ibs. 10. If the same number of tubes are arranged in a single pass, what will be the velocity and length of path of the circulating water? Ans. f ft. per sec. and 8 ft. ART. 221 PROBLEMS 213 11. What will be the final temperature of the circulating water? Ans. Same as in Problem 2. 12. Why is the water usually circulated through a condenser with a high velocity in spite of the fact that the theoretical final temperature of the water is the same when it is circulated at low velocity? 13. Water is supplied to a jet condenser having a temperature of 60. The tem- perature of the steam in the condenser is 110, and the quality of the steam 90 per cent. How many pounds of circulating water must be supplied per pound of wet steam condensed? Ans. 18.5 Ibs. 14. If the vacuum gage of the above condenser shows 24 inches, while the barometer shows 29 inches, what is the air pressure in the condenser? Ans. 1.19 Ibs. per sq.in. 15. What will be the reading of the vacuum gage of the above condenser, if the capacity of the air-pump is doubled? Ans. 25.2 in. Hg. V CHAPTER XIV COMBUSTION 222. The Nature of Combustion Combustion, in the sense in which it is used in engineering, is the act of chemical union of the oxygen of the air with the carbon and hydrogen of a fuel, with an accompanying evolution of heat and light. The fuels commonly used for the purpose of steam generation are coal, coke, wood, and oils. These consist of carbon and hydrogen, together with traces of sulphur and phosphorus and also of oxygen and inert elements and compounds. Coal and coke contain free carbon. Coal, wood, and oils also contain compounds of carbon and hydrogen and of carbon, hydrogen and oxygen. Carbon and its compounds are the sources of practically all of the heat developed by combustion in thermodynamic apparatus. 223. Heat of Combustion. When a pound of any substance is burned in oxygen, we find that a definite quantity of heat is evolved as a result of the reaction. This heat is first imparted to the products of combus- tion, and by them conveyed to the bodies in their neighborhood. The heat of combustion, as this quantity is termed, is expressed in B.T.U. per pound of combustible. The heat of combustion of various substances is given in Table XII on page 215. In the first column of this table will be found the names of the elements and chemical compounds, commonly found in fuels, and also of most of the common fuels. In the second column the physical state of the substances at atmospheric pressure and temperature is given. In the third column will be found the chemical symbol of the substance. In the fourth column will be found the atomic weight of the substance, in case it is an element. In the fifth column are given the molecular weights of elements and compounds. In the sixth column will be found the weight of the products of combustion in pure oxygen. In the seventh column are the chemical symbols of the products of combustion. In the eighth column is given the heat of combustion, assuming that the prod- ucts of combustion are reduced to atmospheric pressure and temperature, and the steam formed is condensed to water. In the ninth column the latent heat at 70 F. of the steam formed by the combustion of 1 pound of the substance is given. In column ten is given the number of pounds of oxygen theoretically required per pound of combustible. In column 214 ART. 223 HEAT OF COMBUSTION 215 ^ "5 OS O rH O CO CO T^ I s - CO O OS ^^ 1^- f*^ 00 00 CO COCOpwc which S ives ^ the and the rate of combustion. relation between the efficiency of the heating surface and the amount of heating surface for a constant rate of combustion. This same curve also, of course, shows the relation between the efficiency of the heating surface and the rate of combustion when the amount of heating surface remains constant. It will be seen that, as the heating surface is increased, or the rate of combustion reduced, the efficiency of the heating surface increases slowly, approaching, but 100 f 80 > r>0 10 ART. 248 EFFECT OF AIR LEAKAGE 245 never equaling the value E = The curve in Fig. 135 shows the "relation between the rate of driving and the efficiency of the heating surface. Inspection shows that the efficiency falls off more rapidly for a given percentage increase in the rate of driving, than for the same percentage increase in the rate of combustion. 100 90 80 a so "o >> 40 0) 10 2000 4000 6000 8000 B.T.U.per Hr. per Sq. Ft. of Heating Surface. FIG. 135. Relation between efficiency and rate of driving. 10,000 248. Effect of Air Leakage. The effect of an increase in the num- ber of pounds of air per pound of fuel upon the efficiency of a boiler is shown in the two curves in Fig. 136. The dotted curve shows the rela- tion when the rate of combustion is constant, while the full line shows the relation when the rate of driving is constant. It will be noted that an increase in the ratio of air to fuel has a more serious effect in reducing the efficiency of the boiler than any of the other elements affecting this efficiency, for the range of values commonly found in practice. 249. Effect of Increasing the Conductivity of the Shell. An increase in the conductivity of the boiler plates is equivalent to an extension of the boiler surface. This explains why the removal of scale from a 246 THE STEAM BOILER ART. 250 boiler does not very greatly increase the efficiency of a boiler, although it may considerably increase the conductivity of the heating surface. At the normal rates of driving even a considerable reduction in the resistance of the heating surface to the passage of heat, has very little effect upon the efficiency of the boiler, just as at the normal rate of driving a considerable increase in the heating surface will have but 100 10 15 20 25 30 Lbs. of Air per Lb. of Coal . 35 40 FIG. 136. Relation between the efficiency and the ratio of air to fuel. Curve I is for a constant rate of combustion. .Curve II is for a constant rate of driving. little effect upon the efficiency. An increase in the pressure of the steam, and therefore of the temperature of the water in the boiler, has but little effect upon the efficiency of the boiler, as may be seen by reference to Fig. 137, which shows the relation between the temperature of the steam and the efficiency of the boiler, for the conditions given. 250. Effect of Radiation on Boiler Efficiency. A boiler, like any other heated body, radiates a considerable amount of heat into the surrounding air. This amount may vary from 2 to 20 per cent of the quantity of heat generated in the furnace and depends upon the tem- perature of the boiler and furnace., and the thoroughness with which the ART. 250 EFFECT OF RADIATION ON BOILER EFFICIENCY 247 84 83 boiler is clothed in non-conducting materials and the area of radiating surface exposed. This loss by ra- diation is independent, or almost so, of the rate of driving. In considering the efficiency of the boiler, it is necessary to con- sider the loss due to radiation. The surface of the setting in- creases with the square of the dimensions of the boiler, while the heating surface of the boiler increases with the cube of its dimen- sions, hence the radiating surface increases in proportion to the two- thirds power of the heating surface. ^ 1 Q _ m, , ,. . FIG. 137. Relation between the efficiency The loss of heat due to radiation and the tem perature of evaporation, may be taken as being independent of the rate of driving and proportional to the radiating surface, or 1001 80 79 78 \ \ \ x \ k \ c rs Sag \ \ \ \ p = 200 Gag< \ 200 240 280 320 360 Temperature of the Steam. 400 90 80 70 &60 2000 4000 6000 8000 10,000 B.T.U.per Sq- Ft. of Heating Surface per Hour. 12,000 FIG. 138. Relation between the efficiency and the rate of driving, allowing for radiation. Curve I is for 5 per cent radiation loss. Curve II is for 10 per cent radiation loss. Curev III is for 15 per cent radiation loss. 248 THE STEAM BOILER ART. 251 to the two-thirds power of the heating surface. If we assume that this radiation loss in a boiler of normal design is 10 per cent of the heat generated when the boiler is operated at the normal rate of driving, we will have the relation between the efficiency and rate of driving shown in Fig. 138. Curves are added showing the relation of the efficiency and the rate of driving when the radiation loss is 5 per cent and also 15 per cent of the heat generated at normal load. It will be seen from these curves that there is a definite limit, depending upon the per cent of radiation loss, which determines the most efficient rate of driving and the proper allowance of heating surface per boiler horse-power. It will be seen that a boiler with an excess of heating surface may be prac- tically less efficient than a smaller boiler which is operated at a higher rate of driving, besides being more costly. The rate of driving commonly adopted at the present time is that rate which experience shows to give the best efficiency. 251. Heat Losses in a Boiler Plant. The heat losses incurred in the operation of a boiler plant arise from four sources. The first source of loss is caused by incomplete combustion. Such loss is due to the dropping of unburned coal through the grates, the escape of unburned gases to the stack, etc. The second source of loss is the inefficiency of the heating surface. Loss from this source is usually termed stack loss. The third source of loss is radiation. The fourth source of loss is the latent heat of the water formed by combustion. Loss from this source is usually exceedingly small. Improvement in the efficiency of the boiler plant must be looked for from the following sources: By improvement in the management of fires and the construction of furnaces we may increase the furnace temperature, reduce the quantity of air required per pound of fuel, and reduce the loss due to incomplete combustion. By careful arrangement and construction and properly clothing the boiler in non-conducting materials, we may reduce the radiation loss. Whenever the radiation loss is sufficiently reduced to warrant it, we may reduce the rate of driving by increasing the heating surface per boiler horse-power. Finally, we may so arrange the gas passages and heating surfaces that the gases are brought into thorough contact with the heating surfaces, thus increasing their conductivity. 252. Distribution of Losses as Shown by a Boiler Test. The following example will serve to show the distribution of losses in a boiler and the method of computing these losses from the results of a boiler test. The coal used in this test was shown by proximate analysis to contain 4.5 per cent of moisture, 16.0 per cent of volatile matter, 71.1 per cent of fixed carbon, and 8.3 per cent of ash. The heating value as obtained by the Parr calorimeter was 13,640 B.T.U. per pound. The analysis of the flue gas gave for CO 2 10.0 per cent, for O 2 9.8 per cent, for CO, 0.2 per cent; ART. 252 DISTRIBUTION OF LOSSES AS SHOWN BY A BOILER TEST 249 and for nitrogen, by difference, 80.0 per cent. The total weight of water fed to the boiler was 2832 pounds. The total weight of coal fired was 469 pounds. 59.0 pounds of ash were taken from the ash pit at the end of the test. The average temperature of the feed- water was 73.5 F. The average steam pressure was 82.2 pounds absolute, and the average quality of the steam as shown by the throttling calorimeter was 98.7 per cent. The total heat available from the combustion of 469 pounds of coal was 6,390,000 B.T.U. From the analysis of this coal 8.3 per cent or 39 pounds is incombustible. Since 59 pounds of ash fell through the grates during the test, 20 pounds of this must have been unburned carbon. The potential heat contained in this 20 pounds of unburned carbon is 290,000 B.T.U. The heat trans- ferred to each pound of water evaporated from 73.5 and at 82.2 pounds absolute will be, since the quality is 98.7 per cent, 898.8 X .987 +284-41.55 = 1120 B.T.U. The heat transferred to the entire quantity of water evaporated is 2832X1120 = 3,170,000 B.T.U. The remainder of the heat then passed up the chimney in potential form in unburned gases, or was carried away in the sensible and latent heat of the flue gas, or was radiated into the boiler room and so lost. From the flue gas analysis, we find that the number of c.c. of oxygen accounted for in 100 c.c. of flue gas will be 9.8 + 10 + ? = 19.9 c.c. The oxygen represented by the nitrogen is .261X80 = 20.87 c.c. The difference, or 1.0 c.c., united with hydrogen to form water. The number of pounds of carbon burned per pound of oxygen supplied was equal to The number of pounds of hydrogen burned per pound of oxygen supplied was 80 The excess of air was 383X9.* -s-81.6%. 80-3.83X9.8 The number of pounds of air supplied per pound of combustible was The number of pounds of nitrogen in the flue gas per pound of combustible was 250 THE STEAM BOILER ART. 252 The number of pounds of carbon dioxide in the flue gas per pound of combustible was 5.27X10.0 _ 80 X. 2074 ~ The number of pounds of carbon monoxide was 3.36X0.2 80 X. 2074 The number of pounds of water vapor was 4.20X1.0 80 X. 2074 The number of pounds of free oxygen was 3.83X9.8 80 X. 2074 =0.04. -.25. = 2.27. Adding the water equivalents of these various gases we will have 5.274. The latent heat of evaporation of the water vapor will be 262 B.T.U. Each pound of combustible shown by the flue gas consists of .2014 -^ -.-. =.971 Ibs. of carbon. .2074 and .0060 = .029 Ibs. of hydrogen. .2074 The heating value per pound of combustible will then be .971 X 14500 + .029 X 62000 = 15880 B.T.U. Of the coal burned in the furnace 20 pounds, or 4.26 per cent, dropped through the grates in the form of unburned carbon. The amount of heat lost in this manner was .0426X14500-620 B.T.U. per pound of coal, leaving 13640-620 = 13020 B.T.U. per pound of coal due to the burning of combustible substances appearing in the flue gas. Dividing this quantity by 15,880 we will have .820 pounds of combustible accounted for in the flue gas for 1 pound of coal fired. The total weight of combustible accounted for in the flue gas will therefore be .820X469 = 384.5 pounds. Since the boiler room temperature is 70, and the stack temperature 765, the flue gases will be rejected at a temperature 695 higher than their original tempera- ture. The sensible heat carried away in the flue gases may be found by multiplying this difference in temperature by the water equivalent of the flue gas per pound of combustible and the product by the number of pounds of combustible shown by the test to be present in the flue gases. This gives 695X5.274X384.5 = 1,410,000 B.T.U. The latent heat carried away by the water vapor in the flue gas will be 262X384.5 = 101,000 B.T.U. The number of B.T.U. lost as potential heat in the CO in the flue gas will be .04X384.5X4380 = 67,400 B.T.U. Adding together the heat lost in the flue gas, the heat imparted to the water and the heat lost by incomplete combustion, we will PROBS. 1-7 PROBLEMS 251 have 5,038,000 B.T.U. Subtracting this from 6,390,000 B.T.U. which was the total heat supplied, we will have the radiation loss, which was 1,352,000 B.T.U. Expressing these various heat losses as percentages of the total heat in the coal fired, we will have 4.54 per cent, for the loss through the grates, 49.6 per cent of the total heat imparted to the water, 22.05 per cent for the loss in the sensible heat of the flue gas, 1.58 per cent for the loss in the latent heat of the water vapor in the flue gas, 1.05 per cent for the loss in the unburned CO and 21.2 per cent for the radiation loss. The radiation loss in this case was unusually high, since the boiler was a vertical fire tube boiler and was not protected by any non-conducting covering, the plates of the boiler being exposed to the air of the fire room. The distribution of heat may be tabulated as follows. B.T.U. Per Cent. Heat supplied Heat utilized 6,390,000 3 170 000 100 49 6 Stack loss' Sensible heat 1,410 000 22.05 Stack loss; Latent heat 101,000 1.58 Incomplete combustion' coal through grates 290 000 4 54 Incomplete combustion ; loss in CO 67 400 1.05 Radiation and error 1 352 000 21 18 The efficiency of a grate is found by subtracting from 100 per cent the heat loss in per cent due to the unburned carbon which drops through the grate. In this case the efficiency of the grate was 1004.54 = 95.46 per cent. The efficiency of the boiler and grate is found by dividing the heat imparted to the water evaporated by the total heat in the coal fired. The efficiency of the boiler and grate in this case was 49.6 per cent. The efficiency of the boiler is found by dividing the efficiency of the boiler and grate by the efficiency of the grate. In this case the efficiency of the boiler was 51.9 per cent. PROBLEMS 1. A boiler evaporates steam at a temperature of 400 F. 20 Ibs. of air are used per pound of coal (i.e., 1 Ib. of coal produces 21 Ibs. of flue gas). The tempera- ture of the furnace is 2400 I 4 '. Assuming that the value of B in Eq. (6) in Art. 242 is 5.5 and that coal is burned at the rate of 1 Ib. for every 4 sq.ft. of heating sur- face, find the probable final temperature of the flue gas. Ans. 578 F. 2. What is the theoretical efficiency of the heating surface in the above problem? Ans. 78% 3. A boiler contains an aggregate of 1400 sq.ft. of heating surface. What is its nominal horse power? Ans. 117. 4. How many Ibs. of water will it evaporate per hour into steam of 98 per cent quality at a pressure of 100 Ibs. gage from feed-water at a temperature of 70, at rated load. Ans. 3,46C Ibs. 5. How many square feet of grate surface will be required for the above boiler, if 20 Ibs. of coal of 13,000 B.T.U. are burned per square foot of grate, and the boiler is assumed to be of 70 per cent efficiency. Ans. 21.5 sq. ft. 6. What will be the final temperature of the flue gases in Problem 1, if the rate of combustion be doubled? Ans 997 F. 7. What will be the theoretical efficiency of the heating surfaces in this case? ADS. 64.5%. CHAPTER XVI BOILER PLANT AUXILIARIES 253. The Chimney. Height Required. The chimney is a device for producing a draft or difference of air pressure, which is utilized to force air through the fire, and thence through the furnace, the boiler itself, and the breeching through which the furnace gases are discharged into the chimney. The chimney depends for its operation upon the difference in weight of the column of gas which it contains, and of a column of equal height and cross-section of the outside air. The weight of a column of flue gas or air of unit cross-section is proportional to the barometric pressure, to the absolute temperature of the gas or air, and to the height of the column. Let H be the height in feet of the top of the chimney measured from the grates, T a be the absolute tem- perature of the atmosphere, T c be the mean absolute temperature of the chimney gases, B be the normal barometric reading in inches of mercury for the region in which the chimney is erected, N. be the per cent of CO 2 in the flue gas, and D be the draft produced or required, measured in inches of water. The weight of one cubic foot of air will be, from the characteristic equation of gases the pressure in pounds per square foot will be P = 70.7215 ......... (2) The density of carbon dioxide is 1. 52 X that of air. Consequently, the density of the flue gas will be increased by .0052 for every per cent of carbon dioxide present. Therefore the weight of one cubic foot of flue gas will be lb,, . (3) and the weight of a column one foot square and H feet high will be (l * C 252 ART. 254 DRAFT REQUIRED BY A BOILER PLANT AT NOMINAL LOAD 253 The weight of a column of external air, one square foot in cross-section, and H feet high, will be 1.329 B H .. yi Ibs (5) The difference in pressure produced at the base of the chimney in pounds per square foot is therefore Since a column of water one inch high produces a pressure of 5.19 pounds per square foot, the draft produced by the chimney will be (7) Solving the above equation for H, in order to find the height of chim- ney required to produced a given draft we will have In the absence of more definite data we may assume that in most actual cases of chimneys serving boiler plants without economizers, under normal atmospheric conditions we will have for the draft produced. D=.Q07H, (9) and for the required height of chimney, H=14QD (XO) 254. Draft Required by a Boiler Plant at Nominal Load. When air or gas flows through a restricted passage, a difference of pressure is required to give it motion, both to give the air velocity, and in order to overcome friction. It follows, therefore, that in its passage through the fire, the boiler, the damper, the breeching and the chimney, the flue gas encounters at every point a resistance to its motion. The resist- ance is measured by the difference in pressure required to move the gas through the passage considered, and is shown by experiment to be nearly proportional to the 1.8 power of the quantity of the gas passing in a given time. When a boiler and furnace of ordinary design are operated at their rated capacity, we find that the difference in pressure required to draw air through the fire is from .10 to .30 inches of water. The former figure is for free-burning bituminous coal consumed at the rate of 24 pounds of coal per square foot of grate, and the latter figure is for anthracite buckwheat consumed at half this rate. These are the 254 BOILER PLANT AUXILIARIES ART. 255 usual rates of combustion in furnaces properly designed for burning these fuels when operated at their rated capacity. The resistance of the furnace and boiler passages to the current of gases, ranges from .15 to .30 inches of water, approaching the lower value in the case of small boilers and of water tube boilers, and the higher one in the case of large boilers and of fire tube boilers. Unless the breeching is excep- tionally long and tortuous, its resistance will range from .05 to .20 inches of water. The resistance offered by the chimney itself, when properly designed and operating at rated load, ranges from 10 per cent to 20 per cent of the total draft produced, and includes the difference in pressure required to produce the actual velocity of the gases in the chimney. The total draft required of a chimney operating a boiler plant at rated load ranges from .40 to 1.00 inches of water, according to the character of the plant and the kind of fuel, and in most practical cases the draft required will be between .55 and .75 inches of water. 255. Draft Required by a Boiler Plant when Operating at an Over- load. If, however, it is desirable or necessary to operate the plant, or any part of it, at more than rated load, the chimney must be of sufficient height to provide a greater draft than is called for in normal service. After the draft required to operate the plant at rated load has been ascertained, we may compute the maximum draft required by the formula /Maximum Load \ 1>8 r rotated Load / in which D is the draft required for the maximum overload, and D r is the draft required at rated load. From the above it will be seen that at 25 per cent overload the draft required will be 1.50/) r , at 50 per cent overload it will be 2.0SD r , and at 100 per cent overload it will be 3.50Z) r . In practice it has been found that the minimum height of chimney which will give satisfaction with plants of normal design, ranges from 80 feet in the case of free-burning bituminous coal to 200 feet in the case of anthracite slack; heights which give under ordinary atmospheric conditions a draft of from .55 to 1.4 inches of water and permit overloads of about 10 per cent. It is usual in the case of plants burning anthracite coal of small size to assist the chimney by a steam jet or fan blower. The jet or blower furnishes the excess of pressure necessary to force the air through the fire, while the chimney serves only to draw the gases through the boiler passages and breeching and prevent their escape into the fireroom. Were it not for this, the height of chimney required to produce a reasonable overload capacity in such plants would be excessive. Chimneys above 200 feet in height are not therefore usually required in practice, nor are they economical to build. ART. 256 REQUIRED DIAMETER OF CHIMNEYS 255 They are sometimes necessary, however, in order to discharge smoke or noxious gases at such a height that their discharge will be harmless. It may be remarked that when a boiler plant operates at an over- load, the temperature of the chimney gases is increased, which makes the overload capacity of a chimney rather more than theory would indicate. If the top of a chimney is properly formed, wind increases the draft, and if there is no wind, the column of hot air rising above the chimney acts to increase its effective height. Chimneys, especially hort chimneys of large cross-section, may therefore be expected to give a somewhat greater draft than theory would indicate. 256. Required Diameter of Chimneys. From experiment it is known that the loss of pressure which a fluid suffers in passing from one point to another in a tube of uniform diameter is directly proportional to the distance between the points and to the 1.8 power of the velocity of the fluid, and inversely proportional to the 1.3 power of the diameter of the tube. This loss also depends upon the density and viscosity of the fluid and the character of the inner surface of the tube, but the proportionality factor for any given tube and for any given fluid of a constant density is a constant quantity. Applying this law to the case of a chimney we will find that the draft required to produce a given velocity of the chimney gases, will be 1-8 .... . . - (1) in which D c is the draft, in inches of water, required to produce the given velocity; H is the height of the chimney in feet, V is the velocity of the chimney gases in feet per second, and d is the diameter of chimney in inches. Solving equation (1) for V we will have v If we make the allowable loss of draft in the chimney some fraction of the total draft which the chimney will produce, then since the total draft is proportional to the height of the .chimney, we may replace ~ by a constant, and obtain the equation K 2 d- 72 ....... (3) Since the capacity of the chimney is proportional to the product of the velocity of the flue gases and the area of the cross-section (which is proportional to d 2 ) we may write 2 ). (4) 256 BOILER PLANT AUXILIARIES ART. 257 In which HP is the nominal capacity of the chimney, in terms of the boiler horse-power which it will serve. Solving equation (4) for the diameter of the chimney, we will have d = K (HP)' 37 (5) A study of chimneys of good proportion giving satisfactory service shows that the value of the constant K should be about 5.5, in which case the resistance of the chimney to the passage of the gases, at rated load, is about 15 per cent of the total draft produced, in the case of plants of rather poor economy. Therefore in order to find the total draft required in the case of a chimney designed by this formula, we must multiply the draft found by equation (1) in Art. 255 by 1.17. In order to facilitate computation equation (5) may be written in the form log d=. 37 log HP + .75. . (6) in which d is the diameter of the chimney in inches, and HP is the nominal horse-power of the boiler plant which it is to serve. 257. Effect of Overloading the Boiler Plant upon the Capacity of the Chimney. In case a chimney designed by the above rule is called upon to handle a greater quantity of flue gas than that for which it was designed, more than 15 per cent of the total draft must be utilized in overcoming the resistance of the chimney itself. Since the resistance of the chimney is proportional to the 1.8 power of the velocity of the gases, the amount of draft required to overcome the resistance of the chimney will be D. -i c M /actual load\ l>8 J-'c -15 Lf [ - , _. ! -j- I , \ rated load / in which D c is the draft required to overcome the resistance of the chimney and D is the total draft produced by the chimney. It has already been noted that chimneys are usually made of sufficient height to provide a s.mall overload capacity, usually from 10 to 25 per cent. If it is desired to increase the power of a boiler plant and yet to use the old chimney in carrying away the gases, this excess of height affords an opportunity for increasing the capacity of the plant by reducing slightly the overload capacity of the individual units. If D equals the total draft available, in inches of water, and Df be the amount of draft required to overcome the resistance of the fire, the boiler and the breeching when the individual boilers are operated at the desired rating, the difference is available for overcoming the resistance of the chimney. If this difference is greater than 15 per cent of the total draft produced, the capacity of the chimney will exceed that given by Equation (4), Art. 2c6., and the ratio of the capacities will equal the 1.8 root of the ratio of the draft actually available for overcoming the chimney resistance to that assumed in equation (6) to be available. Writing this as an equation we will have in which HP a is the nominal rating of the boilers which the chimney will serve under the assumed conditions of overload, HP r is the rating of the chimney from formula ART. 258 EXAMPLE OF CHIMNEY DESIGN 257 4 Art. 256, D is. the total draft the chimney will produce, and Df is the resistance of the furnace, boiler and breeching, when operated under the assumed conditions of overload. 258. Example of Chimney Design. The following example will serve to make clear the application of the principles developed above. A chimney is required to burn buckwheat anthracite in a region where the normal barometer reading is 28 inches, and the normal summer temperature 70. The plant will be required to develop about 25 per cent overload and is of 1000 horse-power nominal capacity. Assume the temperature of the gases to be 500 F., and the per cent of CO 2 to be 10 per cent. The draft required by the fire at normal load = .30". The draft required to overcome the boiler resistance at normal load = .25". The draft required to overcome the resistance of the breeching at normal load = .10. The sum of the above = . 65". Draft required to overcome resistance of chimney = . 65" X. 175 = .12". Total draft required at rated load = .77". Total draft required at 25 per cent overload = .77"X 1.25 1 ' 8 = 1.15". Substituting the proper values in formula 8, Art. 253, for the height of chimney, we will have # = 3.905 -^L, .v - 194 ft. 960 In order to find the diameter of this chimney, we use equation (5), Art. 256, which gives d = 5.5X1000' 37 =72 inches. Should it be desirable to extend this plant at any future time, its power may be greatly increased, provided the individual units are not required to carry 25 per cent overload. If they are required to carry rated load merely, the nominal power of the station will be, according to the formula in Art. 257, . .l/o X .60 = 2280 horse- power. 259. The Injector. An injector is an apparatus for forcing water against pressure by utilizing the impact of a jet of steam. The apparatus is shown in principle in Fig. 139, in which A is a pipe supplying steam to the nozzle B, in which the steam, expanding adiabatically, acquires a high velocity. The jet of steam from this nozzle passes through the tube C, which is known as a combining tube, anpl in doing so carries with it any air in the neighborhood. As a result a vacuum is created which sucks the water through the suction pipe. D into the chamber surrounding the jet. As soon as the steam comes in contact with the water so drawn in, it is instantly condensed and imparts its momentum to the water, forcing it into the combining tube. The water issuing from the combining tube in the form of a jet passes into a third tube E, which is known as the discharge tube, in which its velocity is trans- 258 BOILER PLANT AUXILIARIES ART. 260 formed into pressure. After passing through the discharge tube, the water flows through a check valve and into the boiler or other region into which it is desired to force it. Before the current of water is established the water escapes around the space between the combining and the discharge tubes and flows away through an opening F, termed the overflow. As soon, however, as a solid stream of water of suffi- ciently high velocity is flowing through the combining tube, no water will escape through the overflow. FIG. 139. Diagram of an injector. 260. Efficiency of the Injector. In order to illustrate the principle of the injector, we will assume one taking dry and saturated steam at a pressure of 100 pounds absolute and delivering the water against the same pressure. Assume that the absolute pressure within the suction chamber is 10 pounds per square inch. The kinetic energy of the jet, per pound of steam flowing, is 127,000 foot-pounds, its velocity is 2840 feet per second, and its momentum 2840 pounds feet per second. The head against which the water is discharged is (100 10) X 2.31 =208 feet. Allow- ing 25 per cent excess for friction we will have, say, 250 feet. The velocity of the jet issuing from the combining tube must be F = v'20/i=v'64.4X250 = 128 ft. per sec. The momentum of the jet, which is composed of x pounds of water and 1 pound of steam, must from the principles of mechanics, be equal to that of the steam jet. Hence (1+^)128 = 2840, and a: = 21. 2 pounds of water pumped per pound of steam supplied. The work done per pound of steam is 21.2X250 = 5300 ft.-lbs. The efficiency of the injector as a pump, is therefore only 5300 127400 =4-15 per cent, of the efficiency of a Rankine cycle engine working through the same pressure range. It will be seen from the above example that as a pump the injector is very inefficient, although all of the heat of the steam is returned to the boiler. Of the kinetic energy of the steam jet, only from 3 to 6 per cent is available to force the water into the boiler, the remainder being transformed into heat as a result of the inelastic impact of the steam upon the water. ART. 261 BOILER FEED-PUMPS 259 The injector is often a troublesome instrument to operate, since the condition of the apparatus must be perfect before it will give satisfactory service. The stoppage of any of its small passages by a piece of coal or by the accumulation of scale FIG. 140. Boiler feed pump. renders it inoperative. It is commonly used in the case of locomotive and port- able boilers, but is not usually used in stationary service. Many modifications of the injector are in use and are known by different names. In some modifications, one injector is arranged so as to deliver water to the suction chamber of a second injector, such an injector being known as an inspirator or a double tube injector. 261. Boiler Feed-pumps. Boilers are usually supplied with feed- water by means of a direct-acting steam pump, such as is illustrated in Fig. 140. These pumps are of various types, but almost all of them use steam non -expansively and are very wasteful. The exhaust from these pumps, however, is usually employed to heat the feed-water, and on FIG. 141. this account no loss is experienced from their use, since they return to the boiler all of the heat which is taken for their operation. Of late years, in places where economizers are installed, motor-driven centrif- ugal pumps have been used for boiler feeding. Such a pump is illustrated in Fig. 141. These pumps are, of course, practically as economical as 260 BOILER PLANT AUXILIARIES ART. 2G2 are the main engines themselves. They run at nearly constant speed, maintaining a constant pressure in the delivery pipe and the quantity of water delivered and power required automatically adjust themselves to the needs of the boiler for feed-water. 262. Feed-water Heaters. In order to avoid losses incident upon supplying a boiler with cold feed-water, the heat of the exhaust steam of the engines and pumps is usually utilized for heating the feed-water. A gain of from 10 to 12 per cent may be realized under usual conditions by using a feed -water heater. Feed-water heaters are of two kinds, known as closed and open heaters. In the closed heaters, the water to be heated is usually forced through tubes which are surrounded by the exhaust steam, which does the heating. Such a heater is shown in section in Fig. 142. Sometimes the water surrounds the tubes and the exhaust steam passes through them. In open heaters, the feed-water is brought into direct contact with the exhaust steam. Usually the water- coming from an open heater is a few degrees hotter than that coming from a closed heater. The theory of heat transfer in the closed heater is the same as in the case of the surface con- denser, and they may be designed by the same principles. The following problem will serve to illustrate the economy obtained by the use of a heater. Assume that a boiler operates at a pressure 165 pounds absolute, that the feed -water sup- plied has a temperature of 70 and that by the use of a suitable heater the feed temperature may be raised to 205. The total heat which must be imparted to the feed -water in evaporating it from 70 at 165 pounds is found by subtracting the heat of the liquid at 70 from the total heat of the steam at 165 pounds. In the same way, the heat required when the heater is used will be found by subtracting the heat of the liquid at 205 from the total heat of the steam. We find in one case 1156.9 B.T.U. are required, while in the other case only 1022.0 B.T.U. are required, showing that if the heater is adopted, the quantity of fuel required by the boiler in a given time will be reduced more than 11.7 per cent, since not only is less heat needed to evaporate the required quantity of water, but the rate of driving of the boiler is decreased, and therefore the efficiency of the boiler plant is improved. FIG. 142. Section of a closed heater. ART. 263 THE ECONOMIZER 261 263. The Economizer. The economizer is an apparatus which utilizes the waste heat of the flue gases to heat the water entering the boiler. It is possible by the use of a suitable economizer to reduce the temperature of the chimney gases to within 200 of the temperature of the feed-water and to heat the water entering the boiler practically to the temperature of vaporization. It will be seen that the use of the economizer will very greatly reduce the fuel required for a given quantity of steam generated. Economizers are usually built with cast-iron tubes and headers, and are provided with sliding rings which scrape the soot from the tubes. When an economizer is used, it is usually necessary to use a fan to create the necessary draft, since the temperature of the gases entering the chimney is not sufficiently high to cause a good draft. The theory of the heat transfer in the economizer is different from that of the boiler, .since the water entering the economizer is at a low temperature and it gradually increases as it passes through the economizer. The current of hot gases flows through the economizer in the opposite direction to the current of the water, so that the hottest gases come into contact with the water entering the boiler and the coolest gases into contact with the water entering the economizer. By this means the temperature of the gases leaving the economizer may be reduced below the temperature of the water entering the boiler. The difference in temperature between the flue gases and the water varies at different points in the economizer, usually being greater at the end next the boiler than at the cool end of the economizer. The water equivalent of the flue gas discharged per second by the boiler is usually less than the weight of the feed-water supplied to the boiler in the same time. It will be seen therefore that the fall in temperature of the flue gases between any two points in the economizer will be greater than the rise in temperature of the feed-water and the less the excess of air used for combustion the more pronounced will be this effect. It is usual to supply from 3^ to 5 square feet of economizer surface per boiler horse-power. When an economizer is so proportioned, the feed-water entering the boilers is usually heated to about 300 F. The .Greene Economizer Company give the following empirical formula for the rise in temperature of the feed-water in passing through an economizer : in which x = the rise in temperature of the feed-water; 7 7 1 = the temperature of flue gas entering the economizer; ti = temperature of feed-water entering economizer; 262 BOILER PLANT AUXILIARIES ART. 264 w = pounds of feed-water per boiler horse-power per hour; G = pounds of flue gas per pound of combustible; C = pounds of coal burned per boiler horse-power per hour; y = square feet of economizer heating surface per boiler horse- power. 264. The Superheater. The use of superheated steam in connection with the steam turbine is becoming very common on account of the great gain in efficiency resulting therefrom. Superheaters may form a part of the boiler and be heated by the gases on their way through the boiler. Many superheaters, however, are independently fired, having their own furnace and gas passages. The use of a superheater in con- nection with a boiler plant does not directly affect the efncienc}^ of the boiler plant. It does, however, permit the use of a small boiler plant, since less steam will be required from a boiler plant equipped with superheaters, on account of the greater efficiency of the engines. In case the size of the boiler plant is not reduced, the effect of the introduction of superheaters will be to reduce the rate of driving and so increase the efficiency of the boilers. Superheaters are usually formed of heavy seamless steel tubing, expanded into forged steel headers and sometimes protected by cast- iron rings from the direct action of the hot gases. A superheater requires greater care in its operation than is usually required with a boiler, since the superheaterelements are not filled with water, and therefore are easily overheated. The conductivity of a unit area of superheater surface is considerably less than that of the same area of boiler-heating surface, since the heat is transferred from the metal to a gas or superheated vapor in the case of a superheater, while it is transferred from the metal to a liquid in the case of a boiler. The amount of superheater surface required per boiler horse-power varies according to the required temperature of the steam, and the temperature of the gases in contact with the superheater surface. The following empirical formula has been proposed by J. E. Bell : 105 2(T-t)-S' in which x = the number of square feet of superheater surface per boiler horse-power; /S = the superheat in degrees F; T = the temperature of the flue gases at the point where the superheater is located ; i = the temperature of the saturated steam. PROBS. 1-7 PROBLEMS 263 PROBLEMS 1. What height of chimney will be required to give a draft of 1.2 inches of water under ordinary operating conditions ? Ans. 168 ft. 2. A boiler plant having a stack 100 ft. high will operate satisfactorily when evaporating 10,000 Ibs. of water per hour. To what height must the stack be raised in order that the plant shall evaporate 12,000 Ibs. of water per hour ? Ans. 139 ft. 3. What diameter of chimney will be required for a boiler plant of 2000 horse- power ? Ans. 91 inches. 4. A non-condensing engine f is used in connection with a feed-water heater. Without the heater, the temperature of the feed is 65. With the heater, the tem- perature of the feed is 190. What per cent of coal is saved when the heater is employed? The boiler generates steam at a pressure of 80 Ibs. gage and of 98% quality. Ans. 10.8%. 5. The feed-water heaters of a plant bring the temperature of the feed to 160. When an economizer is employed the temperature of the feed is brought to 280. What per cent of coal is saved by the economizer if the boilers produce dry and saturated steam at a pressure of 165 Ibs. absolute? Ans. 11.2%. 6. An economizer is required to raise the temperature of the feed-water 100. The temperature of the feed is 150, the temperature of the flue gas entering the economizer is 600, the boilers require 30 Ibs. of feed-water per horse-power per hour, 4 Ibs. of coal are burned per horse-power per hour, and 20 Ibs. of flue gas are produced per Ib. of coal. Find the number of square feet of economizer surface required per boiler horse-power. Ans. 2.98 sq.ft. 7. A superheater is required to superheat steam of a pressure of 180 Ibs. absolute, 100. The temperature of the gases is 1300. Find the number of square feet of super- heater surface required per boiler horse-power. Ans. 0.57 sq.ft. CHAPTER XVII WATER-COOLING APPARATUS 265. Advantage of Using Water-cooling Apparatus. Condensing water is usually taken from lakes or streams, or, at the seaboard, from the sea. When a power plant is erected at some point distant from a stream or other body of water, the plant may be made non-condensing, or it may be provided with some method for cooling the condensing water. A condensing plant not provided with any method for cooling water usually requires from 300 to 500 pounds of condensing water per horse-power per hour, and a non-condensing plant usually requires from 25 to 35 pounds of water per horse-power per hour, while a conden- sing plant equipped with a cooling apparatus will require only from 12 to 18 pounds of water per horse-power per hour. Hence, in all those cases where the plant is large and cooling water is expensive, either because only small quantities of water are available, or city water must be purchased, water-cooling apparatus is a necessary adjunct to the plant. The use of the cooling tower or other water-cooling device not only permits of economy in the consumption of water, but also of fuel, since a condensing plant will use only from one-half to two-thirds of the quantity of fuel required by a non-condensing plant of the same power. 266. The Cooling Pond. The simplest method of cooling condensing water is to construct an artificial pond having an impervious bottom from which the cooling water is drawn, and into which it is discharged aiter passing through the condenser. The evaporation from the surface of the pond and radiation of heat from the water into the surrounding air will keep the temperature of the water down in spite of the fact that heat is being continually added to it. The water must of course be replaced as fast as it evaporates. The pond must be of sufficient area so that the evaporation may go on at a rate which will dispose of the heat imparted to it without allowing the temperature of the cooling tower to become too great. The area required will depend upon the mean summer tem- perature, upon the dryness of the air, upon the character and amount of the load of the station, upon the depth of the water, and upon the amount of wind which may ordinarily be expected in the region. The rate of evaporation and consequently the rate at which the water is cooled is. of course, proportional to the area of water surface exposed, so that, 264 ART. 267 RATE OF EVAPORATION FROM THE SURFACE OF WATER 265 other things being equal, the area of the pond must be proportional to the power of the station. The higher the summer temperature of the region, the warmer the water in the pond must be for a given rate of evaporation per square foot of surface. During cold winter weather, although evaporation proceeds at a slower rate than in summer, the pond will lose heat more rapidly on account of radiation into the surrounding cold air. The humidity of the atmosphere and the amount of wind to be expected is also a very important factor in settling the size of the pond. If the air is dry, the water will evaporate rapidly from the surface of the pond, while if the climate is humid, the evaporation will proceed slowly. If the load upon the station is constant, the depth of water in the pond makes no particular difference. If, however, the load is variable, a much smaller pond may be made to serve if the water is deep, since this large mass of water will serve as a heat reservoir; absorbing the heat during the periods of peak load, with a small rise in temperature, and slowly recovering its normal temperature during the periods of light load. 267. Rate of Evaporation from the Surface of Water. The rate of evaporation per square foot of water surface exposed to air is, in theory, proportional to the difference between the quotient of the square root of the absolute temperature of the water into the density of saturated steam at that temperature, and the quotient of the square root of the absolute temperature of the air into the density of the water vapor present in the air. 1 We may, therefore, in engineering computations, take the rate of evaporation per square foot of surface as being proportional to the difference between the saturation pressure of water vapor at the temperature of the water and the actual pressure of the water vapor in the air. It has been found that in still air 2 the difference in pressure required to evaporate 1 pound of water per square foot of water surface per hour is about 3.2 pounds per square inch. In cllse a brisk wind is blowing over the surface, the rate of evaporation will be from four to six times as great as is given by the above rule. The following problem will serve to illustrate. the principle: Assume that the temperature of the water is 80, that the temperature of the air is 70, and that the humidity is 60 per cent. The saturation pressure at 80 is 0.505 pounds per square inch. The pressure of the water vapor in the atmosphere is 0.36X0.60 = 0,22 pounds per square inch. The difference in pressure is 0.285 pounds per square inch. Since the difference in pressure required to evaporate 1 pound of water per 1 See Chapter XXVI. 2 By still air is meant air in which the only currents are those produced by the difference in density of hot moist air and cool dry air. It does not mean air in which all currents are prevented by artificial enclosure. 266 WATER-COOLING APPARATUS ART. 268 square foot per hour is about 3.2 pounds per square inch, a difference of pressure of 1 pound will evaporate 0.30 pounds of water per square foot per hour in still air. The rate of evaporation from the surface will be in this case 0.285X0.30 = 0.085 pounds per square foot per hour in the case of still air. 268. Determining the Area of a Cooling Pond. It will be seen from the above that the area of a cooling pond required for a given station may be determined in the following manner. From the records of the Weather Bureau, the mean summer temperature and humidity for the region may be found: From these data, the mean pressure of the water vapor in the atmosphere may be determined from a steam table. Assum- ing the temperature to which the condensing water is to be cooled, find in the steam table the saturation pressure corresponding to this temperature and from it deduct the mean summer pressure of the water vapor in the air. Multiplying the difference- so obtained by 0.30 we will have the quantity of water evaporated per hour per square foot of surface from the cooling pond. Dividing this quantity into the average quantity of steam rejected per hour by the engines of the station, we will have the required area of the cooling pond in square feet. Good condensing plants will on the average require an evaporation of 15 pounds of water per horse- power per hour from the cooling pond. The total quantity of water which the pond must evaporate in twenty- four hours may be found by multiplying the twenty-four-hour factor of the station by its rated horse-power and their product by 15. In case it is known that the station is likely to be inefficient, it will be neces- sary to allow more than 15 pounds of water per hour. The following problem will serve to illustrate the method of finding the area of a cooling pond. The mean summer temperature as obtained from the Weather Bureau reports is 75, and the humidity 60 per cent. It is desired to coot the water in the pond to 80. The station is to be of 1000 rated horse-power, and the twenty-four-hour load factor is 40 per cent. From the steam tables the pressure of saturated water vapor at 80 is 0.505, and at 75 temperature and 60 per cent humidity it is 0.429X0.60 =0.26 pounds per square inch. For the difference we will have 0.505 -O.26 =0.245. The rate of evaporation will then be 0.245 X 0.30=0.073 pounds per square foot. The average horse-power of the station will be 1000X0.40=400. The required rate of evaporation will be 400X15=6000 pounds per hour. The cooling surface will then be 6000 =82,000 square feet, or the pond required will be approximately .073 290 feet square. The cooling surface allowed in the above pond is 82 square feet per rated horse-power. Since 82 square feet of water will weigh about 5100 ART. 269 THE SPRAY POND 267 pounds for every foot in depth, it will be seen that a comparatively shallow pond will serve to carry great overloads for a short period of time. Allow- ing 600 pounds of condensing water per horse-power per hour, it will be seen that the above pond will contain 8^ hours' supply of condensing water for eveiy foot of depth. It is generally well to make the pond deep enough to carry from twelve to twenty-four hours' supply of con- densing water, allowing 600 pounds per horse-power per hour at the rated horse-power of the station. If the above pond be made 2 feet deep, the quantity of water contained will be ample. It may be seen from the above computations that a cooling pond must be quite large. For small powers, say up to 500 horse-power, the cooling pond is a cheap and simple method of solving the problem of condensing water supply, provided land is cheap. In case land is expensive or the station is large, the spray pond or cooling tower will be a preferable method for obtaining a supply of condensing water. 269. The Spray Pond. A second method of cooling condensing water is by spraying the water into the air over the surface of the small pond, which may be, and quite often is, placed upon a roof of a building. In case the water is sprayed into the air in this way, the required area of the pond is very much less than when spraying is not used, but since the quantity of water contained in the pond is small, it is necessary to provide sufficient capacity to take care of the peak load of the station. 270. Area of Spray Pond Required. When water is sprayed in this manner, it will be cooled by evaporation from the surface of the drops, and since the surface exposed by the drops is vastly greater than the surface of the same quantity of water exposed in a pond, the evaporation will be very much more rapid. The final temperature of the water will, of course, be higher than the temperature of the dew point, and it will be found, as a usual thing, that the pressure of saturated water vapor of the final temperature of the water will be about 0.15 pounds per square inch higher than the pressure of the water vapor in the atmosphere. Thus, if water be sprayed into air having a temperature of 70, and a humidity of 70 per cent, the pressure of the water vapor in the air will be 0.70 X0.36 =0.25 pounds per square inch. The temperature of the water will then be reduced to the temperature corresponding to the pressure of 0.25+0.15 = 0.40 pounds per square inch. From the steam tables, this temperature is 73. In case the drop in temperature of the water is large, (i.e., above 40 or 50 F.), it will be found that air in the neighbor- hood will become so saturated with moisture that the evaporation will not take place freely, in which case it may be necessary to spray the water twice in order to bring it to a sufficiently low temperature. It will usually be found preferable to use such a quantity of water that the required reduction in temperature will not exceed 40. One square foot of pond 268 WATER-COOLING APPARATUS ART. 271 surface will be sufficient for the cooling of 200 pounds of water (about 3 per cent of which will be evaporated) and the spray nozzles should be placed a sufficient distance apart so that each will be allowed the area given by the above rule. It will usually be found that 3 square feet of pond surface per horse-power will suffice, but the total surface provided on such a basis must be estimated on the maximum and not the rated or mean horse-power of the station. If the efficiency of the station is low, so that the quantity of heat rejected per horse-power is more than is required to evaporate 15 pounds of water, the surface allowed per horse-power must be suitably increased. 271. Power Required by Spray Nozzles. When condensing water is cooled by the use of a spray pond, it is necessary to pump the water to the spray nozzles at a pressure of from 15 to 20 pounds per square inch. This takes a considerable amount of power. Assuming that 3 per cent is evaporated and that the quantity is 15 pounds per horse-power per hour, it will be seen that the quantity pumped per horse-power will be about 500 pounds. If this water be pumped against a head of 46 feet (which corresponds to a pressure of 20 pounds per square inch) and the efficiency of the pumping plant be 60 per cent, the work required to do this pumping will be 38,300 foot-pounds per hour, or 0.019 horse-power. The power required for pumping will therefore be between 1J and 2 per cent of the power of the station. In case steam pumps are used for this purpose, and they are run condensing, an extra allowance of water must be made for them, since such pumps are much less efficient than large engines, and the estimated evaporation of 15 pounds of water per horse- power per hour will not be sufficient to furnish them with cool condensing water. 272. The Cooling Tower. In large plants the cooling tower is the preferred method of providing a supply of condensing water. Cooling- towers are divided into two classes, known as natural draft and mechanical draft towers, according as to whether the air is drawn through the tower by a chimney-like action, or forced into the tower by means of a fan or other form of mechanical impeller. In theory, the action of the cooling tower is as follows : the water coming from the condensers, which usually has a temperature of approximately 100, is introduced at the top of the tower, which is filled either with wooden or tile checker work or heavy galvanized, iron wire partitions. As the water descends through the tower, flowing over the checker work or wire mesh, it exposes a large area to the action of the air which is flowing upward through the tower. The air entering the tower has the temperature and humidity of the outdoor air. As it ascends through the tower, coming into contact with warm water, it chills this water by the evaporation of a small portion of it, and finally leaves the top of the tower at almost the temperature of the ART. 273 CAPACITY OF A COOLING TOWER 269 entering water and laden almost to the saturation point with moisture. Since it is warmed as it ascends through the tower, it expands in volume and consequently is able to hold more moisture than it would were it not for this expansion. The addition of the water vapor which it absorbs also increases the volume. A portion of the heat taken from the water is carried away in the form of sensible heat in the air, on account of its rise in temperature. The most of it, however, is carried away in the form of latent heat, on account of the evaporation of a portion of the water. The following problem will serve to make clear the action of such a cooling tower. 273. Capacity of a Cooling Tower. Assume that a cubic foot of air enters the tower at a temperature of 70 and a humidity of 70 per cent. Were this air saturated with moisture, we find from the steam tables that the pressure of the water vapor present would be 0.36 pounds per square inch. The actual pressure of the water vapor will be 70 per cent of this or 0.25 pounds per square inch. The pressure of the dry air is therefore 14.70 0.25=14.45 pounds per square inch. The quantity of moisture contained in the air is 0.001148X0.70 = 0.000804 pounds per cubic foot. From the equation PV=XR T we find the weight of one cubic foot of dry air to be 14.45X144 533X630 = The total heat of the moisture contained in the air is found by adding the heat of superheat to the total heat at the temperature corresponding to the pressure of the water vapor. Since the superheat is 11, the specific heat of superheated steam of this temperature is 0.46, the total heat is 1085.4 B.T.U. per pound and the weight of moisture in the cubic foot of air is 0.000804, we will have for the total heat of the moisture in 1 cubic foot of air, the value .000804 (11X0.46+ 1085.4) =0.876 B.T.U. Let us assume further that the air comes from the cooling tower at a temperature of 100 and saturated with moisture. The pressure of the moisture contained in the air is now 0.946 pounds per square inch, which leaves as the pressure of the dry air 13.753 Ibs. per square inch. The volume of what was 1 cubic foot of air will now be increased, the new volume being to the old volume inversely as the absolute pressure of the dry air and directly as its absolute temperature. We therefore have for the new volume of this quantity of air 14.45 560 270 WATER-COOLING APPARATUS ART. 274 This quantity of air will contain 0.002851 X 1.11 = 0.00316 pounds of water- vapor at a temperature of 100 when saturated, and the total heat of this vapor will be 1103.6X0.00316 = 3.49 B.T.U. It will be seen that the amount of heat carried away in the water vapor is equal to 3.49 0.88 = 3.61 B.T.U. for each cubic foot of air introduced in the tower. The air itself was heated from a temperature of 70 to a temperature of 100, and this 30 rise in temperature added to it 0.0737X30X0.238 = 0.525 B.T.U., a quantity found by multiplying the weight of the air by its rise in tem- perature and the product by the specific heat of the air at constant pressure. The total quantity of heat carried away by each cubic foot of the air introduced into the tower is then 0.520 + 2.61 = 3.14 B.T.U. When a cooling tower is working at approximately its rated capacity the water will be cooled until its temperature is about that of saturated water vapor having a pressure from 0.15 to 0.25 pounds per square inch higher than that of the water vapor in the entering air. The air will leave the tower with a temperature from five to ten degrees lower than the entering water and with a humidity of from 90 to 100 per cent. We are usually safe therefore in assuming that each cubic foot of air delivered to the tower will carry away at least 2.5 B.T.U. from the condensing water. Since a condensing steam plant of good economy will reject from 10,000 to 15,000 B.T.U. per horse-power per hour, it will be seen that we must supply to the cooling tower from 60 to 100 feet of air per minute for each horse-power developed by the plant. 274. Method of Designing a Cooling Tower. In designing a cooling tower it is necessary to provide a sufficient surface of checkerwork to evaporate the required quantity of water; to provide a sufficient cross- section in the air passages so that the pressure required to circulate the air through the tower will not be excessive; to arrange the water distribu- tion system so that the water will be distributed evenly; to arrange the air passages so that the supply of air will be distributed uniformly to all parts of the checkerwork; and to provide means for moving the air and pumping the water. In case the distribution of water or air is uneven, the efficiency and capacity of the tower will be seriously impaired. The first point to be determined in cooling tower design is the area of checker work which must be exposed to the action of the air. The rate of evaporation from the surface of checker work in a cooling tower having forced draft is about five times that which occurs in the case of an open pond exposed to still air. The rate of evaporation per square foot of surface per hour will therefore be found by multiplying the difference between saturated water vapor of the temperature of the water leaving the tower and the actual pressure of the water vapor in the air entering the tower by 1.5. Having found the rate of evaporation and knowing the temperature of the water entering the tower, we may compute by the ART. 275 EXAMPLE OF THE DESIGN OF A COOLING TOWER 271 converse process, the approximate temperature and humidity of the air leaving the tower, and from this we may determine the quantity of heat and of moisture carried off per cubic foot of air supplied. From the total heat rejected by the engine when working at its rated load, we may determine the total quantity of air required, and the total area of the checker work. The depth of the checker work will depend on the available draft in case the tower is a natural draft tower and may be given any reasonable value in the case of a forced draft tower. It is usual to make the depth of checker work in the latter case twice the least dimensions of the base of the tower. 275. Example of the Design of a Cooling Tower. We will assume the following problem to illustrate the method of cooling tower design. Temperature of the air entering 75, humidity 70 per cent, required temperature of condensing water 80, temperature of water entering the cooling tower 110. The pressure of water vapor of 80 temperature is 0.505 pounds per square inch. The pressure of the water vapor in the air is 0.428X0.70=0.30 pounds per square inch. The pressure difference is therefore 0.20 pounds per square inch, and the rate of evaporation is 0.20X1.5=0.30 pounds per square foot. The pressure corresponding to the temperature of the enter- ing water is 1.27 pounds per square inch. Subtracting the 0.20 pounds difference in pressure to maintain the computed rate of evaporation we will have for the pressure of the water vapor in the air discharged, 1.07 pounds per square inch, which corre- sponds to a temperature of 104. We may, in practice, assume that the air will come from the tower saturated with moisture at this temperature and neglect the super- heat of the water vapor entering the tower. The weight of water vapor entering the tower per cubic foot of air supplied is 0.00135X0.70=0.00095 and its total heat will be 1094.3X0.00095 = 1.04 B.T.U. The pressure of the dry air entering the tower will be 14.700.30 = 14.40. The pressure of the dry air leaving the tower will be 14.70 - 1.07 = 13.63. The final volume of the air will be 14. 40 . . 460 + 104 KeS* 460 + 75 =LllcU ' ft - The quantity of moisture in the air leaving the tower will be 1.11X0.00319=0.00353 pounds per cubic foot of air supplied, and the total heat will be 0.000353X1033.4=3.64 B.T.U. The amount of heat carried away by the evaporation of the moisture will therefore be 3.64 1.04 = 2.6 B.T.U. per cubic foot of air supplied. The air itself will be increased in temperature from 75 to 104, and the sensible heat carried away will be (since a cubic foot of dry air weighs approximately 0.075 pounds) 0.075X29 X0.238=0.52 B.T.U. The heat carried away per cubic foot of air supplied will then be 0.52 + 2.6 = 3.12 B.T.U. Assuming that the engine rejects 15,000 B.T.U. per horse-power per hour, we will then have for the required air supply, per hour or 80 cubic feet per minute. The quantity of water evaporated by each cubic foot of air supplied is 0.003520.00095=0.00257 pounds. Hence the quantity of water evaporated per horse-power per hour will be 4800X0.00257 = 12.4 pounds. We have already determined that the evaporation per square foot of checker work will be 272 WATER-COOLING APPARATUS ART. 275 0.30 pounds. Consequently the number square feet of checker work required per horse-power will be 12.4 0.30 = 41. If this checker work be assumed to consist, as it often does, of 1-inch cypress planks laid up in such a way as to make a series of vertical flues 4 inches square, as shown in Fig. 143, we will have an evaporative surface of 7.7 square feet per cubic foot of checker work. This will give us about 5.3 cubic feet of checker work per horse-power. In the case of a 1000 horse-power cooling tower we would have a tower 14 feet square with a depth of checker work of about 28 feet. Under these circumstances, the net area of the air passages will be about 125 square feet, and since the total quantity of air required is 80,000 cubic feet per minute, the velocity of the air in the passages will be 10.5 feet per second. The pressure required to produce this velocity in a tower of this height is about the pressure produced by a column of water f inches high. The resistance offered by such a tower to the passage of the air varies directly as the depth of the checker work and as the 1.8 power of the velocity of the air. Since it is impracticable in the case of a natural- draft tower, to obtain by means of the difference in density of the air within and without the tower a difference in pressure as great as the figure given, a natural-draft tower will have a less depth of checker work and a much larger ground area for the same capacity. In general, on account of the lower velocity of the air, the rate of eva- poration in a natural-draft tower per square foot of checker y/ork will be about 60 per cent of the rate in a forced-draft tower, consequently, about If times as much evaporative area must be provided as would be provided in the case of a forced draft tower. In order to produce th9 re- FIG. 143. Arrangement of checker quired draftj a ghaft or chimney extends from 50 to 100 feet above the top of the checker work on a natural-draft tower. The draft which such a tower will produce may be found by rinding the difference in weight of a cubic foot of external air and a cubic foot of the air coming from the checker work and multiplying this by the vertical distance from the top of the checker work to the top of the tower. The product will be the difference in pressure in pounds per square foot, which may be reduced to inches of water by multiplying by 0.192. A natural-draft tower of the same capacity as the one we have just designed would have 8 cubic feet of checker work per horse-power, or 8000 cubic feet altogether. The weight of the external air per cubic foot will be work for cooling tower. 14.40X144 + 0.00093 =0.0740 Ibs. 53.3X535 The weight per cubic foot of the air in the shaft will be 13.63X144 53.3X564 + .003 19 = .0687. PROBS. 1-11 PROBLEMS 273 The difference in density will be 0.0053, and the draft produced will be 0.001 inches of water per foot in height of the shaft. Assuming the same depth of checker work as in the forced- draft tower, the ground area will be 1.66 times, and the air velocity only 0.60 times the former value. The resistance of the checker work will therefore be fX0.60 1-8 =0.15 inches of water. The height of tower required would be 150 feet, which is excessive. Since the resistance of the tower for a given air velocity is proportional to the depth of checker work, and the velocity is inversely proportional to this depth, the height of the shaft is proportional to the 2.8 power of the depth of the checker work. Assuming a reason able height of shaft, say, 60 feet, we will have for the depth of the checker work The area of the base of the tower will then be 8000 26 =-286 sq.ft., or the tower will be then 17 feet square. The volume of the checker work and the draft required to maintain the required air velocity varies greatly with the form of the checker work. The draft needed can be computed only from the observed performances of similar towers. In forced draft towers the power required by the fans is about one per cent of the power of the station. PROBLEMS 1. It is desired to maintain the temperature of a cooling pond at 75. The mean summer temperature is 65 and the humidity 50 per cent. It is used in connection with a 200 horse-power station operating 12 hours per day, using 18 Ibs. of water per horse-power per hour. Find the area of cooling pond required. Ans. 21,8CO sq.ft. 2. What area of spray pond would be required for the above plant ? Ans. 600 ft. 3. One cubic foot of air enters a cooling tower at a temperature of 80 and a hu- midity of 80 per cent. Find the total heat present in the water vapor, disregarding the superheat of the vapor. Ans. 1.375 B.T.U. 4. Within the tower this cubic foot of air is raised to a temperature of 110 and saturated with moisture. Find its final volume. Ans. 1.122 cu.ft. 5. Find the total heat of the water vapor contained in this air. Ans. 4.680 B.T.U. 6. Find the increase in the sensible heat of the air. Ans. 0.52 B.T.U. 7. Find the heat carried away per cubic foot of air supplied. Ans. 4.08 B.T.U. 8. Find the heat carried away per pound of water evaporated. Ans. 1.370 B.T.U. 9. Water comes from the above cooling tower at a temperature of 95. What is the rate of evaporation per square foot of checker work, assuming forced draft. Ans. 0.615 Ibs. 10. Find the number of square feet of checker work required for a power plant of 1000 horse-power, rejecting 12,000 B.T.U. per horse-power hour. Ans. 14,200 sq.ft. 11. How many cubic feet of air will be required per hour by the above plant? Ans. 2,940,OCO cu.ft. CHAPTER XVIII HOT AIR ENGINES 276. Characteristics of the Hot Air Engine. The hot air engine is a heat engine which uses air or other permanent gas as a working fluid. Since there is no advantage gained by employing any other gas, air is the working fluid invariably chosen. The hot air engine may be dis- tinguished from the internal combustion engine by the manner in which the working fluid is heated, namely by the conduction of heat from some external source and not by the combustion of the working fluid itself. It is, therefore, unnecessary for the hot air engine to reject the working- fluid and take a fresh supply at the completion of each cycle, as is done in the case of the internal combustion engine. The hot air engine, since the advent of the internal combustion engine, is not of great commercial importance. However, several of these engines afford excellent illustra- tions of important principles which are of great interest in connection with the probable development of internal combustion engines and refrigeration machinery, and are therefore worthy of careful study. 277. The Carnot Air Engine. The most efficient, and in theory the simplest cycle which may be performed by the working fluid of a hot air engine, is the Carnot cycle. The Carnot cycle has never been used in any practical engine for the reason that the cylinder volume and the pressure range required in order to produce a very moderate amount of power, are very great. This may be seen by reference to Fig. 144, which shows to scale the Watt dia- gram of the Carnot cycle for air for the temperature range from 70 to cSOO F. It will be noted that the FIG. 144. Theoretical card, to scale, from a Carnot cycle air engine. card is extremely " thin, 3 although the pressure range is very large. 274 ART. 277 THE CARNOT AIR ENGINE 275 This is a condition of affairs which makes for very low mechanical efficiency and multiplies greatly the practical difficulties of operation. Assume that the Carnot cycle engine whose Watt diagram is illus- trated in Fig. 144 uses 1 pound of air for its working fluid at an initial temperature (T c ) of 530 absolute, an initial pressure (P c ) of 2000 pounds per square foot (i.e., 13.9 pounds per square inch) and an initial volume (V c ) of T7 WRT C 1X53.3X530 V c = -- -- - 14.2 cu.ft. Assume that this air is compressed isothermally until its volume at d (Vd) is 7.1 cubic feet and its pressure (Pd) is 4000 pounds per square foot. Next, the air will be compressed adiabatically from d to a, until its tem- perature (T a ) is 1060 absolute. The pressure (P a ) will be __ T \ r i /1f)fiO\ -4 P a = Pd? - 4000 = 45,000 Ibs. per sq.ft. \ The volume of the air will of course be The gas will now expand, the ratio of isothermal expansion being the same as the ratio of isothermal compression, namely two to one, and the volume and pressure at b will become 2.52 cubic feet and 22,700 pounds per square foot, respectively. The efficiency of the cycle is y a -y c _ 1060 -530 T a 1060 which is about the theoretical efficiency of the internal combustion engine cycles usually employed. The net work done during the cycle is 50 per cent of the mechanical equivalent of the heat supplied during isothermal expansion, and is JPi Vi log e r = iX45,OOOX 1.26Xlog e 2-39,200 ft. Ibs. Dividing this by the swept volume, which is V v , V a or 12.9 cubic feet, we will have 3040 pounds per square foot for the mean effective pressure. It will be seen from the above computations that the maximum pres- sure is 320 pounds per square inch, while the mean pressure is only 20 pounds per square inch, or less than y 15 of the maximum pressure. In the case of the steam engine, it is very seldom that the mean effective pressure falls below one-half or one-third of the maximum pressure. Since the friction loss in an engine of a given power is approximately pro- portional to the ratio of the maximum to the mean pressure, it may be seen that the friction loss in the case of a Carnot cycle hot air engine is from 276 HOT AIR ENGINES ART. 278 I- five to eight times that of a steam engine of equal indicated power. Owing to this fact, no hot air engine operating on the Carnot cycle or any approximation to it has ever been successfully used. 278. The Joule Hot Air Engine. The simplest of the practical cycles employing hot air as the working fluid is the Joule cycle. The operation of the Joule cycle may be un- derstood by reference to Fi'g. 145. In cylinder A, a quan- tity of air is compressed adiabatically to some high pressure and is then dis- charged at constant pressure into the heater chamber B. Cylinder C takes the same mass of air from the heater chamber and expands it down to its original pressure. The volume of the heating and cooling chambers is so great that no sensible variation in. pressure occurs. After ex- FIG. 145. Diagram of a Joule cycle air engine. pansion, the gas is rejected to the cooling chamber d at con- stant pressure. Here its temperature is reducc-d to the initial temperature and it again enters cylinder A to repeat the cycle. It is not necessary that a cooling chamber be provided, as the working fluid may be rejected to the atmosphere and a fresh quantity taken from the atmosphere by u g i h FIG. 146. Watt diagram from a Joule cycle engine. cylinder A. The equivalent series of processes consist of first, compres- sion at constant pressure, second, adiabatic compression; third, expan- sion at constant pressure; fourth, adiabatic expansion. The Watt diagram is illustrated in Fig. 146. Assume that the temperature of the air in ART. 278 THE JOULE HOT AIR ENGINE 277 the heater chamber is 1200 absolute (740 F.) and the temperature of the atmosphere 530 absolute (70 F.), that the pressure in the heater chamber is 150 pounds absolute, per square inch, and that one pound of air is introduced into and withdrawn from the heater, per cycle. The temper- ature of compression (at a) may be found by the formula; r-i or 71.^0 \ = 1030, 150 \ 14.7/ ~ which is the temperature of the air entering the heater chamber. The work of compression in cylinder A may be obtained by the formula: U=n- - 53.3 -_ = 6 The work required to deliver the air from cylinder A into the heating chamber will be RT, which becomes 53.3 X 1030-= 54,900 foot-pounds (area g a f o). The heat imparted to the air in raising its temperature from 1030 to 1200 at constant pressure is which is 185.5X170 = 31,700 foot-pounds. The work done by the air while entering the cylinder C is equal to 53.3X1200 = 64,000 foot-pounds. (area fbio) The air is expanded from a pressure of 150 pounds absolute and an initial temperature of 1200 to a pressure of 14.7, and its final temperature is therefore 286 = 618 The work of expansion will be 77500 ft.lb, (area b c j i) . The work done by the air in entering cylinder A from the cooler is 53.3X530 = 28,300 foot-pounds (area e d h o). The work done in expelling the air from cylinder C is 53.3X618 = 33,000 foot-pounds (area ecjo). The heat rejected in the cooling chamber will be (618- 530) X 186.5 =16,400 ft.lbs. 278 HOT AIR ENGINES ART. 279 The quantity of work done is the difference between the work done upon the air in compressing it and delivering it to the heater and rejecting it to the cooler and that done by the air in entering the cylinders and expand- ing in cylinder C, and is 15,300 foot-pounds (area abed). Dividing this by the mechanical equivalent of the heat imparted to the pound of air in the heater, we will have for the efficiency of the engine 48.2 per cent. An inspection of the above work will show that the heat supplied is proportional to T b T aj the heat rejected to T c Td, and the work done to (T b -T a )-(T c -T d ). The efficiency of the Joule cycle is therefore given by the expression frr i rri nn nn lb+ J d~ lg i c 7\ T y * b * a in which T b = the temperature of the air leaving the heater, 7^ = the temperature of the air entering the heater, 7^ = the temperature of the air entering the cooler, or rejected from the engine, Td = the temperature of the air leaving the cooler, or taken into the engine. 279. The Stirling Hot Air Engine. The Stirling engine utilizes the regenerator principle in order to attain the efficiency of the Carnot cycle without the accompanying mechanical disadvantages. The theory of this engine will be best understood by reference to Fig. 147 although [the parts of the engine, in practice, are arranged in an entirely different manner. In the figure, A is a piston which works within the large cylin- der B y C is a piston which works within the small cylin- der Z), which is connected with the large cylinder by the pas- sage F. Assume that both pistons are at the lowest point of their stroke, as shown in the illustration. If piston A now be caused to rise, it will trans- fer the air above it from its upper to its under side, causing it to flow through the regen- erator, marked R, which may FIG. 147. Diagram of a Stirling air engine. consist of a large quantity of wire gauze. The air above the piston A is exposed to the action of a cooler, as shown, and is therefore at the temperature of the cooler, T c . The air below the piston A is exposed Cooler Heater ART. 279 THE STIRLING HOT AIR ENGINE 279 to the fire, or to some other source of heat, and is therefore at the tem- perature of the heater, 7 1 /. In passing through the regenerator, the tem- perature of the air will be raised from the temperature of the cooler to the temperature of the heater, by the regenerative action. As a result of this transfer and increase in temperature of the air, its pressure will rise. When piston A has reached the top of its stroke, the pressure of the air will have risen from its original value P c , to the value Pf. Piston C is now permitted to rise, the air expanding isothermally, absorbing heat and performing work during the process. Piston C having reached the top of its stroke, piston A is now depressed, forcing the air below it through the regenerator and past the cooler into the upper part of B. As it passes through the regenerator, the air is cooled from the temperature of the heater to the temperature of the cooler. Piston C is now forced downward, isothermally compressing the air, while it rejects heat to the cooler. No work is done by or upon piston B } and the net work of the cycle is the difference between the work performed upon piston D during its upward stroke, and by it during its downward stroke. The efficiency of a Stirling engine is in theory the same as the efficiency of a Carnot cycle engine. In practice, of course, it is necessary that there be a considerable tempera- ture difference between the heater and the air under the transfer piston, between the cooler and the air above the transfer piston, and between any point in the regenerator and the air passing that point. The card given by the working cylinder of the engine is shown in Fig. 148. Line a b represents the expan- sion of the air during the rise of piston C. Line b c represents the fall in pressure of the air at constant volume (i.e., while the piston C is at the top of its stroke) on account of its transfer by piston A. Line c d represents the compression of the air while piston C descends. Line d a represents the rise in pressure at constant volume, while the transfer piston is transferring the air from the upper to the lower side. Assuming that 1 pound of air having a pressure of 100 pounds per square inch absolute at point d, is used as the working fluid, that the ratio of isothermal expansion is 2, that the temperature of the air above the transfer piston is 70 F., and that below the transfer system piston 740 F., and neglecting the volume of the regenerator FIG. 148. Watt diagram from a Stirling engine. 280 HOT AIR ENGINES ART. 279 spaces and air passages, we will obtain the following results from the Stirling cycle. During the rise of the transfer piston, no work will be done or absorbed, the tem- perature of the air will rise from 530 absolute to 1200 absolute and the pressure will rise from 100 to 226.5 pounds per square inch. The air is heated by heat stored in the regenerator, and during this portion of the cycle it receives no heat from the heater. During the rise of piston D, the air expands isothermally, receiving heat from the heater in order to maintain its temperature constant. The amount of heat so received is equal to the amount of work done by the air upon piston C, which is 53.34X1200Xlog e 2 = 44,350 foot-pounds. This is the mechanical equivalent of the heat received by the air from the heater, during this portion of the cycle, and is represented by the area a b ef. At the end of isothermal expansion, the pressure of the air has fallen to 113.25 pounds per square inch. During the descent of the transfer piston, a part of the air is transferred through the regenerator, and its temperature falls to that of the cooler. No work is done or absorbed during this portion of the cycle and no heat is taken from the heater or imparted to the cooler. Since the ratio of expansion is 2 to 1, the volumes of the transfer cylinder and the working cylinders are equal and are each 530X53.34 Hence after the transfer of part of the air to the upper side of piston B has been effected we will have 1.964 cubic feet of air at a temperature of 530 and 1.964 cubic feet at a temperature of 1200. Since the pressures and the volumes are the same in each case, the masses will be inversely proportional to the absolute temperatures, and the quantity in the transfer cylinder will be 1200 0.694 Ibs. 1200+530 The pressure of this air (P c ) will be 0.694X53.34X530 ~ ~ = per square ' During the descent of piston D, the remainder of the air which is contained in cylinder C, is transferred through the regenerator and the cooler to the upper s'de of the transfer piston, and the whole quantity of air is compressed. That portion of the air within cylinder C which is continually diminishing in quantity rejects to the heater the heat equivalent of the work performed in compressing it. The air in the transfer cylinder, which is continually increasing in quantity, rejects to the cooler the heat equivalent of the work spent in compressing it. In order to find the amount of work done during the compression, we must determine the relation between the pressure and volume on the whole mass of gas contained in the engine during the descent of the working piston. Let V be the volume of the working cylinder. Then the mass of the air in the working cylinder, W l} will be to the mass of the air in the transfer cylinder, TF 2 , directly as the volume of the air in the working cylinder is to that in the transfer cylinder and inversely as the temperature of the air in the work- ing cylinder is to that in the transfer cylinder. Consequently, we may write = 530 V 1 530 V + 1200 XI. 966* ART. 279 THE STIRLING HOT AIR ENGINE 281 The pressure of this mass may be obtained from the formula PV^W^^RT and will be 53.34X1200X530^ 63,900 530 F + 2360 ~ F + 445' The work done upon the gas will therefore be rv d ri.966 JY I V rfF=63,900 ( -^ . JV C Jo F + 4.45 Integrating, we obtain 63,900 log e |^i|j = 23,400 ft.-lbs. Subtracting this from 44,350 foot-pounds the work done by the gas during the rise of the working piston, we will have 20,950 foot-pounds for the net work of the cycle. The swept volume is 1.964 cubic feet and the mean effective pressure is 20,950 = 74.0 Ibs. per square inch. 144X1.966 The ratio of the maximum to the mean effective pressure is T-TT, or about 3 to 1, a condition of affairs very much more favorable to mechanical efficiency than is the case when the Carnot cycle is employed. The quantity of heat rejected to the cooler is equal to the work done in compressing the variable quantity of gas contained above the transfer piston during the descent of the working piston. Since V equals the volume of gas in the working cylinder during this period, the total volume of the gas will be V + 1.966. The amount of work done during any small portion of the stroke of the working piston upon the two quantities of gas will be proportional to their volumes at that instant. Consequently, by multiplying the total work done during any instant by the ratio of the volume of the transfer cylinder to the total volume of the gas at that instant we will have the work done upon the gas in the transfer cylinder during that instant. Multiplying the equation for the work performed upon the gas during 1 966 the descent of the working piston by ^^ -^^, we will have V i* J- .t.'UO This may be written Integrating this, we will have .416-41. 1-4X8.74\ 1.966 125 600 ( 1 \ 25 ' 6 \41.10 -4 X8.74J Solving this we will have for the mechanical equivalent of the heat rejected to the cooler 16,540 foot-pounds. Subtracting this quantity from the total work done upon the gas in compressing it we will have the mechanical equivalent of the heat restored to the heater, which is 6,860 foot-pounds. In order to obtain the efficiency of the cycle, we must divide the net work of the cycle by the net heat supplied, which HOT AIR ENGINES ART. 280 is equal to the heat supplied during isothermal expansion less the heat restored to the heater during compression, and we will obtain 20,950 44,350- 6860 It will be noted that the cycle is composed exclusively of reversible processes, and the efficiency of the cycle is in consequence that of the Carnot engine, and is, for the case chosen, 1200-530 which is the same as was obtained by computation of the work performed, and the heat supplied and rejected. Had the working cylinder been connected with the upper end of the transfer cylinder the cycle would have differed from that described, in that during the descent of the working piston the compression would have been isothermal, and during the rise of the working piston, heat would have been absorbed from both the heater and the cooler. The efficiency of the cycle would l>e exactly the same as before. In practice, the Stirling engine is subject to several losses, and the card given by the engine is not exactly of the form computed, since the regenerator and the connecting passages have some volume. Neither is the action of the regenerator a perfectly reversible process in practice. Usually, the temperature difference between the air entering and that coming from the cool end of the regenerator is from 5 to 20 per cent of the difference in temperature of the two ends of the regenerator. On this account, the actual efficiency of the Stirling engine is only about 60 per cent of its theoretical efficiency. In addition, there are practical difficulties encountered in its use, which may, however, be overcome by the use of proper materials. Modifications of the Stirling cycle will probably serve as a basis for future improvements in the internal com- bustion engine, since this engine is in theory the most efficient one which has ever been practically successful. 280. The Ericsson Hot Air Engine. The principle of the Ericsson hot air engine is shown in Fig. 149. This engine is usually built only in small sizes and used for pumping water. The method of operation is as follows: Within the cylinder A is a gas-tight piston B, termed the working piston. Through a stuffing-box in this piston there passes a rod which operates the loose-fitting plunger, C. The purpose of this plunger is to transfer the air from the lower to the upper end of the cylinder and back again, and it is therefore termed the transfer plunger. Both piston and plunger being at the top of the stroke, as is shown in Fig. 149, the plunger descends, transferring the air from the furnace at the bottom to the comparatively cool region at the top. In its passage ART. 280 THE ERICSSON HOT AIR ENGINE 283 the air flows in a thin sheet over the water-cooled surface of the cylinder, and its heat is transferred to the water jacket. The air being cooled, its pressure is reduced. While the transfer plunger remains at the bottom of its stroke, the working piston descends, compressing the air con- tained in the cylinder. The transfer plunger now rises while the piston remains stationary, transferring the air to the lower end of the cylinder, where it is heated, with resulting increase of pressure. The piston now rises as a result of the increase in pressure and performs work. Since this engine lacks a regenerator, it is. less efficient than the Stirling engine. Its principal merit is that it is very. simple and unlikely to get FIG. 149. FIG. 150 out of order. In practice, the piston and plunger are so connected to the crank of the engine that they both are in motion continually, instead of each one stopping while the other is performing its stroke. This is accomplished by the mechanism shown in Fig. 149, the piston and water pump being operated by the walking-beam, while the transfer plunger is operated by the bell crank. It will be seen that the pmnger is near the end of its stroke and is almost motionless while the piston has its maximum velocity and is at the middle of its stroke. The form of card given by the Ericsson engine is shown in Fig. 150. 284 HOT AIR ENGINES PROBS. 1-11 PROBLEMS 1. Find the diameter and length of stroke which would theoretically be required by an engine utilizing the Carnot cycle worked out in Art. 277. Assume a speed of 150 revolutions per minute, that the length of stroke is 1? times the diameter, that the engine is 100 horse-power and is single acting. Ans. 22"X33". 2. Find the length of stroke and the diameters of the compression and working cylinders of an engine utilizing the Joule cycle worked out in Art. 278. The engine is of 100 horse-power and makes 150 revolutions per minute. Assume the length of stroke to be equal to 1^ times the diameter of the compression cylinder and that the cylinders are single acting. Ans. 30.5" X 45.7" and 32.9" X 45.7". 3. A Stirling engine operates between temperatures of 200 and 1000 F. The pressure when both pistons are in their lowest positions is 150 Ibs. per sq.in. Find the pressure after the transfer cylinder is raised. Ans. 332 Ibs. per sq.in. 4. Assuming 1 Ib. of air as the working fluid and that the volume of the transfer cylinder is twice the volume of the working cylinder, find the work of isothermal expansion. Ans. 31,550 ft.lbs. 7. Find the pressure ta the end of isothe^^nal expansion. Ans. 221 Ib per sq.in. 6. Y'md the pressure of the air after the descent of the transfer piston. Ans. 122 Ibs. per sq.in. 7. Find the value of the index of the compression curve, assuming that it follows the law PV n = a constant. Ans. n=-51 8. Find the work of compression on the same assumption. Ans. 16100 ft.lbs. 9. Find the net work of the cycle. Ans. 15450 ft.lbs. 10. Find the net work per cubic foot of swept volume of the working cylinder. Ans. 18,940 ft.lbs. 11. Find the size of working cylinder required for a 100 horse-power engine, oper- ating at 150 revolutions per minute, utilizing the Stirling cycle just developed. Make the stroke 1^ times the diameter of the cylinder. Ans. 11. 95" X 17. 9". CHAPTER XIX THE INTERNAL COMBUSTION ENGINE 281. Characteristics of the Internal Combustion Engine. An internal combustion or gas engine is a heat engine in which the working fluid consists of a mixture of air and inflammable gas or vapor, the combustion of which furnishes the heat necessary for the operation of the mechanism. The internal combustion engine differs from all other heat engines in that the combustion which supplies the heat occurs within the working cham- ber or cylinder of the engine itself. In all other heat engines, the working fluid and the combustible are separate substances, and the working fluid is usually heated in a separate chamber from that in which it performs its work. As in any heat engine, the working fluid of the internal com- bustion engine is caused to perform a thermodynamic cycle whose form is determined by the nature of the fluid and the arrangement of the engine mechanism. 282. The Otto Cycle Engine. The internal combustion engine cycle which is in most common use is usually termed the -Otto cycle, and was first proposed by Beau de Rochas. It is also known as the constant -volume cycle, and as the four-stroke cycle. The operations of the Otto cycle may be understood by reference to Fig. 151. The engine cylinder is an iron FIG. 151. Diagram of a four-cycle gas engine. casting A provided with an inlet valve I and an exhaust valve E. Within the cylinder moves a gas-tight piston which is often made of the form shown, performing at the same time the functions of a piston and of a cross-head. This type of piston is known as a trunk piston. As the 285 286 THE INTERNAL COMBUSTION ENGINE ART. 283 crank revolves in the direction shown by the arrow, the piston is moved back and forth. Assume that the engine is in the position shown, with the crank on the outer center, then as the crank revolves it will begin to force the piston inward. The valve E being held open by the mechanism of the engine during this stroke, the contents of the cylinder will be expelled. This first stroke is therefore termed the exhaust stroke of the cycle. When the piston has reached the end of its exhaust stroke, the valve E closes and the valve / opens. The piston then begins to move forward, and draws in a quantity of air with which is mixed a combustible gas. This second stroke is known as the suction stroke of the cycle, and the mixture drawn into the cylinder is termed the charge. When the piston reaches the end of this stroke, the valve / also closes, and the crank continuing to revolve, the piston is again forced inward, adiabatically compressing the charge into the clearance space at the end of the cylinder. This third stroke is known as the compression stroke. The volume of the clearance space, which usually ranges from 12 per cent to 30 per cent of the swept volume of the cylinder, is termed the clearance volume. When the pis- ton reaches the end of the compression stroke, the charge, which is now highly compressed and heated, is ignited, usually by means of an electric spark. On account of its high temperature and pressure the charge burns almost instantly, and the heat so generated, by raising the tem- perature of the charge, very greatly increases its pressure. During the fourth stroke of the piston the charge expands adiabatically. Because of the great pressure resulting from its explosion much more work will be done by the charge during this stroke than was done upon it during the compression stroke. The fourth stroke is therefore known as the working stroke of the cycle. When the piston reaches the end of the working stroke, the exhaust valve E again opens, and both the working- fluid and the mechanism of the engine return to their original condition. It will be seen that it requires four strokes of the engine to complete the cycle. During the first or exhaust stroke the pressure upon the piston is only slightly above that of the atmosphere and during the second or suction stroke only slightly below. Although the amount of work per- formed in expelling the burned charge and in drawing in a fresh one varies somewhat with the speed of the engine and the size of the valves and gas passages, it is very small under ordinary conditions. Hence the suction and exhaust strokes need not be considered in connection with the thermodynamic cycle, which is performed during the compression and working strokes only. 283. The States of the Working Fluid During the Otto Cycle. The pressure-volume diagram of the working fluid of an Otto cycle engine is shown in Fig. 152. The horizontal distance Oc f represents the clearance volume, while the distance c'a' represents the swept volume of the cylin- ART. 283 THE STATES OF THE WORKING FLUID 287 der. a c is the adiabatic compression line, the cylinder containing a charge at atmospheric temperature and pressure at point a. At point c, the charge is instantly heated at constant volume by the explosion, the pressure rising as represented by line ex. Line xt is the adiabatic expansion line of the charge and the line t a represents the cooling of this charge at constant volume at the end of expansion. The computations of the a' FIG. 152. Theoretical card from an Otto cycle engine. pressures, temperatures, and so on of the -working fluid at various point K in the cycle may be performed as follows: Let P a = the absolute pressure of the atmosphere in pounds per square foot ; F a = the swept volume + V C in cubic feet; T a = the absolute temperature of the atmosphere; P c = the absolute pressure of compression in pounds per square foot ; F c = the volume of the compression space in cubic feet; T c = the absolute temperature of compression ; P x = ihe absolute pressure of explosion; V x = F c = the volume at explosion; 7^ = the absolute temperature of explosion; P/ = the absolute terminal pressure in pounds per square foot; Vt = V a the terminal volume in cubic feet ; T t = the absolute terminal temperature ; H a = the heat in B.T.U.'s added at explosion; H r = the heat in B.T.U.'s rejected at exhaust; TF=the weight of gas contained in the cylinder; V a V c = the swept volume in cubic feet = Vt V x < 288 THE INTERNAL COMBUSTION ENGINE ART. 283 The weight of the charge will be The volume of the compression space will be j_ v = v (jr) r (2) The temperature of compression will be \* c The rise in temperature resulting from the explosion will be IT rp rp _ a f A\ ^ Wc~' The heat added as a result of the explosion will be H a = WC.(T,-T C ) ....... (5) The terminal temperature will be T T V "\~ l T ( P '\' T * T *- ....... It will also be rr, m ^a J- x / 7 x m , ......... (7) since T c :T a ::T x :T t (8) The fall in temperature at the end of expansion will be The heat rejected will be # r = WC v (T t -T a ) (10) The efficiency of the cycle will be or C v (T x -T c )-C v (T t -T a ) ART. 283 THE STATES OF THE WORKING FLUID 289 Simplifying, this becomes E =1- T t -T T T ' J- x 1 c which on substituting from (7) reduces to (13) (14) It appears from the above equation that the higher the compression temperature (or pressure), the greater the efficiency of the cycle, and that the efficiency is theoretically independent of the explosion and terminal temperatures and pressures and of the amount of heat added. The relation between the compression pressure and the efficiency of the cycle may be seen in Fig. 153. w 25 50 75 100 125 150 175 200 Compression Pressure in Lbs. per Sq. In. Gasre. FIG. 153. Relation between the efficiency and compression pressure. The work of compression is P c V c -P a V a R(T c -T a ) U ac = The work of expansion is P,V c -P t V a R(T x -T t } (15) (16) The work done is equal to U = ^ (P x -P c )Vc-(Pt-Pa)Vg . (17) 290 THE INTERNAL COMBUSTION ENGINE ART. 284 Afef The work done per cubic foot of swept volume is U V a -V c ' The theoretical horse-power of an engine employing the cycle is d8) HP - - (19) ~ 33,000 (V a -V e )' in which N is the number of cycles (i.e., one-half of the number of revolu- tions) per minute. Also for convenience in computation, it may be noted that (20) v and P x :P e ::P t :Pa ........ (21) The compression volume is generally expressed as a per cent of the swept volume thus y c (in per cent) = ~- ....... . (22) V n V r. (I It will be shown in the next chapter that the actual cycle performed in the Otto gas engine differs slightly from the theoretical cycle. The differences are not so great as they are in the case of steam engine cycles, however, and the actual card has very nearly the form of the theoretical card. 284. Example Showing the Method of Computing the States of the Working Fluid. The following example will serve to show the method of computing the form of the theoretical indicator card, the work done and the efficiency of an Otto cycle. Assume that the compression pressure is 140. pounds absolute (i.e., about 125 pounds gage), that the temperature of the gases after explosion will be 3500 absolute, and that the temperature of the mixture entering the cylinder is 70 F. The compu- tations will be carried out for 1 pound of air. The initial volume is obtained from the equation PV-WRT, and is The volume of the compression space per pound of air will be J_ V c = 13.32 (-^ \ " =2.69cu.ft. ART. 284 EXAMPLE OF AN OTTO CYCLE 291 The swept volume per pound of air will be 13.32-2.69=10.63 cu.ft ...... . . . . (3) The temperature of compression will be (1 40 \ 29 j = 1020 absolute ........ (4) The pressure of explosion will be o f-OO P x = JQ^X140 = 480 Ibs. absolute ........ (5) The efficiency of the cycle will be 530 = 48 per cent .......... (6) The quantity of heat added at explosion will be H a = 0.169(3500 -1020)= 419 B.T.U ....... (7) The work done per pound of air will be 419X0.480X777.5 = 156,200 ft.-lbs ........ (S) The pressure at release will be Pt = ' =42.9 Ibs. per square inch ...... ' (9) The work done per pound of air may be checked in the following manner. The work of compression is The work of expansion is / ^ ">no\ 53.3 X (3500 -530^) 0307~ = 220,200 ft.-lhs (11) The difference is the net work of the cycle, or 220,200-64,200 = 156,000 , . (12) The net work per cubic foot of swept volume per cycle is '- - = 14,650 ft. -Ibs. per cubic foot (13) The mean effective pressure shown by the card is AM|_ = io2 Ibs. per square inch (14) The horse-power theoretically developed by an engine operating on this cycle would be 14,650 N(V a -Vc) 33,000 in which N is the number of cycles, or one-half the number of revolutions per minute. The card for the engine may now be constructed by locating points P a V a , P C V C , P X V C , and P t V a , drawing perpendiculars between the first and fourth and the second 292 THE INTERNAL COMBUSTION ENGINE ART. 285 and third, and adiabatics between the first and second and third and fourth. This is the card illustrated in Fig. 152. 285. Methods of Governing the Otto Cycle Engine. Four methods are employed for controlling the speed and amount of power developed, in an Otto cycle engine. The first method is to cause the engine to miss explosions, thus reducing the number of working strokes which the engine makes in a given time. This is known as hit-and-miss governing. The second method is to throttle the port through which the charge enters the engine, reducing the weight of charge taken in and the power developed by its explosion. This is known as throttle governing. The third method is to reduce the proportion of combustible gas contained in the charge, and so to weaken the explosion. The fourth method is to delay the instant of ignition, and so to reduce the power developed by a given weight of charge. If the power developed within the cylinder of an Otto cycle engine equipped with a hit-and-miss governor is greater than is necessary to keep the engine up to speed, the engine will gain speed. In order to prevent this, it is customary to so arrange the governing mechanism that it will prevent explosions so long as the engine is operating at more than normal speed. This may be accomplished in several ways. One method is to cause the governor to hold the exhaust valve open until the speed becomes normal. If the inlet valve operates automatically (i.e., if it is opened by the suction of the piston and not by some mechanical device), this will prevent the engine from sucking in a charge during the suction stroke, since it will cause it to take suction from the exhaust pipe, and no explosion will occur at the beginning of the next working stroke. A second method is to cause the governor mechanism to hold the inlet valve closed. A third method (which is, however, very seldom used) is to cause the governor mechanism to hold the inlet valve open during the compression stroke. When an engine is equipped with heavy fly-wheels and a sensitive governor, the hit-and-miss system gives fairly close regulation and very great economy. When extremely close speed regulation and uniform turning moment is unnecessary, it is the preferable method of speed regulation. Throttling the mixture as it enters the engine cylinder gives a card of the form shown in Fig. 154. Line a b is the exhaust stroke, line b d is the suction stroke, line d c the compression stroke and line x t the work- ing stroke. The dotted lines show the form of card which would be given were there no throttling. The area d e b is the work required to suck the charge through the throttle, and is a loss. Since the compression pressure is reduced, the efficiency of the cycle is reduced somewhat, although this is partly counterbalanced by the lower terminal pressure resulting from the more complete expansion of the charge. This method of gov- erning, therefore, reduces the efficiency of the engine. It is mechanically ART. 285 METHODS OF GOVERNING THE OTTO CYCLE ENGINE 293 satisfactory so long as the compression does not fall too low. When it does fall too low, on account of extreme throttling, ignition fails to take place, and other methods of regulation must be resorted to. Throttling the inflammable component of the charge reduces the heat added at the instant of explosion, and therefore gives a card of the form shown in Fig. 155. The card shown in dotted lines represents the form FIG. 154. Card given by a throttle governed gas engine. FIG. 155. Card given when the gas is throttled. of card given with the gas unthrottled. Theoretically this method of governing makes no reduction in the efficiency of the cycle. Practically its efficiency is less than that of the hit-and-miss method. As the mixture grows weaker it becomes more difficult to ignite, so that at low loads ignition fails. A fourth method of governing a gas engine is to " delay the spark." This method is wasteful, since by retarding the ignition to some point in the working stroke, a portion of the power available is not utilized. The form of card produced may be seen in Fig. 156. The card shown in dotted lines is the one which would be given by the same charge were the spark properly advanced. It will be seen that a considerable amount of power is wasted. This method of governing is used in connection with throttle governing in operating auto- mobile or other portable engines in which it is desired to vary the speed of the engine as well as the power. This method is there employed on account of its extreme convenience and adaptability, in spite of its inherent wastefulness. \ FIG. 156. Result of delayed ignition. 294 THE INTERNAL COMBUSTION ENGINE ART. 286 Combinations of any of these methods of gas-engine governing may be used in the case of the Otto cycle engine. The usual method is to use hit- and-miss governing alone where a fairly constant speed is required in stationary work, to use hit-and-miss in connection with throttle governing where a constant speed and close regulation are required; and to use throttle governing in connection with delayed ignition where variable speed and power are required of the engine. 286. The Two-cycle Engine. The thermodynamic principle of the two-cycle engine is exactly the same as that of the Otto cycle engine. The details of the engine are, however, quite different. In Fig. 157 is shown a section of a two-cycle engine. The cylinder is an iron casting which is water jacketed in the manner shown. The crank case b is so arranged that it is practically gas tight. During the upward stroke of the piston P, a charge is drawn into the crank case through the check valve V. This charge consists of a mixture of air and combustible gas or vapor. When the piston descends, this charge is compressed within the crank case, its pressure rising to from 7 to 12 pounds gage, depending upon the volume of the crank case. When it reaches the bottom of its stroke, the piston uncovers two ports, one on each side of the cylinder. The port at the left marked E is the exhaust port, while that at the right marked / is the inlet port. Since the inlet port connects the crank case with the cylinder, the charge in the crank case will be forced into the cylinder on account of the difference in pressure. The form of the top of the piston is such that this charge is directed upward and into the cylinder, and as it enters, it expels the gases contained within the cylinder through the exhaust port. During the upward stroke of the piston, the charge now contained within the cylinder is adiabatically compressed. When the piston reaches the top of its stroke, the charge is ignited by the spark plug marked S and explodes. The piston descends during the working strokeof the engine. During its upward or compression stroke it has sucked a fresh charge into the crank case and during its downward or working stroke it compresses this charge. As the piston reaches the end of its stroke, the exhaust port is un- covered and the burned charge escapes from the cylinder on account of its pressure. An instant later the inlet port (which is nearer the FIG. 157. Section of a two- cycle engine. ART. 28G THE TWO-CYCLE ENGINE 295 bottom of the cylinder than the exhaust port) is uncovered, and the crank case compression forces the fresh charge into the cylinder. It will thus be seen that the engine makes one compression stroke and one work- ing stroke each revolution. It is usual in small two-cycle motors to employ the crank case as a pump in the manner already described. In large two-cycle engines, separate pumps are provided for compressing the gas and the air, and the engine is sometimes made double-acting in the manner shown in Fig. 158. In this engine the pumps deliver the charge to the working cylinder through the valve 7, while the working piston P is in the position shown. The entering charge expels the spent charge through the ports marked P. As the working piston moves to the right it compresses the fresh charge, which is exploded when the piston reaches the end of its stroke. When it moves to the left, the right-hand charge is performing its working Gas -Section through the working cylinder of a Koerting two-cycle double acting engine. stroke while the left hand charge is being compressed. The length of the piston is such that the single set of exhaust ports serves for both ends of the cylinder. The advantages of the two-cycle over the four-cycle engine are that it requires a less number of valves and that it makes twice as many work- ing strokes in a given number of revolutions. At low speed, a two-cycle engine gives nearly twice the power of a four-cycle engine of the same speed and size. At high speeds, however, a part of the fresh charge is apt to escape from the cylinder and a part of the spent charge is apt to remain. This results in a serious reduction in the power and efficiency of the two-cycle engine. The theoretical efficiency of the two-stroke cycle is, however, exactly the same as that of the four-stroke cycle having the same compression pressure, and the pressures, temperatures, volumes, and work done are computed in exactly the same manner. 296 THE INTERNAL COMBUSTION ENGINE ART. 287 287. The Sargent Cycle Engine. The Sargent cycle has been developed in order to provide a cycle having a greater efficiency than the Otto cycle, and also to provide better means of speed regulation for engines of large power. The theoretical card of a Sargent cycle engine is illustrated in Fig. 159. In the Sargent cycle, the admission of the charge is stopped at some point during the suction stroke. This point is marked A on the card. During the remainder of the stroke the charge is expanded below atmospheric pressure, its final pressure and volume being represented by the point n. During compression stroke the charge is compressed to the point C. Explosion then occurs, the pressure rising to point X. Adiabatic expansion then follows, the charge expanding to point L. The exhaust valve then opens and the pressure falls to that of the atmos- FIG. 159. Theoretical card from a Sargent cycle engine. phere, represented by point m. The spent charge is now expelled from the cylinder. A fresh charge is then drawn in during the early part of the suction stroke and the cycle is repeated. The amount of power developed is adjusted by causing the governor to close the inlet valve at the proper point in the suction stroke, the valve closing early when the power required is small, and remaining open until the end of the stroke when the max- imum power is required of the engine. It will be seen from an inspection of the Sargent cycle card that it consists of two parts, a c x t being the equivalent of an Otto cycle, and a-t-l-m being an additional amount of work realized from the same quantity of heat. The Sargent cycle is therefore somewhat more efficient ART. 287 THE SARGENT CYCLE ENGINE 297 than is the Otto cycle, since it expands the gas more completely, reducing its terminal temperature (i.e., the temperature at point /) and therefore the amount of heat rejected. The computations of the pressures, volumes, etc., of the Sargent cycle will be as follows,: Let P a , V a , and T a be respectively the pressure in pounds per square foot, the volume in cubic feet, and the absolute tem- perature of the charge at point a, and designate the same quantities for the charge at points c, t, x, I, m, and n by appropriate subscripts. Let H a =the heat added at explosion and H r the heat rejected at exhaust. We will then have for the swept volume of the cycle V m V c . The weight of the charge will be RT a ' The volume of the compression space will be i (1) V V I * c ~ y a\ r> v^c The temperature of compression will be /-- 1 rji rj~i ( ' \ n^ 11 /Q\ * c ~~ * a \ T) I ~ * a \ ~-ir~~ j (y) \*-a / \" c / The rise in temperature resulting from the explosion will be The heat added as a result of the explosion will be H a =WC v (T x -T c ) The terminal temperature will be (6) x l 1 " 1 - T ( P '\" r v) Tl \ x ) The fall in temperature at the end of expansion will be The heat rejected will be H r =WC v (Ti-T a ). (8) 298 THE INTERNAL COMBUSTION ENGINE ART. 288 The efficiency of the cycle will be = J ^ .- (9) or C\(T X -T C ) or v, T x -T c -Ti + T a It will appear from this equation that the efficiency of the Sargent cycle, unlike that of the Otto cycle, depends on the temperature of explosion. The work represented by the area, c' c, a a', is P V P V IT T TJ L c'c- t a v a T) I c a U ~ ~ the work of expansion is P x V x -PiVi the work represented by the area a' a. mm' is of course, U am = Pa (V m -V a ); ....... (14) the total work of the cycle is P x V x -Pi Vl - P c V c +P a V a -P a V m +P a V c g) +2P a V a 288. The Diesel Cycle Engine. Another cycle which had been em- ployed for the internal combustion engine, and which is especially adapted for oil fuel, is known as the Diesel cycle. This also is a four-stroke cycle, and the card is shown in Fig. 160. During the first or exhaust stroke, the products of combustion are expelled from the cylinder. During the second or suction stroke, a charge of pure air is drawn into the cylinder. During the third or compression stroke, this air is compressed from point a to point c, the pressure rising to from 500 to 700 pounds per square inch. ART. 289 THE DIESEL CYCLE ENGINE 299 At the end of the compression stroke, as the piston again moves forward, expanding the charge, a quantity of fuel is injected into the cylinder by means of a pump. As a result of the adiabatic compression, the tem- perature of the air has been raised to such a value that the fuel is kindled and burns as it flows into the cylinder, imparting heat to the charge. It was originally proposed that this fuel should be injected at such a rate that the expansion of the charge would be isothermal, the heat supplied by the burning fuel being just equal to the work performed by the expand- ing charge. After the injection of the fuel ceases, the charge expands adiabatically. The isothermal expansion line is the line c d', and the c d FIG. 160. Theoretical cards from a Diesel cycb engine. adiabatic expansion line, the line d' e r in Fig. 160. Governing is effected by increasing or decreasing the quantity of fuel injected, which involves a change in the length of the isothermal, and in the final state of the work- ing fluid at point e' '. Increasing the quantity of fuel injected raises the final temperature of the charge and so reduces the efficiency of the cycle. Isothermal expansion of the charge during the fuel injection period results in a cycle of high thermodynamic efficiency for a given tempera- ture range. On the other hand, it is impossible to design a mechanism which will inject the fuel at exactly the proper rate to give isothermal expansion, and the mechanical efficiency of the engine employing it will be small. It has been shown in practice that it is better to admit the fuel at such a rate as to maintain the pressure practically constant during the early part of the working stroke. After all the fuel has been injected, adiabatic expansion commences. The form of card given by such an engine is shown in the same figure. Line c d, representing the isobaric, and line d e the adiabatic portion of the 300 THE INTERNAL COMBUSTION ENGINE PROBS. 1-4 expansion period. Comparing this card with the first one, it will be seen that the ratio of the mean to the maximum pressure is much greater in the case of isobaric than in the case of isothermal expansion, and that the mechanical efficiency of the engine is correspondingly better. In addi- tion, the engine employing isobaric expansion gives much more power, although the parts of the two engines must be of the same weight and cost. The practical advantages will thus be seen to lie entirely with the cycle which employs isobaric expansion. The methods of computing the states of the working fluid at the various points in the cycle are identical with those employed for the Otto cycle. The quantities of heat added or rejected, and the work performed during the several periods of the cycle may be readily computed. With a com- pression pressure of 600 pounds per square inch absolute, an original 1 23456789 10 Ratio of fuel Injection Period to Working Stroke. FIG. 161. Relation between efficiency and fuel injection period for a Diesel cycle engine employing isobaric expansion. pressure of 14.7 pounds per square inch, an original volume of 1 cubic foot, and an original temperature of oSO ' absolute, the compression volume will be 0.0714 cubic feet, and the compression temperature 1550 absolute, or 1090 F. The efficiency of the cycle under varying conditions of load may be seen by reference to Fig. 161, in which the abscissae are swept volumes up to the point d j expressed as a per cent of the total swept volume 100(F 6 -F C )\ ,. - - ^ ) and ordmates are efficiencies. a V c) / i.e., values of (V PROBLEMS 1. An Otto gas engine has a compression pressure of 90 Ibs. gage. Find the temperature of compression, assuming the air temperature to be 70 F. Ans. 935 abs. 2. Find the efficiency of the cycle. Ans. 43.3%. 3. Find the explosion pressure, assuming the rise in temperature to be 2500. Ans. 386 Ibs.-abs. 4. Find the terminal temperature. Ans. 1950 abs. PROBS. 5-24 PROBLEMS 301 5. Find the work done per pound of working fluid. Ans. 142,300 ft.-lbs. 6. Find the volume of the compression space per pound of working fluid. Ans. 3.31 cu.ft. 7. Find the terminal volume per pound of working fluid. Ans. 13.34 cu.ft. 8. Find the swept volume per pound of working fluid. Ans. 10.03 cu.ft. 9. Find the work done per cubic foot of swept volume per cycle per pound of working fluid. Ans. 14,200 ft.-lbs. 10. Assuming that a Sargent cycle engine, having the same compression as the Otto cycle engine in Problem 1 and the same explosion pressure as in Problem 3, expands its charge to atmospheric pressure, what is the terminal volume per pound of working fluid ? Ans. 33.6 cu.ft. 11. Find the work of expansion. Ans. 273,000 ft.-lbs. 12. Find the work of compression. Ans. 52,700 ft.-lbs. 13. Find the work represented by the area a' a mm' in Fig. 159. Ans. 43,000 ft.-lbs. 14. Find the net work of the cycle per pound of working fluid. Ans. 177,200 ft.-lbs. 16. Find the heat added per pound of working fluid. Ans. 423 B.T.U. 16. Find the efficiency of the cycle. Ans. 54.0% 17. In a Diesel cycle the compression is carried to 700 Ibs. absolute. The initial temperature is 70 F. Find the compression temperature. Ans. 1620 abs. 18. Find the volume of compression space per pound of working fluid. Ans. 0.86 cu.ft. 19. Assuming that the temperature of the working fluid is doubled during isobaric expansion, find the work done per pound of working fluid during isobaric expansion. Ans. 86,600 ft.-lbs. 20. Find the work done per pound of working fluid during compression. Ans. 142,000 ft.-lbs. 21. Find the work done per pound of working fluid during adiabatic expansion. Ans. 239,000 ft.-lbs. 22. Find the net work of the cycle per pound of working fluid. Ans. 186,000 ft.-lbs. 23. Find the heat added. Ans. 384 B.T.U. 24. Find the efficiency of the cycte. Ans. 61.5%. CHAPTER XX NOTES ON THE DESIGN AND PERFORMANCE OF INTERNAL COMBUSTION ENGINES 289. Thermal Behavior of the Charge during Induction and Com- pression. In the theory of the Otto cycle developed in the previous chapter the charge entering the cylinder was assumed to have the properties and temperature of atmospheric air. Actually the charge consists of a mixture of air and combustible gas, and its properties are therefore some- what different from those of pure air. Since the wall of the cylinder has a temperature somewhat higher than that of the atmosphere, the charge is heated as it enters the cylinder. As it is drawn into the cylinder, it mixes with a considerable volume of spent charge whose temperature is relatively high. In consequence, the temperature of the working fluid contained in the cylinder at the beginning of compression is almost always considerably higher than that of the atmosphere, and the effect is, of course, to reduce the power of the engine by reducing the weight of the working fluid. During the compression stroke the temperature of the charge rises. As soon as its temperature exceeds that of the cylinder wall, it parts with heat by conduction and radiation. The compression is therefore not adiabatic, but is approximately poly tropic, the actual compression line lying between the adiabatic and the isothermal lines. The index of the compression line ranges from 1.25 to 1.35, its exact value depending upon the size, the speed, and the design of the engine. In general the index of the compression curve will have a high value in the case of a large fast-running engine with a small area of wall surface exposed to the charge, and will have a low value when the opposite conditions obtain. Leakage has the same apparent effect upon the form of the compression curve as does heat absorption by the cylinder wall, and, like it, produces more serious effects in small or slow-speed than in large or high-speed engines. Leakage, however, is more detrimental than heat absorption in its effects upon the*power and efficiency of the engine. 290. Thermal Behavior of the Charge during Ignition and Expansion. At the end of the compression stroke, combustion begins. In develop- ing the theory of the Otto cycle, it was assumed that combustion took place instantly. Such is not the case in practice, since combustion is a 302 ART. 290 THERMAL BEHAVIOR OF THE CHARGE 303 chemical reaction, and a chemical reaction is a progressive and not an instantaneous process. The rate at which a reaction occurs is variable, depending upon the temperature and density of the reacting substances, and upon the extent to which they are diluted by inert substances and the compounds produced by the reaction. The result of the combustion is to greatly increase the temperature of the charge, to reduce the density of the reacting substances, and to dilute them with the products of com- bustion. Each of these effects reduces the rate at which the reaction progresses, so that although it is rapid at first, the rate quickly drops off, and the reaction in theory takes an infinite time for its completion. When the temperature of the exploding charge reaches a value of about 3300 to 3600 absolute, which it does almost immediately, the reaction Suction Line -* FIG. 162. Actual and theoretical Otto cycle cards compared. practically ceases, and further combustion takes place only after the temperature begins to fall. This phenomenon is known as delayed com- bustion, as suppressed combustion, and as dissociation. As a result of the comparatively gradual and incomplete combustion of the charge, the rise in pressure resulting from the explosion takes an appreciable time, which modifies the card by giving it the form shown in Fig. 162, where the explosion line c-x is curved instead of being vertical, as would be the case were the combustion instantaneous. Further- more the temperature and pressure realized as a result of the explosion are only a fraction of. what they would be were the combustion instant and complete. Hence in order to obtain a given rise in pressure, and therefore a given quantity of work from the charge, it is necessary to use a larger quantity of fuel than theory would indicate. The actual efficiency 304 NOTES ON INTERNAL COMBUSTION ENGINES ART. 291 of the engine is therefore seriously reduced by the phenomenon of sup- pressed combustion. The most of the fuel remaining unburned at point x begins to burn as soon as the adiabatic expansion of the charge permits of a sufficient fall in temperature. This is known as after burning. The combustion is not absolutely complete at the end of the expansion stroke, but it is usually so far completed that only slight traces of unburned gases can be discovered in the exhaust. The temperature of the charge, as a result of the explosion, usually reaches a value of from 3000 to 3600 absolute. At these extreme tem- peratures gases readily part with heat to their surroundings by conduc- tion and radiation. The walls of the cylinder are of course cooled by a water jacket or other suitable means. Since the jacket maintains the walls at a temperature usually ranging from 150 to 250, the rate at which the gases give up heat to the walls is very great. That portion of the charge which is in immediate contact with the wall is cooled by con- duction almost to the temperature of the wall itself. The remainder of the charge is at a very much higher temperature and radiates its heat to the wall. As a result of the phenomenon of after burning the charge receives heat during the working stroke. At the same time, it is losing heat by conduction and radiation to the cylinder walls and by transform- ing it into the work of expansion. The expansion which takes place during the working stroke is therefore not adiabatic, and the rate of heat transfer is usually such that more heat is lost to the wall than is gained from the after burning of the charge. The index of the expansion line is therefore usually somewhat greater than the index of the adiabatic expansion line, sometimes ranging as high as 1.7, although its usual value lies between 1.41 and 1.45. The same operating conditions which tend to reduce the heat loss to the cylinder wall during the compression stroke tend to reduce the heat loss during the working stroke, but whereas these conditions tend to raise the value of the index of the compression curve, they tend to lower the value of the index of the expansion curve. 291. Form of the Actual Card. The form of the actual card obtained from an Otto cycle engine is that shown in full lines in Fig. 162. The line which would be obtained were the compression of the charge adiabatic is the dotted line ac'. It will be noted that the actual compression pres- sure is less than that which would result from adiabatic compression. In consequence, the actual compression temperature will also be con- siderably less than that resulting from adiabatic compression, and the efficiency of the actual cycle will therefore be less than the efficiency of theoretical cycle. Were the combustion of the charge instantaneous, the line ex would be vertical. Since such is not the case, the line will have the general form shown; its exact form depending on the instant at which ignition ART. 292 LOSSES IN THE GAS ENGINE 305 commences, the speed and size of the engine, the character of the charge, etc. The actual expansion line x-t, falls below the adiabatic expansion line, x't' ', since its index is greater than the index of the adiabatic line. Were the entire heat of combustion contained in the ,charge utilized in instantly raising its temperature, and were the specific heat of the charge constant, its pressure would rise to the point x" as a result of the explosion, the adiabatic expansion line would be the line x" t" , and the work of the cycle would be very greatly increased.' On account of wire drawing and fluid friction, the corner of the card at t is rounded, and the suction line falls below the exhaust line in the manner already shown in Fig. 154. This results in reducing the pressure at the beginning of compression, and the loop enclosed between the suc- tion and exhaust lines represents negative work. 292. Losses in the Gas Engine. The losses which occur in an Otto cycle engine may be classified as follows: First: Losses due to delayed or suppressed combustion. Second: Losses due to the radiation and conduction of heat to the cylinder walls. Third : Losses due to the leakage of the charge. Fourth: Exhaust losses or losses due to the sensible heat of the charge at the termination of expansion. Fifth: Losses due to fluid friction and wire drawing of the charge. Sixth: Losses due to the mechanical friction of the engine. It is obvious that the efficiency of the actual cycle must always be less than that of the theoretical cycle. Hence the sum of the six losses is always greater than the exhaust loss of the theoretical Otto cycle having the same compression pressure, and supplied with the same quantity of heat energy. The theoretical loss made necessary by the form of the cycle can be reduced only by increasing.the compression pressure. As the compression pressure is increased, the explosion pressure is increased in very nearly the same proportion. This makes necessary a corresponding increase in the strength and weight in the parts of the engine, and increases the cost of its construction. Compression pressures higher than 200 pounds gage are therefore not practicable except when very lean fuels are employed. When fuels of high heating value (such, for instance, as gasoline vapor), are employed, the compression pressure must be much less than 200 pounds in order to avoid excessive explosion pressures. The effect of delayed combustion is, of course, to reduce the explosion pressure and therefore to reduce the amount of work performed during the cycle and the efficiency of the engine. Were the charge to reach the temperature which would result from complete combustion, the loss to the cylinder walls would be greater than is actually the case. Since .the 306 NOTES ON INTERNAL COMBUSTION ENGINES ART. 292 combustion of the charge continues during the working stroke, a small part of the heat so developed is transformed into work, but the most oJ it is rejected in the sensible heat of the exhaust. Any portion of the charge remaining unburned at the instant of release is, of course, rejected and the potential heat contained in it is lost. The effect of suppressed combustion is therefore to increase the loss in the exhaust and to decrease the loss to the water jacket. The loss from suppressed combustion may be diminished by the employment of a lean charge (i.e., one which has a comparatively low heating value). The effect of the lean charge is to reduce the theoretical maximum temperature of explosion, and therefore to make possible a quicker and a more complete burning of the charge. The effect of the heat transfer from the charge to the walls of the cylinder, where it is absorbed by the jacket water, is to reduce the work required for compression, the explosion pressure, and the work done dur- ing the expansion stroke. The net result is that the work done during the cycle is diminished somewhat, and the efficiency of the cycle is unfav- orably affected. A considerable part of the heat transferred to the water jacket is, however, heat that would otherwise be rejected at exhaust, and the amount of heat lost to the water jacket is not a true measure of the power and efficiency lost as a result of water jacketing. While it is well to reduce the jacket loss to minimum, it is not as serious in its effects upon the engine efficiency as are other forms of losses. The effect of leakage during the compression stroke is to allow a portion of the charge to escape after work has been done upon it, but before it has returned any portion of this work. Furthermore it carries away the potential heat of combustion, which is, of course, entirely lost. Leakage during the expansion stroke does not affect the efficiency of the engine so seriously, but it does produce some loss by lowering the mean pressure during the expansion period. It might be thought that on account of the high pressures employed, leakage would be a serious matter in the case of the gas engine. When, however, the valves, the piston, the cylinder, and the rings are in good order, no appreciable leakage can take place. The exhaust loss may be reduced by expanding the charge more completely, as is done in the Sargent cycle engine. The additional amount of work obtainable in this way is not, however, very great, as may be seen by reference to Fig. 159, in which the area a t I m represents the power usually obtained in such a cycle from the exhaust losses of the Otto cycle. It will be seen that the area in question is a rather small portion of the entire area of the card. It has often been proposed to save some of the exhaust loss by compounding the gas engine (i.e., by discharging the exhaust from the first cylinder into a larger cylinder in which it may be more completely expanded). It will usually be found, however, ART. 293 LIMITS OF THE ROTATIONAL SPEED 307 that the amount of work realized after deducting the extra losses incurred in transferring the charge from one cylinder to another, will not be sufficient to overcome the friction of the added cylinder. The employ- ment of the Sargent cycle is a preferable alternative for utilizing the available energy of the exhaust. The Tosses due to friction and wire drawing of the charge may be reduced by the employment of large valves which are opened, promptly by properly designed mechanism. These losses increase with the speed of the engine, but do not become serious at the speeds ordinarily employed in stationary practice. The conditions of high mechanical efficiency in the gas engine are the same as in the steam engine. It is not possible, however, to improve the mechanical efficiency of the gas engine by compounding, as may be done in the case of the steam engine. The mechanical efficiency of the gas engine may be improved only by careful attention to the details of the design of the mechanism and to the lubricating system. The friction losses are usually from 50 to 100 per cent higher in gas engines than in steam engines of equal power. It will be seen from the above discussion that the conditions which favorably affect the efficiency of the gas engine are, in general, a high speed of rotation, the use of units of large power, the adoption of that form of cylinder which reduces the wall area per pound of charge per cycle to a minimum, and the employment of a lean charge. The most serious loss is that due to the delayed combustion of the charge. The Diesel cycle engine avoids the difficulty of delayed combustion and there- fore gives promise of higher practical efficiency than does the Otto cycle engine, although other forms of loss (e.g., loss due to leakage) produce more serious results in the Diesel engine than in the Otto engine. 293. Limits of the Rotational Speed of Internal Combustion Engines. It has already been pointed out that the higher the speed at which a gas engine operates, the greater will be its efficiency. At ordinary speeds the power of the engine is increased by increasing the speed, since at ordinary speeds the work per cycle remains practically constant, and the number of cycles increases in direct proportion to the speed. It is not possible, however, to indefinitely increase the power of an internal com- bustion engine by increasing its speed. As the speed of the engine increases, the effect of wire drawing in reducing the quantity of charge taken in per cycle also increases. At speeds below 400 or 500 revolu- tions per minute, this effect is scarcely noticeable when the engine is equipped with mechanically operated valves. At speeds greater than this, however, the net work per cycle gradually falls off on account of the wire drawing of the charge. The speed at which the power of the engine reaches its maximum value depends upon the size and form of 308 NOTES ON INTERNAL COMBUSTION ENGINES ART. 294 the valves and ports. In general the larger and straighter the gas passages, the higher will be the speed at which the maximum power of the engine is realized. With ports of the usual proportions, it will be found that small two-cycle engines deliver their maximum power at from 700 to 900 revolutions per minute, while four-cycle engines deliver their maximum power at from 1200 to 1800 revolutions per minute. At speeds higher than this, the quantity of charge taken per cycle by the engine diminishes at a faster rate than the speed increases and the power of the engine falls off. At very high speeds, ignition fails from lack of sufficient compression of the charge, and the speed of the engine finally reaches a maximum where the power developed is just equal to that absorbed by friction. In the case of stationary engines, the speed is, of course, very much lower than in automobile and other light high-speed engines. The usual speed for very large engines (i.e., engines of over 1000 horse-power) is from 75 to 150 revolutions per minute, the present tendency being to increase these speeds. In the case of single-acting stationary engines, the speed is usually from 200 to 300 revolutions per minute, although higher speeds are possible. As a usual thing, the speed of a large gas engine is limited by the highest speed at which the valve motion will work quietly and without undue wear. It will thus be seen that the speed of a gas engine is really limited by the design of its parts, and will of necessity be lower in the case of a large engine having heavy parts than in the case of a small engine having light parts. There is no reason, however, why much higher speeds may not be employed in stationary service, with an accompanying gain in economy of operation. 294. The Design of Internal Combustion Engines. In designing an internal combustion engine, it is usually sufficient to assume that the charge is taken in at atmospheric pressure and temperature, that the compression and expansion lines are polytropic, that the index of the compression line is 1.35, that the index of the expansion line is 1.45, that the explosion occurs instantly, that the rise in temperature as a result of the explosion is 2500, that the specific heats of the charge are those of pure air; that the card factor is about 90 per cent, and that the mechanical efficiency of the engine is 85 per cent. Where actual cards from engines of practically similar design and approximately the same speed are available, corrections may be made in these figures. The work of compression and of expansion per pound of working fluid may be computed by the methods outlined in Art. 283. Their difference is the net work per pound of working fluid. The volume per pound of working fluid at the beginning and end of compression is next com- puted. The difference between these two volumes is the swept volume per pound of working fluid. Dividing this into the net work per pound ART. 295 METHODS OF IGNITION 309 of working fluid, we will have the net work per cubic foot of swept vol- ume per cycle, a quantity which we may designate by the letter W. The indicated horse-power of the engine will then be HP 0.9 T7 7 N 33.000 ' in which HP is the indicat&d horse-power of the engine, W is the net work per cubic foot of swept volume per cycle, N is the number of cycles (i.e., explosions) per minute, and V is the swept volume of the cylinder in cubic feet. The brake horse-power of the engine at maximum load will be about 85 per cent of its indicated horse-power at maximum load. A gas engine is usually rated at from 2 /3 to 3 / 4 of the maximum brake horse- power which can be obtained under the most favorable conditions of operation. After obtaining the cylinder dimensions and the form of card, the remainder of the design of a gas engine is a matter of proportioning the parts to properly resist the strains which come upon them, and to arrange the valve mechanism so that it operates with a minimum of shock and wear. The design of the details of a gas engine is very similar to the design of the same parts of a steam engine, the only difference being produced by the greater shocks and higher pressures encountered in gas engine work, and the necessity of thoroughly water-jacketing or otherwise cooling all parts exposed to the working fluid. 295. Methods of Ignition. Three methods have been employed for igniting the charge of a gas engine, namely, by an electric spark, by contact with hot metal, or by contact with a flame. The latter method, although formerly much used, is now completely out of date, while the second method, known as hot tube ignition, is seldom used except for stationary engines operating on natural gas. In the early types of gas engines in which, little or no compression was used, a flame was kept burning in a separate chamber and by opening a slide valve in a passage connecting this chamber with the cylinder of the eng'ne at the proper pc hit in the stroke, the flame was communicated to the charge. So long as the compression pressure was low, and the service required of the engine was not severe, this method of ignition was fairly satisfactory. It was, however, soon superseded by the method known as hot tube ignition. The hot tube igniter, which is illustrated in Fig. 163, consists of a passage hi the cylinder wall which terminates in a tube of wrought iron or nickel, kept heated by means of an argand flame which surrounds it. At the beginning of the compression stroke, the tube is filled with spent charge. As the compression proceeds, the spent FIG. 163. Hot-tube igniter. 310 NOTES ON INTERNAL COMBUSTION ENGINES ART. 295 charge is compressed into the hot part of the tube and finally, near the end of the compression stroke, some of the fresh charge enters the hot part of the tube and is ignited. By its expansion, a flame is forced into the cylinder, and the main body of the charge thus ignited. It will be seen that the point in the cycle at which the explosion occurs depends upon the relative volume of the hot tube and the connecting passage, and upon the degree of compression. If ignition fails, or is too late, the volume of the hot tube must be increased. If ignition is early, the length and volume of the connecting passage must be increased, or the volume of the tube decreased. Other things being equal, the higher the degree of compression, the earlier the time of ignition. So long as the quality of the fuel supplied to the engine is uniform and the conditions of operation are steady, hot tube ignition is fairly satisfactory with com- paratively high compression pressures. It can only be used, however, with hit-and- miss governing. Electric ignition is effected in either of two ways, the first being known as the "jump spark" method and the second as the " make-and-break spark" method. The principle of the jump spark is illustrated in the diagram shown in Fig. 164. In this FIG. 164. Diagram of a jump spark ignition apparatus. diagram a-a are two platinum terminals contained within the cylinder of the engine in contact with the charge and separated by about Vs2 of an inch. These terminals are connected with the induction coil shown, which gives a high voltage. At the proper time in the revolution of the engine, a connection is made in the primary circuit of this coil by means of a commutator or contact maker operated by the engine. The flow of primary current through the coil produces a secondary current of immensely higher voltage and much lower amperage, which passes between the terminals of the spark plug, igniting the charge. B is a battery or other source of current for the primary circuit of the induction coil. This current passes through the commutator c when it is in the position shown, thence through the vibrator V, through the primary circuit d and back to the battery. The vibrator is a device for interrupting the current and causes the primary current to be pulsating in character. The secondary current, which is induced by the presence of the pulasting primary current, is similar in character, but since the primary circuit of the induction coil consists of only a few turns, while the secondary circuit consists of many hundreds of turns of wire, all wound around a soft iron core, the voltage of the secondary current will be sufficiently great to force it to jump the terminals of the spark plug. These ART. 296 CARBURETORS 311 terminals must of course be carefully insulated from one another or the current will be short-circuited instead of passing through the charge which is to be inflamed. A condenser / is usually connected into the primary circuit of the induction coil in order to increase the effectiveness of the apparatus. The apparatus used for the make -and -break spark is much simpler, although it has the disadvantage of employing a movable part within the cylinder. The current originates in a battery B as shown in Fig. 165, passes through the spark coil C, which is a coil of wire surrounding a soft iron core, through the platinum terminals of the make-and-break spark plug P, and then returns to the battery. At the instant when it is desired to inflame the charge, the terminals being in contact, they are quickly separated and an arc is created which effects ignition. The purpose of the spark coil C is to intensify the arc by its inductive action. In order to economize current I I illinium FIG. 165. Diagram of a make-and-break ignition apparatus. the mechanism of the spark plug is made in such a way that the terminals are sepa- rated until just before the spark is to be produced, when they come together for the instant just preceding the breaking of the circuit. 296. Carburetors. For portable internal-combustion engines such as are used in automobiles, launches, etc., it is customary to use as the fuel a hydro-carbon vapor usually obtained by the evaporation of gasoline. The gasoline is evaporated and mixed with the air which forms the remainder of the charge, in an apparatus known as a carburetor. Gas- oline, when sprayed into air, rapidly evaporates at all ordinary temper- atures, and fills the air with its vapor. If the air is allowed to become saturated with the gasoline vapor, the quantity of vapor contained in the air will be so great that the mixture is not explosive. A charge in which too little gasoline vapor is mixed with the air, will also fail to ignite. The office of the carburetor is then to introduce into the current of jiir entering the cylinder of the engine, a proper quantity of gasoline, 312 NOTES ON INTERNAL COMBUSTION ENGINES ART. 296 in such a manner that it will be completely evaporated and thoroughly mixed with the air. The simplest form of carburetor is illustrated in principle in Fig. 166. It consists of a bowl or reservoir in which the gasoline is main- tained at a constant level by means of a float feed-valve. This valve consists of a ring r, usually of cork, attached to a lever and pivoted in such a way that when the level of the gasoline sinks, the weight of the float will open the feed valve /, admitting more gasoline. From this chamber the gasoline flows to a small nozzle n, through a valve termed the needle valve. By varying the opening of this needle valve, the quantity of gasoline delivered through it in a given time by a given head of gaso- line, may be varied. The needle valve is placed in a restricted passage in the air inlet. During the suction stroke of the engine, a quantity of air is drawn through this re- stricted passage at high veloc- ity, and in consequence, the pressure of the air in the passage is less than the pres- sure of the atmosphere. The difference in pressure causes a; jet of gasoline to flow from the needle valve in the form of a fine spray, and to mix with the on-rushing current of air. A second supply of air is taken through the check valve v, termed the auxiliary inlet, at a point beyond the needle valve, and mixes with the air containing the gasoline vapor. By adjusting the level of the gasoline in the float-feed chamber, the opening of the needle valve, and the strength of the spring con- trolling the opening of the auxiliary air inlet, the quantity of gasoline vapor in the charge of air may be controlled and a correct mixture obtained at all ordinary engine speeds. Most forms of carburetors at present on the market are modifications of the apparatus described. The arrange- ment of the several parts and the general appearance of the apparatus varies greatly. In some forms of the carburetor, however, the air is FIG. 166. Simplified diagram of a carburetor. ART. 297 THE TESTING OF INTERNAL COMBUSTION ENGINES 313 drawn over a small quantity of gasoline contained in a bowl, instead of spraying the gasoline into the air. Such carburetors are not generally provided with auxiliary air inlets. A float-feed carburetor is not usually used for furnishing gasoline vapor to stationary engines. In the cas& of stationary engines, the speed is usually constant and the range of adjustment required of the gasoline vaporizer is very much less. In some cases, the incoming change of air is draWh over a pan in which the gasoline is maintained at constant level. In other cases the gasoline is simply allowed to leak through a noedle valve into the pipe through which the air supply is drawn. Neither method of vaporization is as satisfactory, however, as the use of a carburetor. 297. The Testing of Internal Combustion Engines. The following quantities must be determined in making a complete test of an internal combustion engine of the Otto type. First, the pressure and temperature of the atmosphere and of the gas in case a gaseous fuel is employed. Second, the heating value of the fuel. Third, the weight or volume of the fuel supplied to the engine. Fourth, the volume of the air supplied to the engine. Fifth, the number of revolutions per minute. Sixth, the number of cycles per minute. Seventh, indicator cards are taken from the cylinders. Eighth, the weight of jacket water used, and its initial and final temperature. Ninth, the brake horse-power of the engine. The precautions which must be taken in making such a test to insure that the data are properly taken, have been outlined by a committee of the A.S.M.E., and the rules have been published by the society in pamphlet form. It is important that the conditions throughout the test should be as nearly uniform as possible. Readings should be taken at frequent intervals, say every ten minutes. A gas engine test may be analyzed graphically in a manner similar to that already described in Art. 195. The actual card of the engine is superimposed upon the theoretical card which would be given were the same quantriy of heat added to a charge of pure air, as was actually introduced into the engine, per cycle, in the fuel used. After determining the indicated horse-power shown by the different sets of cards taken during the test, that card should be chosen whose form and area are nearest to the average. The heat supplied per pound of charge is next computed, and from the dimensions of the engine and the pressure of the atmosphere a theoretical card is drawn. This card 314 NOTES ON INTERNAL COMBUSTION ENGINES ART. 297 is shown in dotted lines in Fig. 167. Upon this theoretical card, to the same scale of pressures and volumes, is superimposed the card shown from the test as best representing the average conditions. Usually the beginnings of the compression lines coincide on the two cards, since the effect of wire drawing in reducing the pressure of the charge at the beginning of compression is inappreciable. The compression line of the actual card a-c will, however, fall below that of the theoretical card a-c' in the manner shown. If the charge were compressed to point c\ 1 and its combustion were then instant and complete, the heat added would raise the pressure to some point x", whose position may be computed. If the charge then FIG. 167. Graphical analysis of the losses in an Otto cycle engine. expanded adiabatically following the line x"t" , the engine would give the card Qr-ci-x"-t". The difference between the area x'-t'-t"-x" and the area CL-C'-CI will then be the power lost on account of the heat transferred to the walls of the cylinder during the compression stroke. The area ti-x\-x"t" then represents the work lost on account of the combined effects of suppressed combustion and heat loss to the cylinder wall during the working stroke. Were the combustion not suppressed, the expansion line would probably have approximately the form x"t^. Were there after burning but no heat transfer to the cylinder wall, the expansion line would have approximately the form x\t" . The available exhaust loss which might be recovered by complete expansion of the charge, ART. 298 ACTUAL EFFICIENCIES OF INTERNAL COMBUSTION ENGINES 3 1 5 is represented by the area t-e-a, which is the power which would be obtained from the charge were it expanded adiabatically down to atmos- pheric pressure. The remainder of the exhaust loss cannot be recovered by expansion of the charge. The^shaded areas represent the loss due to fluid friction, and to the fact that it takes an appreciable time for the explosion pressure to reach its maximum. From a complete internal combustion engine test a heat balance may be made out showing the actual distribution of the heat supplied to the engine. The proportion of the heat lost in friction and that transformed into useful work may be readily computed from the brake and the indicated horse-power of the engine. The heat transferred to the jacket water during the test may be found by measuring the water used and obtaining its rise in temperature. The sensible heat rejected at the exhaust may be found by computing the temperatures of the charge at point ti and at point a and multiplying the difference by the specific heat of the charge at constant volume. The remainder of the heat supplied is rejected in the exhaust in the form of unburned combustible, or is radiated from the engine, or represents the error of the test. It may be noted that the temperature of the exhaust, as obtained by a thermometer, is not the temperature corresponding to the point TI, but is lower on account of the work performed by the exhaust in expansion down to atmos- pheric pressure against the resistance of the air. 298. Actual Efficiencies of Internal Combustion Engines. The total efficiency of a good gas engine usually ranges between 20 and 30 per cent. Efficiencies as high as 38 per cent have been claimed, but it is very doubtful if total efficiencies higher than 32 per cent have ever been realized. In Table XIV will be found the results of typical tests of different forms of internal combustion engines. These are not the highest efficiencies which have been realized, but are those which have been realized continuously in service. It will be seen that the efficiency of the internal combustion engine is higher than that of the steam engine or steam turbine. The cost of fuel is therefore smaller in the case of the internal combustion engine than in the case of a steam engine or steam turbine. The cost of attendance is also smaller. On account of the high cost of an internal combustion engine plant, however, the fixed charges are large. In units of small power, the cost of fuel and of attendance is the principal item of expense. In units of large power the fixed charges upon the invest- ment become the principal item. In general, it will be found that in small powers, the internal combustion engine will be the cheapest one to operate, while in large powers the steam plant, and more especially the steam turbine plant, may be operated at the minimum of expense. When, however, the cost of fuel is high, as it is in certain parts of the 316 NOTES ON INTERNAL COMBUSTION ENGINES ART. 298 world, the internal combustion engine is the prime motor of the highest commercial efficiency. TABLE XIV EFFICIENCIES OF MODERN INTERNAL COMBUSTION ENGINES Kind of Fuel. Nominal Brake H.P. a* w $(*$ F 3 O -^ ^E w . go* .s1 fc o a; j3 wl .Sfe go w Producer Efficiency Per Cent. J (11) the net work of adiabatic compression will therefore be r-i As a usual thing the actual work of compression will be somewhat greater than this. 313. Losses Due to Clearance and Altitude. The indicated power lost on account of the presence of air in the clearance space of the compressor at the end of the discharge period is inconsiderable in amount, since the air performs almost as much work during its expansion as was performed upon it during its compression. Were there no heat transfer to the cylinder walls, there would be no loss of power from clearance. However, the use of clearance necessitates the employment of a compressor cylinder whose swept volume is considrably larger than the volune of the free air com- pressed per stroke. On account of this increase in size of the compressor cylinder, the friction loss in the compressor will be larger and the first cost of the machine will be greater than they would be if a cylinder without clearance were used. The use of large clearance in connection with an air compressor is therefore undesirable and should be avoided as far as possible. The ratio of the quantity of the free air actually taken in per stroke, to the swept volume of the air compressor is termed the volumetric 338 COMPRESSED AIR ART. 315 efficiency of the compressor. A high volumetric efficiency is desirable for the reasons already indicated. This is particularly the case when the compressor is to be operated at high altitudes. At considerable elevations the pressure of the air is much reduced, the pressure dropping off approx- imately at the rate of one-half pound absolute for each thousand feet in elevation above the sea level. The effect of this reduction in the initial pressure of the air is to decrease the weight of a given volume of free air, and therefore, the decrease in volume of compressed air delivered by each stroke of the piston. Consequently larger compressors are required at high altitudes than at sea level, and the volumetric efficiency of the compressor at high altitudes is less than it is at sea level. Compressors are usually rated by the number of cubic feet of free air which they will deliver per minute at normal speed. It is, not however, the number of cubic feet of free air, but the number of cubic feet of compressed air required which determines the size of the compressor. At high altitudes, there- fore, it is an important matter to make certain that the compressor is of sufficient capacity. 314. Mechanically Operated Valves. When an air compressor equipped with automatic valves is operated at high speed, it becomes necessary to provide them with rather stiff springs, in order to insure that they shall close promptly and avoid waste of air. The use of such springs, however, causes a waste of power and a reduction in the capacity of the machine, as was seen when comparing the actual air compressor diagram with the theoretical diagram in Fig. 175. The stiffer the springs with which the valves are equipped, the greater the difference in pressure which will be required in order to cause them to open. In order to avoid the loss in power and capacity resulting from the use of automatic valves, the larger size of air compressors are often equipped with semi-rotary valves similar to the valves used in a Corliss engine, the inlet valves being similar in form to Corliss exhaust valves and the discharge valve similar in form to Corliss inlet valves. In many cases inlet valves of the Corliss type are combined with automatic discharge valves. 315. Blowing Engines. An air compressor which delivers air under a pressure of from 15 to 30 pounds for use in blast furnaces and steel works, is usually termed a blowing engine, and the cylinder of such a compressor is termed a tub. The principles of operation of blowing engines are the same as those of other air compressors. Blowing engines are usually fitted with mechanically operated valves, instead of automatic valves, since they are commonly operated at high speed on account of their large capacity. However, several builders are now equipping blowing engines with automatic valves made of thin sheet steel which are held against their seats by very light springs. Since blowing engines deliver air against comparatively low pressure, the losses due to the heating of ART. 316 MOISTURE IN COMPRESSED AIR 339 the air by adiabatic compression are comparatively small, and those due to fluid friction and the imperfection of the valve action are comparatively large. Consequently, blowing engines are made single stage, and a great deal of care is taken in designing the valves. 316. Moisture in Compressed Air. The principal difficulties encoun- tered in the use of compressed air arises from the moisture which is con- tained in the air. Air which is compressed to a pressure of 80 pounds gage, is reduced to about 15 per cent of its former volume. Consequently a given mass of it can contain at a given temperature only about 15 per cent of the moisture which it was able to contain previous to compression. Hence if the humidity of the air is greater than 15 per cent, some of the moisture will be deposited as water in the receiver and piping system. Usually, from 50 to 80 per cent of the moisture contained in the air is deposited in the piping system on this account and it gives a great deal of trouble, particularly in winter, from freezing. In order to reduce the trouble from this source, it is customary to cool the air coming from the air compressor, in order that the moisture which it contains may be deposited in the receiver and removed before the air enters the piping system. This process is known as after-cooling. In order to reduce the quantity of moisture in the air, and also in order to reduce the amount of work required to compress it, it is advisable to take the supply of air for the compressor from the coolest point possible. 317. Example of Air-compressor Design. The following example will serve to show the method of calculating the size of air-compressor cylinders. Assume that a compressor is required which will deliver 100 cubic feet of compressed air per minute at a gage pressure of 120 pounds. The normal pressure of the atmosphere will be assumed to be 13 pounds per square inch and the atmospheric temperature to be 60. The absolute pressure of compression will be 133 pounds per square inch. The ratio of the final to the initial pressure will be 133^13=10.2. The number of cubic feet of free air required per minute will therefore be 1020. If the compressor is to operate at 60 revolutions per minute, the number of cubic feet of free air compressed per stroke must be 8.53. In order to equalize the work done in the two cylinders of a two-stage compressor, the ratio of compression should be the same in each one. The ratio of com- pression in each cylinder will therefore be The pressure of the air in the intermediate receiver will therefore be 13X3.2 =41.5 Ibs. The volume of the air will be 340 COMPRESSED AIR ART. 318 Assuming that the clearance volume of the cylinder is 4 per cent of the swept volume, we will have for the volume of the air contained in the cylinder at the beginning of the suction period, 4-4-0.438=9.14 per cent of the swept volume. Since the total volume of the cylinder is 104 per cent of the swept volume, the volume of the free air taken in per stroke will be 104-9.14=94.86 of the swept volume of the cylinder. The swept volume of the cylinder must therefore be 8.53 -f-. 949 = 9 cubic feet. Assuming the stroke of the compressor to be 4 feet, the diameter of the low-pressure cylinder will be 20^ inches. In practice, this diameter would be somewhat increased. With the same ratio of compression and the same clearance volume in the high-pressure cylinder the swept volume of the high-pressure cylin- der will be equal to the swept volume of the low-pressure cylinder divided by the ratio of compression. Consequently, the diameter of the high- pfessure cylinder will be 20J -T- V32 - 1 1 inches. The valves of the compressor are usually designed so that the nominal velocity of the air passing through them will be 6000 feet per minute. In order to prevent the cumulative action which would result from the heating of the cylinder w r alls by the adiabatic compression of the air, a water-jacket must be provided. Were it not for this water-jacket, the cylinder walls would become heated by the air and they in turn would heat the entering air. The adiabatic compression of this heated air w r ould still further heat the walls and the result would be that both the temperature of compression and the temperature of the cylinder walls would increase together until radiation from the walls would balance the heat received from the air. As a result, a large quantity of power would be required for the operation of the compressor, its volumetric efficienc}^ would be seriously reduced, and it would be impossible to lubricate the rubbing parts. 318. Flow of Air or Gas in a Tube. When a fluid is caused to pass through a tube it is found that a difference in pressure is required at the two ends of the tube in order to cause the passige of the fluid. The amount of this difference in pressure is usually much greater than that which is required in order to give the fluid the actual velocity which it has in the tube. We are therefore obliged to conclude that there is a force analogous to friction opposing the flow of the fluid, and that the work done by this force is transformed into heat and raises the temperature of the fluid. Experiment shows this to be the case. It further shows that ths amount of this force is proportional to the length of the tube, and to the 1.8 power of the velocity of the fluid and inversely proportional to the 1.3 power of the diameter of the tube. It shows that the force ART. 318 FLOW OF AIR OR GAS IN A TUBE 341 depends upon the character of the walls of the tube, and is greater in the case of tubes having rough walls and less in the case of smooth walls. It shows that the force is proportional to the density of the fluid .and also to a property which we term the viscosity of the fluid. Glycerine, for instance, is not greatly denser than water, and yet we know by experience that it is thicker or more viscous and we find that the force of fluid friction is much greater in the case of glycerine than in the case of water. We may express these observed facts by the equation in which dP is the difference in pressure in pounds per square foot, between two points in a tube through which a fluid is flowing, dL is the distance of these points from one another, in feet, S is the density of the fluid in pounds per cubic foot, v is the velocity of the fluid in feet per second, d is the diameter of the tube in feet, and A" is a constant depending on the character of the interior surface of the tube and also upon the vis- cosity of the fluid. In the case of a gas or vapor, the density depends upon the temperature and pres- sure of the fluid, and since experiment shows that the viscosity of all gases is prac- tically the same we may write for the above equation dL -*' in which P is the pressure of the gas in pounds per square foot, T is its absolute tem- perature, R is the function T^-m, and TV is a factor which depends upon the character of the internal surface of the tube. If we let TF = the number of pounds of gas passing a given cross-section of the tube per second, then the volume of this gas will be given by the expression V-ZIT.. . . ......... (3) The area of the cross-section of the tube is equal to . The velocity of gas in the tube is found by dividing the volume of gas passing in a given time by the area of the tube, hence we may write 4/WRT\ , (4) Raising to the 1.8 power we will have 1 '* R 1 ' 9 T*' (5) Substituting this in equation (2) we have L = K(?^*^-). > . /(6) Collecting like terms we will have Integrating this expression between the limits of P l and P, and zero and L, we will have >-P-*}= KW "* ( ? Tr L, (8) 342 COMPRESSED AIR ART. 319 Which becomes - in which P l is the initial pressure in pounds per square inch absolute at any point in the tube, P is the pressure in pounds per square inch absolute at a point L feet distant from the first point in the direction of flow, W is the number of pounds of gas passing each cross-section of the tube per second, d is the diameter of the tube in inches, R is the density function of the gas, T is the absolute temperature of the gas and K is a constant depending upon the character of the inner surface of the tube. Solving the above equation for the weight of gas transmitted per minute we will have 1 ~ > ( 10) KL(RTY ' Solving for the diameter of the tube required to transmit a given weight of gas per minute with a given loss in pressure will have Solving for the value of the constant when it is to be determined, by experiment, we will have (P i-s_ pi-s\ ,74-9 TT __ 1*1 * ) a /io\ " W l -*(R'T)'*L ' The value of K for iron pipes is usually about 0.026. 319. Applications of Compressed Air. Compressed air may be used as the working fluid in an engine, in exactly the same way as steam is used. The card from a compressed-air motor is similar to one from a steam engine. The amount of power given by the air motor and also the weight of air used may be computed from the card. Since air is a permanent gas, there is no cylinder condensation, and the thermal loss with a compressed-air motor will be much less than with a steam engine. The power developed from a given weight of air may be increased by heat- ing the air before it enters the motor, and if the motor is to be used con- tinuously, it is advisable to preheat the air in this manner. It is usually advisable to use air motors in place of steam engines when compressed air is available and the motors operated for only a small portion of the time. A small steam engine is continually wasting heat when it is not in opera- tion, and much steam is wasted by cylinder condensation in warming it up after each period of idleness. There are ho such losses in the case of an air motor. Compressed air finds its principal application in quarrying and mining, in the operation of rock drills, and channeling machines. In coal mining especially, it is impracticable to use steam for operating such machines, since the boilers must be placed above ground. To transmit steam from a boiler plant at the mouth of the mines, to engines and drills situated ART. 319 APPLICATIONS OF COMPRESSED AIR 343 underground and hundreds or thousands of feet away, would result in a very great waste of heat and in considerable danger to the workmen. When compressed air is used as the working fluid in such machines, there is no radiation of heat from the piping or losses resulting from the intermittent use of the machinery. Consequently, if the air compressor plant is efficient, the cost of operating compressed-air machinery under these conditions is much less than the cost of performing the same work by steam. Another field in which compressed air is used to great advantage is in the driving of percussion tools in shops. The pneumatic riveter which is usually employed in assembling structural work in the field is an example of such a tool. It consists of a heavy cylinder within which a small, but rather heavy piston, termed a hammer, is caused to reciprocate by the action of compressed air. A throttle valve is provided which regulates the pressure of the air admitted to the tool, and so controls the force of the blow. The hammer vibrates at a rate of several hundred strokes per minute and when provided with an extension having a face of suitable form, it rapidly batters the hot metal of the rivet into shape. Since the hammer and its extension are much lighter than the cylinder in which they are contained, the vibration of the cylinder is not so excessive but what it may be held by hand when in use. Similar, but lighter tools are employed in foundries and machine shops, where they are known as pneumatic hammers. The extension pieces which are attached to the hammers are in the form of chisels, calking tools, etc. In work of this kind, while it is desirable that the motors which use the air shall be as economical as possible, it is very much more important that they shall be convenient to operate, shall perform their work rapidly and effectively, and shall be of such rugged construction as not to be injured by hard usage and abuse. Since these conditions are often incompatible with economy, it will be found that rock drills, pneumatic hammers and similar machinery are often inefficient, if we define the efficiency of such a piece of apparatus as the ratio of the work which it performs to the power theoretically required to compress the air which it consumes. PROBLEMS 1. Find the quantity of work theoretically required in order to isothermally com- press 10 cubic feet of free air having a pressure of 14 pounds per square inch and deliver it into a receiver in which the pressure is 70 pounds per square inch. Ans. 32,450 ft.-lbs. 2. Find the work theoretically required to adiabatically compress 10 cubic feet of free air having a pressure of 14 pounds per square inch and deliver it into a receiver in which the pressure is 70 pounds per square inch? Ans. 41,700 ft.-lbs. 3. Find the efficiency of compression when the compression is adiabatic? Ans. 78%. 344 COMPRESSED AIR PROBS. 4-20 4. A multistage compressor compresses air having a temperature of 60 F. from a pressure of 14 pounds per square inch absolute to a pressure of 56 pounds per square inch absolute in the first stage. The air is then cooled to 60 F. In the second stage, the pressure is raised from 56 pounds to 224 pounds absolute. Find the work required per cubic foot of free air compressed, assuming the compression to be adiabatic hi each stage. Ans. 7110 ft.-lbs. 5. Find the work required assuming that the compression was adiabatic and was completed in one stage. Ans. 8650 ft.-lbs. 6. Find the per cent of work saved by the employment of two-stage compression. Ans. 17.8%. 7. A compressor compresses air adiabatically from a pressure of 14 pounds absolute to a pressure of 84 pounds absolute. The clearance volume is 5 per cent of the swept volume. Find the volume of the air contained in the cylinder at the beginning of the suction period, expressed as a per cent of the swept volume of the cylinder? Ans. 17.85%. 8. Find the volumetric efficiency of the compressor. Ans. 87.15%. 9. Assume that the initial pressure in Problem 7 is 10 pounds absolute. Find the volume of the air contained in the cylinder at the beginning of the suction period. Ans. 22.6%. 10. Find the volumetric efficiency of the compressor under these conditions. Ans. 82.4%. 11. What must be the swept volume of a cylinder having the volumetric efficiency obtained in Problem 10, if it is to deliver 6 cubic feet of free air per stroke. Ans. 7.3 cu. ft. 12. Air having a temperature of 80 and humidity of 70% is compressed from a pressure of 14.5 pounds per square inch absolute to a pressure of 72.5 pounds per square inch gage. What quantity of moisture will it contain per cubic foot after compres- sion and cooling to the initial temperature? Ans. .00157 Ibs. 13. How many cubic feet of free air will be required per cubic foot of compressed air? Ans. 6 cu. ft. 14. How many pounds of moisture did this quantity of free air contain? Ans. .00670 Ibs. 15. How many pounds of moisture are precipitated by the compression and cooling of this quantity of air? Ans. .00513 Ibs. 16. What quantity of moisture will be precipitated per day in the pipe lines of an air-compressor system compressing 100,000 cubic feet of free air per day, if the con- ditions are those given in Problem 12? Ans. 513 Ibs. 17. Assuming that the clearance volume of the high-pressure cylinder of the air compressor in Art. 317 is 6 per cent, what will be the volume of the air contained in the cylinder at the beginning of the suction period, in terms of the swept volume? Ans. 13.7%. 18. How many cubic feet of air of a pressure of 41.5 pounds must this cylinder handle per stroke? Ans. 2.665 cu. ft. 19. What must be the swept volume of the cylinder? Ans. 2.89 cu. ft. 20. What will be the diameter of the cylinder? Ans. 11^ ins. CHAPTER XXIII REFRIGERATION 320. Refrigerating Machines. A refrigerating plant is an apparatus for maintaining a low temperature in a desired region by removing heat from that region and transferring it to a region of high temperature. A refrigerating machine is the converse of a heat engine, since it trans- forms work into heat, and then rejects the heat into a region of high temperature. Like the heat engine, the refrigerating machine employs a working fluid and causes this working fluid to undergo a thermodynamic cycle. Since the object of refrigeration is the transfer of heat, and not the performance of work, it is customary to take as the efficiency of a refrigerating system, the ratio of the heat transferred to the work done. Since the mechanical equivalent of the heat transferred is almost always several times as great as the work done, the efficiency of a refrigeration plant is usually greater than unity. A refrigerating machine may employ as a working fluid either a gas or a vapor. On shipboard, air is usually employed as a working fluid, since the leakage of air within the confined space of a ship's engine room is not harmful. In stationary plants the vapor of ammonia is usually employed as the work ng fluid. Other vapors and gases are also employed to a considerable extent. Refrigerating plants may be divided into four classes. Machines of the first class use a permanent gas as their working fluid. After being compressed and cooled, the working fluid is expanded adia- batically and its temperature reduced to a low value. Machines of the second class, which are called vapor-compression machines, liquefy a vapor by the application of pressure, and by the subsequent re-evaporation of this liquid under low pressures the desired temperature is obta'ned. Refrigeration plants of the third class are termed absorption plants. In such plants a volatile vapor, like ammonia, is absorbed by water or some other liquid and then driven off under high pressure by heat in such a manner that it may be subsequently cooled and condensed. It is then evaporated under low pressure, thus producing a low temperature. In apparatus of the fourth class, a gas is compressed to a very high pressure and cooled. When it is subsequently expanded the work done in separat- ing its particles against their mutual attractions lowers its temperature 345 346 REFRIGERATION ART. 321 (a phenomenon already referred to in Chapter III as the Joule-Thomp- son effect). 321. The Air -refrigerating Machine. A machine of the first class, using air as a working fluid, is represented in Fig. 180; In cylinder A air is compressed adiabatically and then forced into the condenser coil B. By its adiabatic compression, its temperature is raised so that it is somewhat higher than the temperature of the water supplied to the condenser. In the condenser, the temperature of the air is reduced a few degrees and the air then enters the smaller cylinder C, where it expands adiabatically to its original pressure. As a result, its temperature is very much reduced. It is then discharged into the coil D, usually termed a va- porizer, where it absorbs heat at low temperature from the substance which is to be cooled. In this coil the temperature of the air is raised a few degrees, and it then enters cylinder A, where it is again compressed. 'The condenser B may consist of a shell filled with tubes through which cooling water circulates, similar in its general arrangement to a surface condenser. This is the form of condenser usually employed on shipboard. In stationary plants, the condenser usually consists of a coil of pipe over which water is allowed to drip. By its evaporation, this water cools the air or other work- ing fluid contained in the pipes. The vaporizer may consist of a coil of pipe enclosed in the space to be cooled, and it usually has this form when air is used as the working fluid. When ammonia is used, however, the vaporizer pipes are usually immersed in brine, and the cold brine is then circulated through pipes in the space to be cooled. It will be seen that the machine described is an apparatus for cooling air by expansion, so that it may absorb heat from a cold body, and then heating it by compression, so that it may reject that heat to a hot body. In practice, the temperature of the air rejected by cylinder A must be considerably greater than the temperature of the water which cools it, and the temperature of the air exhausted by cylinder C must be quite a little less than the temperature of the substance to be cooled. The cycle FIG. ISO. Air-refrigerating machine. ART. 322 EXAMPLE OF THE PERFORMANCE OF AN AIR MACHINE 347 upon which this machine operates is the reverse of the Joule cycle which was described in Chapter XVIII. 322. Example of the Performance of an Air Machine. Assume that a machine of this type is required to maintain a temperature of F., and to reject heat at a temperature of 80 F. In order to insure proper operation, we will assume that a difference of 20 is necessary to effect the heat transfer in each case, so that the air must be expanded until its temperature is 20 F. or 440 absolute, and must be compressed until its temperature is 100 F., or 560 absolute. We will assume that the cycle is performed with 1 pound of air and that the temperature of the air is raised 10 in the vaporizer. The temperature of the air entering the cylinder A will then be 450 absolute. Assume that its pressure is 14.7 pounds per square inch. The final pressure of compression may be found by the formula: Solving we will have for the final pressure LA 560\- 4 P 2 =14.71 j~) =31.6 Ibs. per sq.in., \4oO/ which will be the pressure of the air in the condenser. The work done during this compression may be obtained by the formula The work done in expelling the air into the condenser may be found by the formula RT =53.2X560 -29,900 foot-pounds. The temperature of the air leaving the condenser will be 560X440 550 = 54.7.6 The work which the air does in entering the cylinder B from the con- denser will be equal to 53.2X547.6-29,150 ft.-lbs. The work of expansion in this cylinder will be =14 ,390 ft.-Ibs. 348 REFRIGERATION ART. 322 The work of expelling the air from the expansion cylinder will be 53.2X440 = 23400 ft.-lbs. The work done by the air in entering the compression cylinder is 53-2X450 = 23900 ft.-lbs. The net indicated work will be found to be 447 foot-pounds, which is the difference between the work done upon the air in cylinder A, and the work done by the air in cylinder B. The heat transferred will be found by multiplying the rise in temperature by the specific heat of air at constant pressure and will be 2.38 B.T.U. Reducing this to foot-pounds, we will have 1850 for the mechanical equivalent of the heat transferred. Dividing the heat transferred by the net indicated work, we will have 410 per cent for the efficiency of the machine. The efficiency of the Carnot refrigerating machine transferring heat from a region of F. to a region of 80 F. will, of course, be T 2 460 T 1 -T 2 540-460 It will be seen that the efficiency of the reversed Joule cycle is much less than the efficiency of the Carnot cycle, although the theoretical efficiency obtained by the above computations is considerably higher than would be realized in practice. In practice, it would be found that neither the expansion nor the compression of the working fluid would be adiabatic, and in order to obtain the temperature range desired a larger pressure range would be necessary, which would increase the amount of work required to operate the machine. It will be noted that less than 2i B.T.U. per cycle per pound of work- ing fluid were transferred from the vaporizer to the condenser. In order to transfer any considerable quantity of heat by means of a refrigera- ting machine operating on the reversed Joule cycle, it is necessary that the machine be very large and heavy, and on account of the small amount of net work as compared with the large quantity of work performed in the two cylinders, the mechanical efficiency of the machine will be very low. In order to reduce the size of the cylinders, it is customary to keep the air in the vaporizer at a pressure of several atmospheres, which greatly increases the capacity of the machine without increasing its dimensions. Another type of air-refrigerating machine operates upon the regenerator principle. The air coming from the vaporizer is passed through a regenerator, where its tem- perature is increased almost to the temperature of the condenser. Its temperature is then raised still further by adiabatic compression and it enters the condenser, where it is cooled somewhat. It is then passed through the regenerator in the reverse direction, where it is cooled almost to the temperature of the vaporizer. It is then ART. 323 THE VAPOR-COMPRESSION SYSTEM 349 expanded in a second cylinder and its temperature still further reduced before it is discharged into the vaporizer. It will be seen that in the case of such a machine, the amount of work performed upon the working fluid in the first cylinder, and by the working fluid in the second cylinder, *!e much less than in the case of the machine previously described, although the quantity of heat transferred per cycle by a given weight of working fluid is the same, when the temperature ranges of the two cycles are equal. In consequence of this fact, the regenerator cycle offers certain practical advantages in the matter of mechanical efficiency and cost of installation. 323. The Vapor-compression System. A vapor-compression machine is shown in principle in Fig. 181. Vapor (usually ammonia vapor) is compressed in the cylinder A, and then discharged at high pressure into the condenser B. The temperature of the cooling water being less than the saturation temperature of the vapor at the pressure in the con- FIG. 181. Ammonia-compression plant. denser, the vapor gives up its heat of superheat and then its latent heat of evaporation, and so condenses to a liquid. After condensation, the liquid escapes through the expansion valve E into the vaporizer D, where it evapo- rates under low pressure by abstracting heat from its surroundings. The pump A draws the vapor from the cooling coils as fast as it is formed, and compresses it in order that it may repeat its cycle. Since the temperature of vaporization in the condenser is high, and since it is low in the vaporizer, on account of the low pressure, the machine is able to transfer heat from a cold region to a hot one. It will be seen that no work is performed by the working fluid, so that it is evident that this cycle cannot be a very efficient one. It has the advantage, however, of being extremely convenient and of requir- 350 REFRIGERATION ART. 324 ing only a small cylinder, whose mechanical efficiency will be compara- tively high. It is found in practice that the commercial efficiency of this type of machine is superior to the commercial efficiency of the air machine operating on the reversed Joule cycle. 324. Example of a Vapor Compression Cycle. In order to illus- trate the action of this cycle, we may take the following example. The working fluid is assumed to be 1 pound of ammonia. The temperature range desired is the same as in Art. 322, and we will assume, as before, that the fluid must be worked between the temperature limits of 100 F. and 20 F. In order to solve the prcblem, it will be necessary to make use of a table to the properties of the vapor of ammonia which may be found in Peabody's tables. The pressure of ammonia having a tempera- ture of 20 F. is 17.7 pounds absolute, which will be the pressure of the vapor in the vaporizer. In order to raise its temperature to 100, the vapor must be compressed to a pressure of 210.7 pounds absolute, which will be the pressure of the ammonia in the condenser. The latent heat of evaporation of ammonia at a temperature of 100 F. is 486 B.T.U., which will be approximately the quantity of heat absorbed in condensing 1 pound of ammonia in the condenser. The heat of the liquid at 100 F. is 75 B.T.U. and at- 20 F. it is-57 B.T.U. (i.e., 57 B.T.U. will be required in order to raise its temperature from 20 F to 32 F.) The latent heat of evaporation of ammonia at -20 F. is 582 B.T.U. Of this 75+ 57=132 B.T.U. are supplied by the heat of the liquid of the ammonia, and the remainder, or 450 B.T.U., is absorbed by the vaporizer from the region which is to be cooled. The specific volume of ammonia vapor at -20 F., is 15. 2 cubic feet, and at 100 F. is 1.52 cubic feet. The ratio of compression is therefore 10, and the work done, if the compression is assumed to be hyperbolic is, 210.7Xl44Xl.52xlog e 10-106,000 ft.-lbs., which is the mechanical equivalent of 136.3 B.T.U. The heat trans- ferred is, of course, the heat absorbed by the ammonia in the vaporizer and is 450 B.T.U. The efficiency of the apparatus is then 450-r-136.3 = 330 per cent. In theory the compression of the ammonia is not hyperbolic. The working fluid performs a reversed Rankine cycle in the compressor and the amount of work done can be computed exactly by taking the difference between the total heat of 1 pound of ammonia vapor at a temperature of 100 and 1 pound at a temperature of 20 F. The quality (or superheat) of the vapor at 100 may be determined from its entropy, which is the same as its entropy at 20 The method of computing the work performed in the case of this cycle will thus be seen to be identical ART. 325 THE VAPOR-ABSORPTION SYSTEM 351 with the method employed in computing the work done during a Rankine cycle, as described in Art. 152. This method is, however, much more tedious and probably not very much more accurate than the assumption of hyperbolic compression. It will be seen from the figures given that the efficiency of the vapor- compression machine is slightly less than that of a machine operating on the reversed Joule cycle, but in practice, it is found that the mechanical efficiency and the capacity for a given size of cylinder is so much greater in the vapor-compression machine that the actual efficiency of the apparatus is much greater than that of the air-refrigerating machine. 325. The Vapor-absorption System. The principle of the absorp- tion machine will be understood by reference to Fig. 182. A is a closed cylinder, termed the generator, partially filled with a solution of ammonia Cooling Water to Absorber , ^Exhaust Steam from Pumps r FIG. 182. Ammonia-absorption plant. gas in water under high pressure. On heating the generator by a fire or by steam coils, the ammonia is driven off through the pipe shown, into the condenser B. Since the ammonia is under high pressure, it is there condensed to a liquid when cooled by the condensing water. The liquid ammonia comes from the condenser at a temperature of perhaps 80 F., and passing through the expansion valve H, flows into the vaporizer (7, where it evaporates. From the vaporizer the ammonia vapor passes through the pipe p into a vessel d, which is termed the absorber, and which contains a solution of ammonia. Brine is caused to circulate about the vaporizer coils and is then used to cool the region whose temperature it is desired to lower. The solution of the ammonia by the water in the absorber generates heat which is carried off by circulating cooling water through coils immersed in the absorber. The liquid contained in the absorber is removed by a pump and transferred to the generator through 352 REFRIGERATION ART. 326 the regenerator coil R. The spent liquid from the generator is transferred to the absorber, passing through this same generator coil on the way. The liquid entering the regenerator is thus heated while that entering the absorber is cooled. It will be noted that the only power required by the absorption sys- tem is that required to circulate the various liquids and to force the liquid from the absorber into the generator. It will be seen that the power required is inconsiderable as compared with that required by the compression system. The amount of heat required by the generator is, of course, somewhat greater than the amount of heat required to vaporize the ammonia, so that at first sight it would appear that this system must have an efficiency of less than 100 per cent, which is very low for a refrigera- tion system. However, the efficiency of the engine which furnishes mechan- ical power for the compressor in the vapor-compression system is rarely greater than 10 per cent, so that the efficiency of the absorption system, when considered from the standpoint of the cost of operation and not of the quantity of energy required to effect the heat transfer, is very much greater than that of the compression system. The steam exhausted by the pumps used in connection with the vapor-absorption system usually furnishes sufficient heat to operate the system. The amount of cooling water taken by the system is much greater than that taken by a vapor- compression plant of the same capacity. 326. Apparatus for Liquefying Gases. When very low temperature is desired, as, for instance, when it is desired to liquefy any of the permanent gases, advantage is taken of the cooling which accompanies the expan- sion of the gas due to the work required to separate its particles against their mutual attractions. The apparatus which is employed to liquefy air is illustrated in principle in Fig. 183. It usually consists of 3- or 4-stage compressor which raises the pressure of the air to from 2000 to 2500 pounds per square inch. Next, this air is cooled in the coil C to the lowest available temperature, usually to the temperature of the coldest water available. In case the Joule-Thompson effect of the gas to be liquefied is small at ordinary temperatures, refrigerating agents may be employed to cool the gas in this coil. After being cooled, it is allowed to flow through a long tube which is enclosed within a second tube. At the end of this tube, the air passes through the reducing valve V, and expands into the flask F, in which it is proposed to collect the liquefied air. As a result of the expansion, the temperature of the air is lowered a few degrees. This air returns from the flask to the compressor through the outside tube. These two tubes act as a regenerator, and the temperature of the air coming to the flask through the inner tube is reduced by transferring its heat to the cooler air returning to the compressor through the outer tube. Since the temperature of the air entering the reducing valve is ART. 327 METHODS OF STATING CAPACITY AND EFFICIENCY 353 lowered by the action of the regenerator, the temperature of the air com- ing from the reducing valve is lowered still further, and the action is cumulative, the temperature of trTfe air being gradually reduced until finally it becomes low enough so that a portion of it is liquefied. After passing through the expansion valve, a portion of the liquid remains behind in the flask. As soon as liquefaction commences, no further reduction in temperature takes place, but the air continues to liquefy, and the fresh air, which must be dried and freed from carbon dioxide in order to avoid difficulties from the formation of ice or carbon dioxide snow in the apparatus, must be taken into the compressor to take the place of the air which is liquefied. It will be seen that the heat which is extracted from the air in cooling it after compression is greater than the work of adiabatic compression by the amount of work done by the attraction of the particles of the air 5) FIG. 183. Apparatus for liquefying air. while they were being forced together; this heat was transferred to the cooling water from the air which is liquefied, by the action of the regenerator. This type of apparatus is expensive and not very efficient, but may be employed to advantage when very low temperatures are needed for scientific investigations. Most of the known gases have been liquefied by the employment of this apparatus, and there is no reason to believe that there are any gases which cannot be liquefied in this manner when they can be obtained in sufficient quantities. 327. Conventional Methods of Stating Capacity and Efficiency. It is customary to rate refrigerating machines by the " ice-melting effect " in tons per twenty-four hours. The quantity of heat required for the fusion of 1 pound of ice is very nearly 142 B.T.U. Consequently the quantity of heat absorbed by the fusion of 1 ton of ice is 142X2000 = 284,000 B.T.U, A 1-ton refrigerating machine or system is then a 354 REFRIGERATION PROBS. 1-10 machine or system which is capable of removing 284,000 B T U. per day of twenty-four hours from the vaporizer. Such a machine wi A 'l, in a com- mercial plant, usually be capable of freezing about 1000 pounds of ice per day. In comparing efficiencies of refrigerating machines, it is usual to state the ice-melting effect in pounds in per pound of coal or per indicated horse-power per hour, the indicated horse-power being the horse-power of the engine which drives the compressor. Since the quantity of heat transferred by a given expenditure of power will vary with the temperature range, being less for large temperature ranges than for small ones, it is customary to state the efficiency for a temperature range from F. in the vaporizer to 90 F. in the condenser. PROBLEMS 1. A refrigerating machine is required to maintain a temperature of 30 F. in a region in which condensing water is available having a temperature of 70 F. What is the maximum theoretical efficiency possible assuming a Carnot cycle to be employed? Ans. 1225%. 2. An air-refrigerating machine of the type described in Art. 313 is required to operate between the temperature limits given in Prob. 1. Assume that the air must be cooled by expansion to 10 F. and heated by compression to 90 F. If the pressure of the air in the vaporizer is 50 Ibs. per square inch absolute, what must be the pressure of the air in the condenser? Ans. 85.7 Ibs. per square inch. 3. Assume that the air is warmed 10 in the vaporizer. How much heat is trans- ferred per pound of air per cycle? Ans. 2.37 B.T.U. 4. Find the swept volume of the large cylinder per pound of air per cycle, assum- ing that its volumetric efficiency is 80%. Ans. 4.35 cu.ft. 5. A machine making 60 revolutions per minute is required to transfer 7200 B.T.U. per hour from the vaporizer. What must be the swept volume of the large cylinder? Ans. 1.84 cu.ft. 6. An ammonia compression machine is required to maintain the temperature difference given in Prob. 1. Assume that the temperature in the vaporizer is 10F., and the temperature in the condenser is 90 F. The pressure of ammonia at 10 is 37.8 Ibs. per square inch, its specific volume is 7.44 cu.ft, the heat of the liquid is- 24 B.T.U., the heat of vaporization is 558 B.T.U., and the entropy of the liquid is 558 0.0501, and the entropy of vaporization is - . What is the total heat of the vapor at this temperature? Ans. 534 B.T.U. 7. What is the entropy of the vapor after compression? Ans. 1.139 8. The pressure of ammonia at 90 is 179.6, the heat of the liquid is 64 B.T.U., the heat of vaporization is 494 B.T.U., the entropy of the liquid is 0,1224, the entropy 494 of vaporiaztion is - -- -, and the specific volume is 1.76. What is the entropy of ammonia vapor at 90? Ans. 1.022. 9. Is the ammonia wet or superheated after compression? Ans. Superheated. 10. What quantity of heat is transferred from the vaporizer to the condenser per pound of ammonia per cycle. Ans. 470 B.T.U. PROBS. 11-17 PROBLEMS 355 11. Assume that a compressor making 30 revolutions per minute is required to transfer 1,000,000 B.T.U. per hour from the vaporizer to the condenser? What quantity of ammonia must be compressed per revolution? Ans. 1.18 Ibs. 12. Assuming that the volumetric efficiency of the compressor is 80 per cent, what swept volume per revolution will be required? Ans. 10.96 cu.ft. 13. Assuming hyperbolic compression, what work, will be required per revolution to compress this quantity of ammonia? Ans. 75900 ft.-lbs. 14. What will be the horse-power required to drive the compressor if its mechanical efficiency is 70 per cent? Ans. 98.7 H.P. 15. What is the nominal capacity of the compressor in Problem 11? Ans. 84.5 tons. 16. What is the efficiency of the compressor expressed in pounds of ice-melting effect per indicated horse-power per .hour? Ans. 71.7 Ibs. 17. Assuming a coal consumption of 3 Ibs. per indicated horse-power per hour, what is the efficiency expressed in ice- melting effect per pound of coal? Ans. 23.9 Ibs. CHAPTER XXIV HEATING, VENTILATION, EVAPORATION, AND DRYING 328. The Hygiene of Heating and Ventilation. Within the human body a process of oxidation is continually going on. The products of oxidation are excreted by the lungs and the skin, and thrown off into the air. These products consist of carbon dioxide and water vapor, together with other vapors or gases of very small amount and unknown char- acteristics. Carbon dioxide was formerly thought to be poisonous, but it is now known that when the air contains less than 1 or 2 per cent of it, it has no effect upon animal life, being as inert as so much nitrogen. Water vapor- is also harmless. We know, however j both as a result of scientific investigation and practical experience, that the exhalations from, the human body are dangerous to life, and many authorities are of the opinion that the poisonous exhalations are thrown off by the skin rather than by the lungs. It has been demonstrated experimentally that when the quantity of animal exhalation present in air is great enough so that the carbon dioxide content of the air exceeds 0.07 per cent, the air is unfit to breathe. The carbon dioxide is not to be regarded as an objectionable component, but simply as an indicator which shows the suitability of the air for breathing. The average adult requires about 20 cubic feet of air per hour for respiration, and exhales about 0.6 cubic feet per hour of carbon dioxide. Since it is impossible to avoid the mingling of the exhaled air and the fresh air supplied by ventilation, it is necessary to furnish very much more air per person than the 20 cubic feet actually consumed. If it be assumed that the air exhaled from the lungs mingles freely with the air supplied by ventilation, it is necessary to supply about 2000 cubic feet of fresh air per hour for each person present, in order to prevent the carbon con- tent from rising above 0.07 per cent. In old treatises on ventilation it was assumed that the carbon dioxide was the dangerous constituent of the air, and hence that an additional supply of air was necessary in rooms containing open flames, such for instance as gas jets. Since such flames often give off carbon monoxide, sulphur dioxide, and other objectionable gases, it is advisable to provide extra ventilation in such a case, but this extra ventilation is not made necessary by the carbon dioxide. In large rooms containing a considerable volume of air per person and which are 356 ART. 328 THE HYGIENE OF HEATING AND VENTILATION 357 used for short periods only, as for instance, churches and public halls, it is not necessary to supply 2000 cubic feet of air per person per hour, since some time will elapse before ttfoair in the room is sufficiently vitiated to require renewal. On the other hand, in hospitals, particularly in con- tagious wards, it is advisable to supply a much larger quantity of air per person. In the case of dwelling houses, with unpainted plastered walls and in the case of many other forms of construction a considerable amount of ventilation is secured by diffusion through the walls of the rooms. When the composition of the air in a room having porous walls becomes appreciably different from that of the external air, diffusion takes place, which tends to make the composition of the air in the room identical with that of the external air. While this action may be relied upon to some extent to supply ventilation, it is not a satisfactory substitute for the movement of air in the form of a stream or current. Not only is it necessary to supply an adequate amount of fresh air to effect the removal of the organic exhalations in any inhabited room, but is also necessary to keep the room at a proper temperature and the air in the room at a suitable humidity. The usual temperature at which living-rooms are maintained in America is 70 F. In Europe it is usual to maintain living-rooms at a temperature of about 60 F. Experiments in the so-called open-air schools and cold-air schools indicate, however, that in the case of children wearing ordinary winter house clothing and permitted a reasonable degree of activity, that a temperature between 40 and 50 is the most satisfactory room temperature. The reason for this is that the exhalations from the body, on account of the relatively high temperature, are then sufficiently lighter than the air in the room, so that they rise promptly from the breathing zone and pass out of the room without vitiating the air which the inhabitants are to breathe. Older persons, when engaged in sedentary occupations and espe- cially those who have been accustomed to warm living-rooms, do not find such temperatures agreeable, however, and since it is usually the older persons who determine such matters, the temperature of living- rooms is usually maintained at a higher point than proper hygiene dictates. In most schools at the present time, 68 F. is prescribed as the proper max- imum of temperature, and the tendency is to lower this maximum rather than to raise it. The humidity of the air supplied by ventilation is quite as important a matter as is its temperature. The normal humidity of out-door air is about 70 per cent, and this degree of humidity in connection with a temperature between 60 and 70 F. seems to be most favorable to the proper performance of all the vital processes. 1 is true only in case the ventilation is unusually abundant and effective. When it is not, a lower temperature is desirable in order that the convection currents 358 HEATING, VENTILATION, EVAPORTTION, AND DRYING ART. 329 In an artificially heated building it is difficult to maintain the humidity of the air at a proper point, since the air is taken into the building at low temperature, and therefore contains but a small quantity of moisture, and its temperature is subsequently raised without increasing the moisture content. This makes the air exceedingly dry. The effect of such dry air upon the human body is, of course, to take moisture from the skin and mucous membranes very rapidly. This has a tendency to make the body feel cold on account of the rapid evaporation, to produce diseases of the nose and throat, and to seriously disturb the circulatory system. Hence if proper ventilation is to be maintained in a building, it is neces- sary to introduce steam into the air which is to be circulated by the venti- lating system, in order that its humidity may be that which is proper for health. 329. Systems of Heating. Two systems of heating are employed, which are known as the direct and the indirect systems of heating. Direct- heating apparatus is apparatus which is placed in the room to be warmed. Stoves and radiators are apparatus of this type. Indirect heating apparatus is apparatus which is employed to heat a current of air which is then introduced into the room to be warmed. Direct-heating apparatus is employed principally in connection with dwelling houses, office buildings and other places where ventilation is not a matter of primary importance. Indirect-heating apparatus is employed in schools, hospitals and other places where adequate ventilation is of great importance. 330. Direct-heating Systems. The common coal stove is the sim- plest form of direct heating apparatus. It is reasonably efficient, but on account of the constant attention necessary, and the dirt created by the use of coal and the disposal of ash, the stove is being displaced by other forms of heating apparatus in which the fire is maintained in a place where the handling of dirt and ash is not objectionable. The most common system of direct heating is that which employs steam as the medium for distributing the heat. Steam radiators con- sist of coils of pipe or of shells of cast iron or pressed steel which are supplied with steam by piping from a central boiler plant. The steam condenses within the radiator, transferring its heat to the air in contact with the shell. This heated air rises and cold air flows in to take its place, thus warming the air in the room to be heated. The condensation returns to the boiler through the piping system. The principal differences between the several systems of steam heating usually employed lie in the method of returning the condensation to the boiler. The simplest sys- tem is that illustrated in Fig. 184, amd is known as the single-pipe system. In this system a current of steam ascends from the boiler B through the created by the heat of the body shall clear the breathing zone of undesirable exhala- tions. ART. 330 DIRECT-HEATING SYSTEMS 359 pipe P to the radiator R, and the condensation returns through this same pipe to the boiler. It will be seen that it is necessary to make the pipe of ample size so that the current of steam will not have a high velocity, for if it has, it will retard 4,he returning current of water and may cause the system to become " water bound." It is also necessary that the pipe shall be so arranged that every part of it shall drain freely into the boiler, for if a " pocket " is formed in the pipe which can fill with water, the system will become water bound, and the surging of this water through the pipes under the action of the steam will produce severe " water hammer." FIG. 184. FIG. 185. The return-pipe system, illustrated in Fig. 185, provides a separate pipe for the return of the condensation. With this system, the pipes may be made smaller than with the single-pipe system, and pockets, although they are to be avoided as far as possible, are not fatal to successful operation. When a radiator system is started up the pipes and radiators are of course full of air. In order that steam may fill the system, it is necessary that the air be permitted to escape. The air usually escapes from the radiators through valves termed air valves, which are sometimes automatic in their action, but which are usually of a form requiring personal atten- tion. If only a part of the air escapes from the radiator, those sections of the radiator which are filled with air do not permit the entrance of 360 HEATING, VENTILATION, EVAPORATION, AND DRYING ART. 330 \s steam, so that only a portion of the radiator will be active. This is desir- able in mild weather, when only a small amount of heat is needed. The principal objection to a system of steam radiation is that unless intelligent advantage is taken of the effect of the presence of air in the radiator, it is necessary to leave the steam fully on or to shut it completely off. In order to avoid this difficulty radiators of the form shown in Fig. 186 are sometimes used. In these radiators, the steam enters at the top, and the condensation flows away at the bottom. The steam enters the radiator through the throttle valve V, which may be opened sufficiently to admit the desired quantity of steam. The air, being heavier than the steam, is forced out through the return pipe which is connected into the bottom of the radiator. A balance is quickly established between the quantity of steam supplied and of steam condensed, so that air occupies the bottom of the sections and steam the top, and the amount of heat radiated is determined by the amount of the radiating surface in contact with steam. The amount of radiating surface required when steam radiation is employed is usually determined on the assumption that 250 B.T.U. are transferred per hour from the steam to the air by each square foot of radiating surface. A sufficient amount of surface is provided on this assumption, so that the amount of heat given up by the radiators to the air in the room is equal to the amount of heat lost by the room through radiation and ventilation. In order to estimate the amount of heat lost by a room, it is customary to employ the formula iKrT AT R "3 LTLT t> U D \\r 111/ )_Check Valve 'IG. 186. In this equation H is the number of heat units required per hour for heat- ing and ventilating the given room, c is a factor varying from 1.1 to 1.3 and depending on the exposure of the room, the direction of the prevail- ing winds etc., G is the number of square feet of glass surface in the windows, W is the number of square feet of wall surface exposed to out- door air, n is the number of air changes required per hour for ventilation, C is the number of cubic feet of air space in the room, T\ is the temperature at which the room is to be maintained, and To is the lowest outdoor tem- perature which it is desirable to provide against. ART. 331 EXHAUST-STEAM HEATING 361 The following example will serve to show the method of computing the amount of radiating surface which will be required in a given room. Assume a room 30 feet long, 20 feet wide, and 15 feet high having a side and an end wall exposed to the external air. Assume that the room is provided with four windows, which are each 4 feet wide and 10 feet high, and that it is to house 40 persons. The number of cubic feet of air required per hour will be 40X2000X80,000, which is the value of n C in the formula. The value of G in the formula will be 4X4X10 = 160 square feet of window surface. The value of W, the exposed wall surface, will be (15X20 + 15X30) -160 -590 square feet. The value of c we will assume to be 1.2 and we will also assume that the room is to be main- tained at the temperature of 70 when the temperature of the external air is zero. We will then have for the number of heat units per hour for heating and ventilating the room 70-126,000. For the number of square feet of radiating surface needed we will have 126,000 To Radiators - 331. Exhaust-steam Heating. When exhaust steam from an engine is available, it may be used for heating. In office buildings it is customary to install a plant in which steam engines are used for furnishing light and power for the building and the exhaust steam is employed for heating. The engine usually exhausts into a tank or header, to which the piping system is connected, as shown in Fig. 187. The header is provided with a relief valve R, whose purpose it is to allow the escape of steam when its pressure exceeds a certain value. The steam passes from the header to the heating system, and so long as the amount of steam supplied by the engine is great enough, FIG. 187. the excess will escape through the relief valve. When the amount of steam supplied by the engine is not sufficient to heat the building, steam enters the header from the boiler through the pressure-reducing valve V. If the relief valve 362 HEATING, VENTILATION, EVAPORATION, AND DRYING ART. 332 be set to operate at 3 pounds gage, while the pressure-reducing valve is set to operate at 2 pounds gage, it will be seen that the tank will always contain steam at a pressure of between 2 and 3 pounds. In some systems, termed vacuum-heating systems, the air is removed from the system by means of a vacuum pump or a steam jet and the pressure of the steam within the system is maintained at some value less than atmospheric pressure. The advantage of this system of opera- tion is that it reduces the quantity of steam required by the engine. It is especially adapted to those cases where the amount of steam exhausted by the engine, when operated under high back pressure, would be greater than the amount of steam required for heating purposes. With this type of heating plant, it is important that the system be made air-tight by carefully making all joints and packing the valves so that the quantity of air to be handled by the vacuum pump will be a minimum. 332. Hot-water Heating. A system of direct radiation often used in domestic heating is known as hot-water heating. In this system water is heated in an apparatus similar to a boiler, termed a heater. The water is caused to circulate through radiators, and after being cooled, is returned to the heater. The circulation is produced by the difference in the density of the hot water coming from the heater and the cold water which has passed through the radiators and is returning to the heater. A hot water plant is shown in principle in Fig. 188. H is the heater, which is located at the lowest point in the system and R is the riser which supplies the radiators with hot water. This riser terminates in a tank, E, termed the expansion tank. The purpose of this tank is to permit the expansion of the water without allowing it to escape from the system. Since the water in the riser R will, on account of its tem- perature, be lighter than the water in the return pipe P, it will flow through the radiators, surrendering its heat to the air in contact with them. By partially closing the valve which supplies the water to the radiator, the amount of heat radiated may be controlled, which is a great advantage in house- heating in mild weather. Since the temperature of the water in the radiator averages much lower than the temperature of the steam ordinarily supplied to radiators, it will be seen that a large radiating surface is necessary. It is usual to assume that 1 square foot of hot water radiation will supply 180 B.T.U. per hour to the room in which it is situated. FIG. 188. ART. 334 INDIRECT HEATING 363 333. Indirect Heating. Two systems of indirect heating are in use. In the first system the difference in density between the hot air in the ventilating flues and in the cold air in the building, is depended upon in order to circulate the air required for ventilation; in the second system a fan or other mechanical impeller forces the air to the proper point. The hot-air furnace employed in heating dwelling houses is an example of the first method. Such a heating system is illustrated in principle in Fig. 189. The hot-air furnace is placed at some point lower than the lowest point which it is required to heat. The air is warmed by a fire which is separated from it by a partition, usually of cast iron. The air is carried by flues to the rooms to be warmed. Since the warm air in the flues is lighter than the air in the rooms, the air in the rooms descends to the basement, where it enters the furnace and rises through the flues and registers. When the furnace draws its supply of air to be warmed from the basement itself, the air in the house is not renewed. If, however, the furnace draws a part or all of its supply of air from out of doors through a " cold air box," and the air in the house is allowed to escape instead of being returned to the basement, ventilation is secured. In public buildings where large num- bers of people congregate, it is unde- sirable to recirculate the air, since the demands of ventilation are such that, if the air were used over again, it would JT IG| i9. be too foul. In the case of dwelling houses, however, on account of the small number of inhabitants as compared with the radiating surface of the house, it is desirable to recirculate a large part of the air used, in order to conserve heat. When large buildings are to be heated and ventilated, indirect steam heating is often employed. In this system, steam coils or radiators of special form are placed in the ventilating flues, at a point below the level of the floor of the room to be warmed. Since the air in the flue is highly heated by the radiator, it rises into the room, forcing out the cold foul air which the room contains. On account of the vigorous air circulation and the form of radiator usually employed, a square foot of indirect radiat- ing surface will impart 400 B.T.U. per hour to the air passing it. 334. Forced Ventilation. In the ventilating systems previously described, dependence was placed upon the difference in temperature 364 HEATING, VENTILATION, EVAPORATION, AND DRYING ART. 334 between the air in the ventilating flues and the air in the building in order to secure a proper circulation. However, since weather conditions will often destroy the effectiveness of such a system, it is advisable where adequate ventilation is essential under all weather conditions, to install some mechanical device, such as a fan, for moving the air, in order to insure that a sufficient quantity of it shall be moved to the places where it is needed. Such a system of mechanical ventilation is illustrated in Fig. 190. A boiler B supplies steam to coils of pipe placed in the ventilat- ing duct D. A fan F supplies the air used for ventilation. Through the jets J the steam is introduced to properly humidify this air after it has Room [ ( I I FIG. 190. been warmed. The air rises through the duct to the room which is to be heated. The best method of distributing the air in the room is still an open question. It would be natural to introduce the warm air at the top of the room and to allow it to expel the cool air at the bottom of the room. Since, however, the exhalations from the body are warmer than the air contained in the room, they would tend to rise and then to be forced down again into the breathing zone by the down-coming and slow-moving current of air from above. The best method, (which, however, is quite expensive in application) is to admit the air at the bottom of the room in the manner shown, so that it is uniformly distributed to all parts of the room. The foul air is removed at the top of the room. If incom- ART. 335 EVAPORATION 365 ing air were supplied at localized points, as it would be if supplied through registers, the fresh air would immediately rise to the top of the building and there escape, leaving the foul air behind. By distributing it through very numerous small openings, spaced uniformly over the entire floor area, this difficulty may be avoided. In some cases it is desirable that the air introduced into a building shall be free from dust. This is especially the case in hospitals, since dust acts as a germ carrier. 1 The removal of dust is accomplished by passing the air through a scrubber or other form of gas-washing apparatus before the air is heated. 335. Evaporation. In many of the chemical industries it is neces- sary to evaporate solutions of salts in order to obtain the salts in solid form. In other industries it is often necessary to concentrate solutions by evaporating the larger part of the liquid which they contain. The FIG. 191. Diagram of a double effect evaporator. preparation of salt or sugar are examples of such industries. In order to evaporate the water contained, it is usually necessary to heat the solu- tion to a temperature considerably higher than the saturation temperature of the steam coming from the solution. In order to evaporate a maximum quantity of water by the use of a given quantity of heat (i.e., in order to make the evaporator as economical as possible), it is customary to make use of an apparatus usually termed a double- or triple-effect evaporator. The principle of operation of a double-effect evaporator may be seen by reference to Fig. 191. The evaporation of the liquid occurs in the pans A and B. These pans are provided with steam jackets. The jackets are shown surrounding the pans in the illustrations, although the heat is commonly applied by causing the steam to pass through coils immersed in the liquid. Steam is supplied to the jacket of pan A under high pres- sure, say 100 pounds, per square inch. The temperature of steam at that pressure is 328 F. The steam which is evaporated from the liquid con- tained in the pan is used to jacket pan B. Its pressure will be, let us say, 20 pounds per square inch absolute, which corresponds to a temperature 1 So far as it is known, all air-borne germs are transported while adhering to particles of floating dust. The elimination of dust from the air supplied for venti- lation effectually excludes such germs from a room. 366 HEATING, VENTILATION, EVAPORATION, AND DRYING ART. 336 of vaporization 228. The difference in temperature of 100 F. is sufficient to evaporate the liquid contained in the pan A in spite of the fact that the temperature of the liquid is considerably higher than the 228 correspond- ing to the pressure of the steam formed. The steam which is evaporated from pan B is of a pressure, let us say, of 2 pounds absolute, or at a tem- perature of 126. This steam is condensed by the condenser C. A vacuum pump is employed to remove the air which is brought into the system by the liquid which is to be evaporated. The condensation from the jackets flows away through the drips D and D' to traps which permit it to escape. It will be seen that by the employment of such an apparatus, the heat which would otherwise be rejected with the steam evaporated from the first pan is utilized in evaporating practically the same weight of liquid in the second pan. -This results in doubling the efficiency of the apparatus. Where a high efficiency is desired, three or even more pans may be employed in series. Since the temperature differences between the steam in the jacket and the liquid in the pan will be reduced by increasing the number of pans, it follows that the first cost of the apparatus required to evaporate a given weight of liquid per hour will increase as the efficiency is raised by increasing the number of pans in series. Evaporators are of many forms, and are provided with numerous mechanical devices, in much the same way as are steam boilers, in order to make their operation more efficient and convenient. When exhaust steam is available it is customary to employ it for heat- ing the first pan in a double-effect evaporator, making the temperature drop per pan approximately 50. The capacity of the system will be quite largely increased by improving the performance of the vacuum pumps and so arranging the system that the air to be handled by the pumps will be drawn from the coolest part of the system and will be mingled with the minimum quantity of vapor. Vacuum pumps are not needed for those parts of the 'system where the pressure of the steam is greater than that of the atmosphere, since a small portion of the steam may be permitted to escape through a valve, carrying the air with it. 336. Distilling. In some cases, it is the vapor which is evaporated and not the substance which remains behind in the pan, which is the valu- able product. In such a case, the vapor must be condensed by the use of an apparatus termed a still. A still consists of an evaporating chamber heated by fire or by steam, and of a coil of pipe usually termed a worm, which is immersed in a tank supplied with cooling water at the bottom, the water being drawn away at the top. Any form of apparatus which will act as a condenser, however, is equally suitable for use as a still. Stills are employed in the preparation of alcohol, liquid ammonia, kerosene and many other volatile liquids. When the liquids are likely to bring into a still uncondensible gases, such as air, it is desirable to provide ART. 337 DRYING 367 the still with a vacuum pump in order that the pressure and therefore the temperature of evaporation shall be as low as possible. Stills may be arranged so as to operate in series, the vapor condensed in one worm acting to evaporate the liquid in the second still. 337. Drying. The drying of substances containing only small quan- tities of moisture, as for instance, lumber cloth, etc., is usually effected by exposing the substances to be dried to a current of dry air. At atmos- pheric temperature air, of course, contains water vapor. Since the pressure of the water vapor is less than the saturation pressure corresponding to the temperature of the air, the air will absorb moisture. It may be caused to absorb moisture much more rapidly, however, by heating it, which will decrease its relative humidity and increase very greatly its capacity for absorbing moisture by raising the pressure of the water vapor which it can contain. If such a current of heated air be caused to pass through a pile of lumber, as is done in the kiln-drying process, it rapidly absorbs moisture from the lumber and passes out of the kiln with a much larger moisture content than it had on entering. The air is usually caused to circulate by a fan or other form of mechanical impeller and is heated by the use of coils of steam pipe. These coils are usually supplied with exhaust steam. PROBLEMS 1. How many cubic feet of air per hour will be necessary to properly ventilate a schoolroom in which there are thirty persons? Ans. 60,000 cu.ft. 2. Assuming that this air is taken into the building at a temperature of 32 F. and a humidity of 70 per cent, how many pounds of moisture will if contain? Ans. 12.8 Ibs. 3. How many pounds of steam must be introduced into this air if the humidity of the room is to be maintained at 70 per cent and the temperature at 68? Ans. 47.6 Ibs. 4. A room 30 ft. long, 20 ft. wide, and 10 ft. high is exposed at one side and both ends. It contains six windows each 3^'X6'. What quantity of heat will be required per hour to provide against the radiation loss, if the room is to be maintained at a temperature of 68 F., when the outdoor temperature is 10 F., the exposure being severe? Ans. 20,300 B.T.U. 5. Assuming that four changes of air per hour will be required in Prob. 4, what total quantity of heat will be required per hour? Ans. 44,700 B.T.U. 6. What quantity of direct steam radiation will be required to heat the above room? Ans. 179 sq.ft. 7. What quantity of hot-water radiation will be required to heat the above room? Ans. 248 sq.ft. 8. How many cubic feet of air per hour must be supplied by the ventilating system to the above room? Ans. 24,000 cu.ft. 9. At what temperature must the air be introduced in order that when it is cooled down to 68, it shall part with sufficient heat to provide against the loss of heat by radiation? (Assume that the water equivalent of 1 cu.ft. of air is 0.018.) Ans. 115. 10. How many square feet of indirect radiation will be required to warm this air from a temperature of 10 F.? Ans. 117 sq.ft. CHAPTER XXV ENTROPY DIAGRAMS 338. Nature of the Temperature-entropy Diagram. Entropy was defined in Art. 64 as the sum of the successive increments of heat neces- sary to bring a body from a fixed state to any given state, each divided by the absolute temperature at which the increment of heat occurred, and the definition expressed mathematically by the equation (1) in which JN is the change in entropy, JH is the heat added (or abstracted) to produce this change of entropy, and T is the absolute temperature at which the change occurs. This expression may be transformed into (2) It is very convenient and instructive in certain cases, to represent thermodynamic processes by plotting on a diagram the relation between the temperature and the entropy of the body undergoing the processes. Such a diagram is called a temperature-entropy diagram. Its ordinates are proportional to absolute temperatures, its abscissae to entropy, and its areas, as may be seen from equation (2), are proportional to heat. Lines on such a diagram are termed temperature-entropy lines. Such a diagram may be plotted for any weight of substance, but it is Usual to plot it for 1 pound of the substance. 339. Forms of the Temperature-entropy Lines. Assume a body whose mass is W, whose specific heat is S, whose temperature T , and whose entropy is zero (i.e., a body having the zero state), to have its tem- perature raised to the value T. The head added in order to effect a given small increase in temperature will of course be dH = W S dT ......... (1) The corresponding change in entropy will be , A7 WSdT <*N -- ~ T -. .,,,,,.. (2) 368 ART. 339 FORMS OF THE TEMPERATURE-ENTROPY DIAGRAM 369 The entire change in entropy will be C N C T dT dN = WSl jr -. . (3) Jo JT, 1 Integrating, we will have T - (4) Plotting this relation on a temperature-entropy diagram, we will have the temperature-entropy line shown in Fig. 192. As may be seen from this figure, the entropy of the body at the zero state (i.e., the temperature T ) is zero, the entropy of the body at temperature T is N } and the quan- dN o d FIG. 192. FIG. 193. tity of heat required to raise the temperature from T to T b will be repre- sented by the areas a-b-d-o, as will appear from the following : The strip on the diagram whose width is dN and whose height is T has the area T dN =dH in which dH is the quantity of heat imparted in order to change the entropy by the quantity dN. The total quantity of heat imparted in changing the body from the zero state to state B is the sum of all such strips included under the line a-b. Hence, the heat imparted is equal to the area included under the line. When a body is heated without raising its temperature, as, for instance, when water is evaporated into steam, or a quantity of gas expands adi- abatically, the increase of entropy occurs at constant temperature and the temperature-entropy line is horizontal, as, for instance, the line a-b in Fig. 193. When a body changes in temperature without receiving or 370 ENTROPY ^DIAGRAMS ART. 340 emitting heat, as for instance, when a quantity of gas or vapor expands adiabatically, the entropy is unchanged and the temperature-entropy line is vertical, as is the line b-c in .Fig. 193. When a body absorbs or emits heat and simultaneously changes in temperature, and the quantity of heat absorbed or emitted is proportional to the changes in temperature, the temperature-entropy line will be of the form represented by the equation ......... (5) Such will be the case when the specific heat of the body is constant, or when a gas is heated at constant pressure or constant volume or under- goes poly tropic expansion. When K is positive (i.e., when conditions o f FIG. 194. FIG. 195. are such that the body rises in temperature as heat is added, or falls in temperature as heat is abstracted, the general direction of the tem- perature-entropy line will be like that of a-b in Fig. 194. When K is negative (i.e., when a fall in temperature accompanies an absorption of heat or a rise in temperature and emission of heat) the general direction is that of line c d in the same figure. 340. Thermodynamic Cycles on the Temperature-entropy Plane. Any thermodynamic process involving a body of constant mass may be represented by an appropriate temperature-entropy line. Any series of such processes may be represented by a series of temperature-entropy lines, just as they may be represented by a series of pressure volume lines. Such a diagram may be drawn to represent any thermodynamic cycle, and the cycle is then said to be represented on the temperature-entropy plane. The diagram in Fig. 195 represents the Carnot cycle in which the working fluid expands isothermally from state a to state b at the ART. 341 EVAPORATION AND SUPERHEATING 371 temperature T lt receiving from the heater the quantity of heat represented by the area a-b-e-f. The line b-c represents the process of adiabatic expansion. The line c-d represents the process of isothermal compression at the temperature T 2 , the quantity of heat represented by the area c-d-f-e being rejected to the cooler during this process. The line d-a represents the process of adiabatic compression. An inspection of this diagram will serve to show that the heat absorbed is to the heat rejected as the temperature T l is to the temperature T 2 . Consequently, it may be shown from the diagram that the efficiency of the Carnot cycle, which is is also equal to HI T.-T2 Any other cycle in which a constant mass of working fluid is employed or which is the equivalent of a cycle in which a constant mass of working fluid is employed, may be represented by the temperature-entropy diagram. In case, however, a variable quantity of working fluid is employed, as is the case in the practical steam-engine cycle, only those processes can be properly represented on a temper- ature-entropy diagram during which the quantity of working fluid remains constant. 341. Evaporation and Superheating on the Temperature-entropy Plane. The process of rais- ing a quantity of water from the zero state (i.e., from the liquid state at a temperature of 32 F) to any temperature T, evaporating it into steam, and then superheating the steam at constant pressure, is represented on the temperature-entropy diagram by three lines of the form shown in Fig. 196. Line ab represents the process of raising the tempera- ture of the liquid from 32 to T. Since the specific heat of water is very nearly but not exactly a constant quantity, this line may be represented very nearly, but not exactly by the equation t I I o s FIG. 196. T To (1) During the evaporation of the water the temperature of the entire mass remains constant and the entropy increases. The process is the equivalent of isothermal expansion, and is represented by the line b-d. The process of superheating the steam is represented by the line c-d, which has approx- 372 ENTROPY DIAGRAMS ART. 342 imately the logarithmic form already given, although it does not approx- imate this form as nearly as does the line a-b, since the specific heat of steam at most pressures varies a little with the temperature. On this diagram, the area a-b-go represents the heat of the liquid, the area bc- f-g represents the heat of evaporation, and the area c-d-e-f represents the heat of superheat. 342. The Steam Dome. Fig. 197 represents a form of temperature diagram often termed the steam dome. The line a-b represents the rela- tion between the temperature and entropy of water, and is termed the r m i p FIG. 197. water line. The line cd represents the relation between the temperature and entropy 1 of dry and saturated steam, and is termed the saturation line. Horizontal lines between ab, and cd, like b-c, e-f, g-h, etc., represent the relation between the temperature and entropy of wet steam of a given constant temperature, but of varying quality. The lengths of any of these lines, in entropy units, is, of course, the entropy of evaporation of dry and saturated steam of the given temperature. Since the quality of steam of a given pressure is proportional to its latent heat of evapora- tion, which in turn is proportional to its heat of evaporation, which in turn is proportional to its entropy of evaporation, any temperature- entropy line drawn in such a way as to divide these horizontal lines into 1 When the entropy as steam is mentioned in this chapter, the total entropy is meant. ART. 343 TEMPERATURE-ENTROPY DIAGRAM FOR STEAM CYCLES 373 segments bearing a constant ratio to one another, is a line of constant quality, and represents the relation between the temperature and entropy of steam of a given quality. Line i-k is such a line, and the ratio of any segment, as bi, to the whole line, as be, gives the quality of the steam. Vertical lines on the steam dome are, of course, lines of constant entropy. Lines of the form l-m and n-o are lines of constant volume and represent the relation between the temperature and entropy of a given volume of wet steam at different pressures. Lines of the form p-q and r-s are lines of constant total heat, and represents the relation between the temperature and entropy of wet steam of varying pressure but of a given total heat. In order to save space, it is customary to cut off that part of this diagram which lies below the temperature of 32 F., (i. e. the point a) unless it is necessary to use it for some reason. An inspection of this diagram will serve to make clear a great many points in regard to the properties of steam. It will be seen, for instance, that dry steam expanding adiabatically becomes wet. On the other hand, steam having a quality of less than about 50 per cent becomes dryer as a result of adiabatic expansion. It will be seen that when steam expands without alteration in its total heat, as it does when throttled, the steam becomes dryer. Were the lines a-b and c-d continued upward sufficiently, they would finally meet at the critical temperature of the vapor. 343. Temperature-Entropy Diagram for Steam Cycles. The tem- perature-entropy diagram of the Camot cycle for steam is exact!}- the same as it would be for any working fluid absorbing the same quantity of heat and working through the same temperature range. In Fig. 198 will be found the temperature-entropy diagrams of Carnot cycles for steam superimposed upon the steam dome, for different con- ditions, each diagram being accompanied by the corresponding pressure volume diagram. The temperature-entropy diagram of the Rankine cycle for dry steam is illustrated in Fig. 199. Line b-c represents the isothermal expansion of the steam as it enters the cylinder, line c-d represents adi- abatic expansion, line d-e represents the isothermal compression and con- densation, and line e-b represents the heating of the condensing steam to its initial temperature. The work done is, of course, represented by the area b-c-d-e. The heat imparted is represented by the area b-c-f-g-e. An inspection of the diagram will show that the efficiency of the Rankine cycle must be less than that of the Carnot cycle. That portion of the heat supplied which is represented by the area e-b-h-g, performs work represented by the area e-b-4 f and the efficiency of this portion of the heat supply is - This is manifestly less than the efficiency of the ebhg 374 ENTROPY DIAGRAMS ART. 343 Carnot cycle working through the same temperature range, which is jbie jbhg' The temperature-entropy diagram of the Rankine cycle, using wet steam, is shown in Fig. 200. It will be seen from this figure that the pro- portion of the total heat used inefficiently becomes greater as the quality FIG. 198. of the steam becomes less. Hence the efficiency of the cycle is less when wet steam is used. The diagram of the Rankine cycle using superheated steam is shown in Fig. 20 1, from which it may be seen that the superheated steam is more efficient than saturated steam of the same pressure, but not as efficient as saturated steam of the same temperature. It will be noted that, as the steam expands, its superheat decreases and finally at the point i, the adiabatic crosses the saturation line and the steam becomes wet. ART. 343 TEMPERATURE-ENTROPY DIAGRAM FOR STEAM CYCLES 375 A temperature-entropy diagram of the modified Rankine cycle may be seen in Fig. 202. The cylinder contains a pound of working fluid, a portion J* d\ O g h I FIG. 199. / b c / \ \ a \ \ e OS f FIG. 200. l\ FIG. 201. FIG. 202. \ \ \ \ \ d \ \ of which remains in the clearance space and is adiabatically compressed, while the remainder passes to the boiler where its temperature is raised while it is in the liquid state, by the application of heat. In order to 376 ENTROPY DIAGRAMS ART. 343 draw the temperature-entropy diagram of this cycle, it is necessary to assume that the water in the boiler has the same temperature at every instant during the compression period as does the cushion steam. The cushion steam is of course compressed adiabatically, but the compression line e-b is not an adiabatic, since it represents the relation between the temperature and entropy of the whole quantity of working fluid and not simply that of the cushion steam. In this diagram, line a-h is the water line for 1 pound of working fluid and line a i is the water line for that weight of working fluid rejected from the cylinder each cycle. The abscissa / represents the entropy of the liquid rejected from the cycle at some temperature, the abscissa k represents the entropy of 1 pound of water at the same temperature, the abscissa / represents the total o ts h \ \ \ \ a \ FIG. 203. FIG. 204. entropy of the working fluid during the compression period, at that tem- perature, and the distance m (which is equal to I f) represents the total entropy of the cushion steam at that temperature. Since the cushion steam is compressed adiabatically, its entropy remains constant during the compression period, and the distance m also remains constant. The temperature-entropy diagram of the jacketed cycle with com- plete expansion is shown in Fig. 203. The heat added is now represented by the area ebcdf-g } while the work performed is represented by the area e-b-c-d. The heat added by the jacket is represented by the area c-d-f-h, and the work done by this heat by the area c-d-4. It will be apparent that the heat supplied by the jacket is used less efficiently than that supplied by the cylinder feed, and that the efficiency of the jacketed cycle is theoretically less than that of the un jacketed cycle. ART. 343 TEMPERATURE-ENTROPY DIAGRAM FOR STEAM CYCLES 377 The temperature-entropy diagram of the imperfect cycle without clearance and using dry steam is shown in Fig. 204. That portion of the cycle lying within the area i h d, and cut off from the remainder of the diagram by the constant volume line ih, is work lost on account of incomplete expansion. The less complete the expansion, the greater will be the quantity of work so lost, the constant-volume line c-j represent- ing the limiting condition in which there is no expansion and the indicator card given by the engine is rectangular. The temperature-entropy dia- gram of the jacketed cycle with incomplete expansion is shown in Fig. 205, from which it may be seen that in case the expansion is incomplete, o g \ h I FIG. 205. FIG. 206. the efficiency of the heat supplied by the jacket is even less than when the expansion is complete. In drawing the temperature-entropy diagram of the imperfect cycle with clearance, it is necessary to assume, as we did in the case of the Rankine cycle with complete compression, that the water in the boiler has the same temperature as the cushion steam at every instant during the compression period and that the sum of the weights of the cushion steam and the water in the boiler is 1 pound. By employing such assumptions the temperature-entropy diagram may be drawn, but this temperature-entropy diagram will not, of course, represent truly the actual condition of affairs in a real engine. In Fig. 206 may be seen the temperature-entropy diagram of the imperfect cycle with complete compression. The line e-b is the com- pression line and is found in a manner similar to the line e-b in Fig. 202. 378 ENTROPY DIAGRAMS ART. 343 The work lost on account of clearance is, of course, the area f be e' . How- ever, on account of the cushion steam contained in the clearance spaces it is unnecessary to add the heat represented by the area g' e' f b e g. The ratio of the work lost to the heat saved is, however, greater than the ratio of the work done (area e b c h i) to the heat actually added (area g e b c f) and on this account the efficiency of the cycle is reduced by the use of clearance. In Fig. 207 will be seen the temperature-entropy diagram of an imperfect cycle having clearance and no compression. The line e-b represents the rise in pressure due to the introduction of steam from the boiler, and is a constant volume line. It will be seen that the ratio of the o g'g FIG. 207. O g g' FIG. 208. work lost on account of clearance, (area / b e e') to the heat saved, (area g' e' j b e g) is much greater than the ratio of the work lost to the heat saved in Fig. 206. The use of compression therefore raises the efficiency of the cycle. In Fig. 208 will be seen the temperature-entropy diagram of the imperfect cycle w r ith partial compression. The compression line is line e-kj the admission line is line k-b, the steam line is line b-c, the expansion line is line c-k, the release line is line h-^i, and the exhaust line is line i-e. The heat supplied is represented by the area g e k b c f, while the work done is represented by the area e b c h i. The area i h d represents the loss due to incomplete expansion. The area k m b represents the loss due to incomplete compression. This loss, however, cannot be diminished by ART. 344 DIAGRAM FOR THE ACTUAL STEAM ENGINE 379 increasing the compression pressure, since, with the clearance volume shown by the diagram, if the compression pressure be raised until the compres- sion is complete, the lost work due to clearance wiU be increased by the area e' e k b, while the heat saved will be represented by the area g e k b e' g f . If the ratio of the work lost to the heat saved is greater than the ratio of the work done to the heat supplied for the whole cycle, compression has been carried to too high a point. 344. The Temperature-Entropy Diagram for the Actual Steam Engine. In Fig. 209 will be found such a temperature-entropy diagram as would actually be obtained from a steam engine. The line a-b represents the period of admission. It will be seen that the temperature falls during this period on account of the fall in pres- sure due to wire drawing, and that throughout the admission period the steam line remains below the evaporation line g-h, which represents the temperature of the steam in the boiler. It is assumed that the steam is slightly wet as it enters the cylinder, so that the point h, which is the state point of the steam coming from the boiler, does not fall on the saturation line. The line b-c represents the expansion period . If the expansion were adiabatic, the line would be vertical. Actually the line is of the p IG 2 09. curved form shown. At the point where the admission ceases it will be noted that the line begins to run to the left, indicating that the steam is parting with heat more rapidly than it would as a result of adiabatic expansion. This is because cylinder condensation has not ceased at cut off, but continues until the temperature of the steam is below the average temperature of the surface of cylinder walls. At the point where the tangent to the expansion line is vertical, the rate of evaporation of steam from the clearance area 380 ENTROPY DIAGRAMS ART. 345 is equal to the rate of Condensation upon that portion of the barrel which is just being uncovered by the moving piston, and from that point onward re-evaporation is more rapid than condensation. As a result, the line tends toward the right, indicating an addition of heat. At c, release occurs. The line c-d is not, however, a line of constant volume, since release does not occur at the end of the stroke, and the fall in pressure is gradual and not sudden on account of wire drawing through the exhaust ports. The line d-e represents the period of exhaust during which the back pressure remains practically constant. The line e-f represents the period of compression during which the pressure and temperature of the steam rises. The pressure and temperature of the cylinder feed in the boiler is assumed to rise simultaneously. As has been previously noted, the line d-f will not be a vertical line, in spite of the fact that the com- pression of the cushion steam is adiabatic, since that portion of the work- ing fluid which is contained in the boiler is receiving additions of heat during the compression period. The line f-a is the admission line, and is of course, a constant volume line. 345. Graphical Analysis of the Losses in a Steam Engine. The actual temperature-entropy diagram for a steam engine may be superimposed upon the Rankine cycle temperature-entropy diagram in order to deter- mine the amount and distribution of losses in the engine. In Fig. 209 I p h q is the Rankine cycle diagram with complete compression for 1 pound of working fluid between the temperature limits of the boiler and the discharged condensing water. The quantity of heat supplied is n I p h m. Of this heat, the quantity n I q m would be lost in the exhaust of the Rankine cycle, while the remainder would be transformed into work. Since the imperfect cycle is employed, that quantity of work represented by the area k i q is lost on account of incomplete expansion and that quan- tity represented by / p a' is lost on account of incomplete compression. It is unnecessary, however, to supply the quantity of heat represented by this small area, but since this entire quantity of heat would be trans- formed into work, a considerable loss is represented by its absence. The area e' d' k I represents the loss due to imperfect condenser action. The area b f h i c f represents the power loss with the given quantity of steam and the given terminal volume due to cylinder condensation. The area d' c' j then represents the theoretical loss resulting from the fact that the actual expansion line is not continued to the back pressure line, following the same law of expansion as it does from &' to c' ' . Were the expansion continued to this point, however, as a result of the increased temperature range of the cylinder walls, the form of the temperature-entropy diagram would be changed, and the distribution of losses altered considerably. The shaded areas represent the loss which results from wire drawing and fluid friction and the ratio of the actual temperature-entropy diagram ART. 346 DIAGRAM FOR COMPOUND ENGINE 381 to the diagram bounded by a' b f c' d' e' / is the card factor of the engine. It must not be inferred that all heat losses shown by the temperature- entropy diagram are due to the direct transfer of heat to or from the steam. They may be due to the loss of steam from the working chamber on account of leakage. On the temperature-entropy diagram, as on the indicator card, leakage shows exactly the same effects as does cylinder condensa- tion. We cannot therefore infer that the heat transfer shown occurs between working fluid and the cylinder wall. 346. Temperature-Entropy Diagram for Compound Engine. Usually the weight of the working fluid contained at cut-off in the high-pressure cylinder of a compound engine is different from that contained at cut-off in the low-pressure cylinder on account of the difference in the weight of the cushion steam. It is therefore impossible to draw a temperature- entropy diagram which represents the behavior of the steam in such an engine, although such a diagram may be drawn for each cylinder separately. The diagram of the low-pressure cylinder will fall below that of the high- pressure cylinder when they are superimposed on the same steam dome, and they may slightly overlap in case the indicator cards overlap. Since a temperature-entropy diagram is always drawn for 1 pound of working fluid, it follows that the weight of the cylinder feed shown by the two diagrams will be different, and it is necessary, therefore, to treat the losses occurring in each cylinder separately. The quantity of heat supplied to the second cylinder per pound of cylinder feed will be equal to the total quantity of heat rejected from the first cylinder per pound of cylinder feed, less the quantity of heat lost from the first cylinder by radiation, which is usually extremely small. Hence, in order to obtain the efficiency of a compound engine from such a combined temperature-entropy diagram, it is necessaiy to obtain the efficiency shown by each diagram separately, in which case the efficiency of the engine will be the efficiency shown by the high-pressure diagram plus the efficiency shown by the low-pressure diagram, multiplied by one minus the efficiency shown by the high-pres- sure diagram. The temperature-entropy diagram for a compound engine may be employed in order to analyze the heat transfers occurring within each of its cylinders, and will show the causes and relative amounts of the losses in each of the cylinders. 347. Transferring an Indicator Diagram to the Temperature-Entropy Plane. In order to employ the temperature-entropy diagram to illus- trate graphically the distribution of losses in the steam engine, it is neces- sary to have an indicator card representative of the average conditions in the two ends of the cylinder of the engine for the entire test, and to transfer it to the temperature-entropy plane. In Fig. 210 such a card is shown, in the quadrant P V. In the quadrant P T is the pressure- 382 ENTROPY DIAGRAMS ART. 347 temperature curve of saturated steam. In the quadrant T N, which is the temperature-entropy plane, the desired temperature-entropy dia- gram is to be drawn. In the quadrant V N is drawn the line H H, which gives the relation between the volume and the entropy of 1 pound of water. Since the distance of line H H from line N is extremely small as compared with the other distances to be measured in this quadrant, no serious error will be introduced if this line is omitted and the con- structions are based upon line N instead of line H H. The saturation curve for the quantity of steam which the test shows to be contained in the cylinder per revolution at cut-off, is next drawn in the quadrant P V, and is the line R Q. In the quadrant TON are drawn the lines W and S N, the first being the water line and the second the satu- ration line. In order to transfer any point on the indicator card, as, for instance, point B, to the temperature- entropy plane, the following construction is employed. Draw line A C through B, then draw lines A D and C E. Next draw lines E D and G H, then D H, then B F, and finally F I. The intersection of C E and S N determines the entropy of 1 pound of dry and saturated steam at the temperature represented by point B. The entropy of evaporation of the wet steam at point B is proportional to the increase in its volume which results from its evaporation (i.e., to its quality). By the construction, we have divided the evaporation line G E into two segments, one of which, G I bears the same ratio to G E, as the volume of the steam at B does to the specific volume of dry and saturated steam. The point / is therefore the state point on the temperature-entropy diagram of the point B on the pressure-volume diagram. Other points on the temperature-entropy diagram may be found in the same way, and the diagram drawn. 348. The Temperature-Entropy Diagram for the Steam Turbine. Since a single-stage steam turbine operates upon the Rankine cycle, the theoretical temperature-entropy diagram will be that of the Rankine cycle FIG. 210. ART. 348 DIAGRAM FOR THE STEAM TURBINE 383 for steam of the quality supplied to the turbine. Turbines are usually supplied with superheated steam so that the temperature-entropy diagram will usually have the form shown in Fig. 201. However, after the steam has passed through the nozzle of the turbine, it loses a portion of its kinetic energy, which is retransformed into heat by eddying and fluid friction, so that although the kinetic energy of the steam flowing from a nozzle is in theory equal to the area e b c h d, the work which actually is transferred to the rotating member is much less. Actually, the expansion of the steam in the turbine nozzle is not quite adiabatic, since on account of friction, its entropy is continually increased by the retransformation of a portion of its kinetic energy into I i k FIG. 211. FIG. 212. heat. The diagram which represents the condition of affairs in such a nozzle is shown in Fig. 211, in which line c d represents the relation between the temperature and the entropy of the expanding steam. The kinetic energy of the jet proceeding from the nozzle is not, however, equal to the area b c d e, since a portion of the work generated was transformed into the heat represented by the area c d g f. The actual kinetic energy of the issuing jet is equal to the area b c d e minus the area i d f g. The amount of heat represented by the area i d f g is exceedingly small, however, when the nozzle is properly designed, and its effect in modifying the temperature-entropy diagram is almost imperceptible. The heat supplied in the entering steam is, of course, represented by the area h e b c g. 384 ENTROPY DIAGRAMS ABT. 349 In Fig. 212 may be seen the temperature-entropy diagram of a two- stage impulse turbine. A part of the kinetic energy of the jet issuing form the nozzles in the first stage is retransformed into the quantity of heat represented by the area f k I d. The equivalent area is shown sub- tracted from the work of the first stage and is represented by the shaded area within e b c d. In like manner, in the second stage, a portion of the work efghis retransformed into the quantity of heat represented by the area g i j k and is shown by the shaded area taken out of e fg h. The heat supplied in the entering steam is represented by the area m h b c I, and the useful work is measured b> the unshaded area included within h b c d f g. In the case of a turbine contain- ing a very large number of stages, ^ whether it be an impulse turbine or \ an impulse reaction turbine, the tem- perature-entropy diagram will have approximately the form shown in Fig. 213. The quantity of heat added is that represented by the area h e b c g. A portion of the kinetic energy of the steam flowing in the vanes is retransformed into the quan- tity of heat represented by the area c d f g and the relation between the temperature and entropy of the steam as it traverses the turbine is repre- sented by the line c d. The total amount of heat transformed into work is represented by the area e b c d minus the area i d f g. 349. The Total Heat-Entropy or Mollier Diagram. It is very convenient in designing thermodynamic apparatus, particularly in the case of steam turbines, to make use of the Mollier diagram, which gives graphically the relation between the total heat and total entropy of steam. Such a diagram accompanies both Marks and Davis' and Peabody's steam tables, and is shown in skeleton in Fig. 214. On this diagram are drawn lines of constant quality (such as a-b) or constant superheat (such as c-d) and lines of constant pressure (such as e-f or g-h) which are, of course, lines of constant temperature in that portion of the diagram which represents the properties of wet steam. On this diagram, vertical lines are lines of constant entropy and are therefore adiabatic lines. Horizontal lines are lines of constant total heat. Any point on the diagram is determined ART. 349 THE TOTAL HEAT-ENTROPY OR MOLLIER DIAGRAM 385 by the intersection of four lines, namely a constant total heat line (hor- zontal) a constant entropy line (vertical) , a constant pressure line (diag- onal) and a constant quality or superheat line (sloping) . If, for instance, the pressure and quality of steam are known, its total heat and entropy may be determined. For instance, point ra is the state point on this diagram of steam of 21 pounds pressure and 80 per cent quality. The ordinate to this point gives the total heat of the steam (967 B. T. U.), and the abscissa its entropy (1.45). If any two of the four properties are known, the other two may be determined from the diagram. 1300 800 1.40 1.50 1.60 1.70 Entropy 1.80 1.90 FIG. 214. In order to use such a diagram in the solution of problems, it is con- venient to paste the diagram on a well-seasoned drawing board, and to cover it with a sheet of transparent celluloid, mounting it carefully, so that its coordinates are vertical and horizontal. By graphical construction upon such a diagram, many problems may be solved very quickly. For instance, let it be assumed that in a throttling calorimeter the temperature and pressure of the steam are those shown by point J (this would be possible in case the calorimeter were connected to a condenser in order to increase the permissible wetness of the steam to be tested). By drawing through J a horizontal (i.e., a constant total heat) line, the intersection of this line with the pressure line of the steam in the pipe from which the sample was taken (as at i}, will give the state point of that steam, and its quality will be known. 386 ENTROPY DIAGRAMS ART. 350 In like manner if point k be assumed to be the state point of the steam entering a nozzle, as determined from its pressure and superheat, a vertical (i.e., an adiabatic) line drawn to intersect the pressure line which repre- sents the pressure of the steam as it issues from the nozzle, will determine the properties of steam. If point I is at the intersection of the adiabatic and the terminal pressure line, it is the state point of the issuing steam. The length k-l will then represent the heat transformed into kinetic energy, and by transferring the distance to the velocity scale at the left of Marks and Davis' diagram, the velocity may be read off directly, the final velocity being determined by the distance from the initial velocity of the steam entering the nozzle. Other constructions will readily suggest themselves to the reader for solving various problems in connection with the properties of steam or its behavior in engines and turbines.' 350. Temperature-Entropy Diagrams for Hot-air Engines. The tem- perature-entropy diagram may be used to illustrate the action of the work- ing fluid in a hot air engine. In Fig. 215 will be found the temperature- entropy diagram of a Joule cycle engine. The line d a represents the. adiabatic com- pression of the working fluid, the line a-b the increase in entropy and temperature which occurs in the heater, the line bc represents the adiabatic expansion of the working fluid, and the line c-d, the decrease in temperature and entropy which occurs in the cooling chamber. Lines a-b and dc will, of course, be logarithmic curves, since the specific heat of the gas is con- stant. The quantity of heat supplied is repre- sented by the area / a b e, the quantity of work done by the area abed and the heat FlG 215. rejected by the area d c e f. It will be seen that the efficiency of the cycle will be increased by increasing the temperature range during the adiabatic expansion or compression and that the lower the initial temperature at the beginning of adiabatic expansion, the greater will be the efficiency of the cycle. No temperature-entropy diagram can be drawn for a Stirling cycle engine, since the conditions of operation of the engine are contrary to the fundamental assumption made in drawing a temperature-entropy diagram. In the Stirling engine, a portion of the working fluid is at the temperature of the heater while the remainder of it is at the temperature of the cooler. The temperature-entropy diagram assumes that the entire quantity of the working fluid is at the same temperature, consequently no tempera- ture-entropy diagram can be drawn for this engine. f ART. 351 DIAGRAM OF THE OTTO CYCLE 387 351. The Temperature-Entropy Diagram of the Otto Cycle. The temperature-entropy diagram of the Otto cycle may be seen in Fig. 216. It is bounded by two adiabatics, a-b and c-d, and two constant-volume lines bc and a-d. These lines are, of course, logarithmic curves. It is assumed that the specific heat of the working fluid is constant. The heat supplied is, of course, the area b-c-e-f, and the work done is the area bed a, and its heat rejected is area fa d e. 352. Temperature-Entropy Diagram of other Gas-engine Cycles. The temperature-entropy diagram of the Sargent cycle may be found in Fig. 217. a-b and c-d are adiabatics, b-c is a constant-volume line, d-e is a Of FIG. 216. constant- volume line and e-a is a constant-pressure line. The heat supplied is b c f g and the work done b c d e a. The extra power gained over the Otto cycle is represented by the area d' a e d, line a-d' being a constant volume line. The temperature-entropy diagram of the Diesel cycle with isothermal expansion is seen in Fig. 218. Lines a-b and c-d are adiabatics, b-c is an isothermal, and d-a a constant-volume line. In Fig. 219 is seen the temperature-entropy diagram of the Diesel cycle with isobaric expansion. a-d and c-b are adiabatics, d-c is the isobaric line and b-a the constant- volume line. It will be seen that by increasing the temperature range by isobaric instead of isothermal expansion, the theroretical efficiency of the cycle is increased. 353. The Actual Temperature-Entropy Diagram of an Otto Engine. The form of temperature-entropy diagram which will actually be given by an Otto cycle engine may be seen in Fig. 220. The line a-c is 388 ENTROPY DIAGRAMS ART. 353 the actual compression line. The line c-x, which is, of course, approximately a logarithmic curve, represents the rise in temperature at explosion. The line x-t is the expansion line and the line t-a represents the fall in pressure at the end of expansion. This diagram is shown superimposed upon the diagram a c' x' t f , which is the theoretical temperature-entropy diagram for an Otto cycle engine when the quantity of heat added at explosion is the entire quantity of heat contained in the working fluid. The diagram a c' x" t" is the theoretical temperature-entropy diagram of the Otto cycle for the same temperature limits as occur in the actual engine. It will be noted that the actual compression line a-c at first runs to the right and then turns off to the left. The reason for this is that during -N FIG. 218. i e FIG. 219. the early part of the compression stroke the temperature of the walls is higher than that of the working fluid, the working fluid receives heat from the walls, and its entropy is increasing. The working fluid soon becomes hotter than the walls, however, and begins to lose heat to them, so that its entropy decreases during the latter portion of the compression stroke. During the explosion the working fluid is receiving heat on account of the combustion of the charge, and is losing heat to the cylinder walls. The line c-x represents the net effect of the addition and abstraction of the heat during this period. During the expansion period the working fluid is receiving heat on account of the delayed combustion of the charge, and it is also losing heat to the cylinder walls. On the whole the quantity of heat lost to the walls is greater than that received from ART. 354 I HE AIR COMPRESSOR 389 the combustion of the charge, so that the expansion line tends to the left as it descends. The line t-a is of course identical with the theoretical line. The exact form of tempera- ture-entropy diagram given by an Otto cycle engine will vary with the size of the engine, the character of the charge, and the relative amounts of the several losses. The temperature-entropy diagram is not as useful in ana- lyzing the losses occurring in a gas engine as it is in analyzing those in a steam engine, and care must be taken when employing the diagram to see that the quan- tities of heat represented on the diagram are properly interpreted. 354. The Air Compressor. No temperature-entropy diagram can be drawn for an air-com- pressor cycle, since the quantity of working fluid contained in the cylinder is not constant. It might be thought that the diagram could be constructed by drawing two adiabatics and two constant-pressure lines for air, but it must be borne in mind that the air is expelled from the cylinder at constant temperature as well as at constant pressure. The constant-pressure line of the temperature-entropy diagram assumes that the weight of the working fluid is constant, and that its volume is decreased by changing its temperature. It will be seen then that a tem- perature-entropy line diagram cannot be drawn, since the working fluid does not perform a true cycle. 355. The Temperature-Entropy Diagram of Refrigerating Machines. The theoretical tempera- ture-entropy diagram for a refrigeration cycle is similar in its general appearance to that of a heat- engine cycle. The temperature-entropy diagram of the reversed Joule cycle may be seen in Fig. 221. FIG. 221. I^ ne a ~b represents the absorption of the quantity FIG. 220. a 390 ENTROPY DIAGRAM'S ART. 355 of heat measured by the area / a b e in the vaporizer, which raises the tem- perature of the working fluid from point a to point b and increases its entropy. Adiabatic compression then increases its temperature to point c without changing its entropy. The line c-d represents the process of cooling the working fluid in the condenser at constant pressure, during which time it parts with the quantity of heat represented by the area feed. The area feed represents the heat taken from the vaporizer, / e b a, plus the work done upon the working fluid, abed. The temperature-entropy diagram of the ammonia-compression cycle may be seen in Fig. 222. At point a compression of dry and saturated ammonia vapor begins. The ammonia vapor in practice may be slightly wet or slightly superheated, but it is usually nearly dry and saturated. This vapor is compressed adiabatically along the line a-b and becomes superheated during the process. The super- heated vapor is introduced into the condenser where it is con- densed at constant pressure (after being cooled to the saturation temperature) along the constant-pressure line b-c-d. In passing through the expansion valve, the total heat of the ammonia vapor is unchanged, and the fall in temperature is therefore repre- sented by the constant total heat line d-e. The entropy of evaporation of that portion of the liquid which is evaporated by the heat of the liquid, is represented by the segment 0e. The remainder of the latent heat of evaporation is taken from the vaporizer at constant temperature, the process being represented by the line e-a. The heat abstracted from the vaporizer is, of course, represented by the area g e a /, while the heat rejected to the condenser is equal to the area g e d c b f. The actual temperature-entropy diagram which would be obtained from an ammonia compression plant may be seen in Fig. 223. The vapor that comes to the compressor is usually slightly wet. Since the cylinder of the machine is warmer than the vapor which it compresses, this vapor is almost immediately dried and then continues to gain heat during the ART. 355 DIAGRAM FOR REFRIGERATING MACHINES 391 FIG. 22:?. most of the 'compressed period. The remainder of the diagram is identical with the theoretical diagram, but the compression line a-b is approximately of the form shown. Since the ammonia vapor is not entirely dry as it enters the cylinder, the amount of heat abstracted from the vaporizer per pound of working fluid, represented , by the area g e a /, is less than would be transferred if the ammonia were dry. At the same time, the amount of work required to compress the am- monia and deliver it into the condenseris considerably greater than it was in the theoretical cycle, since the vapor gains heat during the early part of the compression period from the walls of the compressor cylinder. The efficiency of the system is, of course, equal to the area g e a f divided by the area e d c b a. The temperature-entropy dia- gram for an absorption system may be seen in Fig. 224. In this diagram, line a-b represents the vaporization of the ammonia at con- stant pressure in the generator, while line b-a (the same line reversed) represents its condensation in the condenser. The ammonia liquid now escapes through the expansion valve, a process represented by the con- stant total heat line a-c. Within the vaporizer, the remainder of the liquid evaporates, a process repre- sented by the evaporation line c-d. This ammonia is then superheated by absorbing heat at constant pressure along the line d-e. It then con- FIG. 224. denses by absorption in water and \ g fc 392 ENTROPY DIAGRAMS ART. 355 the heat is removed from the absorber at constant temperature, that process being represented by the line e-f. Its temperature is now raised by the application of heat until the liquid is sufficiently hot, so that the ammonia may be vaporized. The heat absorbed in the vaporizer is represented by the area c d g h. The heat supplied to the generator is represented by the area I a b i. The heat taken from the absorber is represented by the area j f e k. The heat represented by the area / / a I is returned by the regenerator coil, from the spent liquid entering the absorber, to the liquid entering the generator. The quantity of heat absorbed by the condenser is represented by the area I a b i. In drawing this diagram it has been assumed that the heat added or abstracted was the latent heat of ammonia vapor. Since, however, ammonia has an affinity for water, additional quantities of heat are transferred, due to the extra heat required to evaporate ammonia from an aqueous solution. No account, however, has been taken of these quan- tities in this diagram. CHAPTER XXVI THE KINETIC THEORY OF HEAT 356. The Kinetic Theory of Gases. All of the phenomena noted in the first seven chapters of this book, and collectively termed the properties of gases and vapors and their mixtures, may be entirely explained by the kinetic theory of heat. This theory assumes that any mass of gas or dry vapor is composed of a great number of very small particles. These particles are perfectly elastic, and in the case of a perfect gas, exert no force upon anything with which they are not in actual contact. In the case of imperfect gases, these particles tend to attract or repel one another. The mass of each particle, although minute, is definite and unchangeable. The volume of each particle is infinitesimal in the case of a perfect gas. In the case of an imperfect gas, the volume is finite, although extremely minute. In case the gas is of homogeneous composition, each of the particles is exactly like every other. These particles are in chemistry termed molecules, and hereafter in this chapter will be designated by that term. Assume that a number of such molecules are confined within the walls of a vessel; and that these walls are motionless and absolutely rigid. Eac*h particle, once it is set in motion, will move with uniform velocity in a right line until it impinges upon one of the walls. Since it is perfectly elastic, and the wall is perfectly rigid, it will rebound from the wall with undiminished velocity and unchanged energy. It will proceed in its path until it encounters a second wall, from which it will rebound in the same manner, and will continue thus to travel in straight lines from wall to wall with unchanged velocity. Each of the particles contained in the vessel will behave in the same manner, arid since they are assumed to be infinitesimal in size, they will encounter each other only at infinite intervals. As the result of the impact upon the walls of the vessel, these walls will experience a pressure whose amount we will now determine. 357. Pressure Exerted on Account of the Motion of the Molecules. Assume that the vessel is a cube bounded by six planes, each 1 foot square. It will then contain 1 cubic foot of gas. Assume that this volume contains a molecule whose mass is m, and whose velocity, normal to a given face, is V l feet per second. Since the distance from the given face to the opposite face and back is 2 feet, the molecule V will strike the given face times per second. Each time it strikes the face its momentum is changed by the amount 2mV l . Each second, the given face will change the momentum of the molecule by the amount m TV- The rate of change of momentum is numerically equal to the force producing the change. Hence the mean value of the force exerted by the face in resisting the impacts of this molecule is m V^. If the space contains, in addition, a second molecule having the same mass, and whose velocity normal to the given plane is Y 2 > then the force exerted by the impacts of the two molecules will be ra(TV + TV), and so on for any number of molecules. Finally, if the space contains n molecules, the force exerted by their impacts upon the face will be +... + V$ . . . . (1) 393 394 THE KINETIC THEORY OF HEAT ART. 358 Designating the product of w and n by M, and n we will have for the pressure in pounds per square foot exerted by the gas P= MVI (2) In the case of an actual gas under an appreciable pressure the molecules are very great in number and are traveling in all directions. The value of \' ^ is therefore the same for each of the six faces of the cube. The square of the velocity of each particle is the sum of the squares of the velocity components normal to each of three adjacent faces. Consequently, the mean of the squares of the velocities of all the molecules is three times the mean of the squares of any component of the velocities. We may therefore write V 2 = 3 V,; (3) Replacing Vn by -y> W and M by in equation (2), we will have 9o WV 2 in which W is the weight of the gas in pounds per cubic foot, V 2 is the mean of the squares of the velocities of all the molecules, and g is the standard acceleration of gravity. Since the weight of the gas per cubic foot is equal to the weight per molecule (w) multiplied by the number of molecules per cubic foot (w) we may write the above equation in the form wV 2 In the above expression, -^ is of course the mean kinetic energy per molecule of the gas. Hence the pressure of the gas is proportional to the mean kinetic energy per molecule, and to the number of molecules per unit of volume. Substituting ^ V for Vn m equation (2), we will have P = JMV 2 , - - (6) when the mass of gas M occupies one cubic foot. If it occupies V cubic feet, we will have PV^MV\ (7) in which P is the pressure of the gas in pounds per square foot, V is the volume of the gas in cubic feet, M is the mass of the gas in kinetic mass units, and is equal to , where yo W is its weight in pounds, and V is the mean of the squares of the molecular velocities. 358. Te nj>jr liu e of a Gas Proportional to the Mean Kinetic Energy of the Molecules. If W3 increase the mean kinetic energy per molecule, we must do so by transferring energy to the gas. If we assume that this energy is transferred to the gas in the form of heat, we will have the mean kinetic energy per molecule increased by AET. 359 LOSS OF ENERGY DURING EXPANSION 395 the addition of heat. We know that the addition of heat to a gas increases its temper- ature and pressure, and if the gas be perfect, the increase in temperature and pressure is proportional to the quantity of heat added. Hence we may conclude that the absolute temperature as well as the pressure of any gas given is proportional to the mean kinetic energy per molecule. A further inspection of equation (5) in the preceding article will show that if we change the mass of a molecule without changing the number of the molecules, that the pressure of the gas will be the same when V is so changed as to make the mean kinetic energy per molecule the same. Certain chemical phenomena point to the conclusion that the number of molecules in a given volume of gas confined at a given pressure and temperature is always the same whatever be the nature of the gas. Hence, we arrive at the conclusion that the absolute temperature of any gas is proportional to the mean kinetic energy per molecule. When a cubic foot of gas is heated at constant volume, the heat will be entirely expended in increasing the velocity of the molecules. Consequently, the heat imparted to the gas, when measured in dynamic units, will be MTV MFi 2 //# = (8) in which F 2 2 is the mean of the square of the final molecular velocities, and V\ 2 is the mean of the squares of the initial velocities. This equation may be written 359. Loss of Energy during Expansion. When the gas is heated at constant pres- sure, a part of the energy is expended in doing external work. If we assume that all of the energy is first transferred to the molecules, then some of this energy will be sur- rendered by the molecules during their impact upon the moving wall of the expanding vessel. The increase in volume of the gas is proportional to the absolute temperature and is consequently proportional to the change in the mean square of the velocity of the moelcules. The work done by the gas is found by multiplying the initial pres- sure by the change in volume. Since the initial volume is 1 cubic foot, and the volumes are proportional to the mean of the squares of the velocities of the molecules, we will have for the change in volume For the pressure of the gas we will have the value D mV* 2n Multiplying (10) and (11) together we will have for the work of expansion PJF=(F 2 2 -F 1 2 )f (12) The increase in the kinetic energy of the molecules is given by equation (9), Art. 358. Adding this to equation (12), we will have for the energy required to heat a cubic foot of the gas at constant pressure 396 THE KINETIC THEORY OF HEAT ART. 360 The quantity of energy given by equation (y) Art. 358, is proportional to the specific heat of the gas at constant volume. That given by equation (13), is propor- tional to the specific heat of the gas at constant pressure. Dividing the latter by the former we will have for the ratio of the specific heats 5M M -Q-+-2= l % = r (14) We may therefore conclude from equation (14) that the value of f for a gas whose molecules have translational energy only, is always If. 360. Intra-molecular Energy. The molecules of a gas will have translational energy only, when each of the molecules consists of one particle w r hose dimensions are infinitesimal. Such a gas is said to be monatomic. If the molecule is composed of two or more particles (in chemistry termed atoms) with a finite distance between them, it will be apparent that they must have a motion relative to one another, which will absorb a portion of the heat energy imparted to the molecule. Such a gas is said to be polyatomic. The energy which the molecule contains in virtue of the relative motion of its atoms is termed intramolecular energy. The energy which it contains in virtue of its mass and the velocity of its center of gravity, is termed translational energy. The sum of the intramolecular and translational energy of the molecule is termed the intrinsic energy. Clausius has shown that the ratio of the mean intramolecular energy to the mean translational energy is a constant for any gas. This ratio is therefore called Clacsius' ratio, and is designated by the letter p. The energy which must be imparted to the gas for the purpose of increasing its temperature will be 1 -f p times that which would be required by the same volume of a monatomic gas. We will have then for the quantity of energy imparted to the gas in heating it, at constant volume, Adding equation (15) to equation (12) of the preceding article, we will have the energy imparted to the gas to heat it at constant pressure, which is JH P = 5 + 3/7 3 Dividing 16 by 15 we will have 5 + 3 p r="-^-- (17) 3-r3,o It may be noted that when p becomes zero, the value ? becomes | -, as it should. Solving (17) for p, we will have for the value of Clausius' ratio for a gas for which the constant f is known, P = ^^- (18) 361. Adiabatic Expansion of Gases. When a gas is confined within an expanding vessel, for instance, a cylinder having a moving piston, the mean intrinsic energy per molecule will diminish, since the molecules which strike the piston will rebound from its face with diminished absolute velocity, their velocity relative to the face of the piston being unchanged in amount and reversed in direction by the impact. The energy thus surrendered by the molecules reduces their mean kinetic energy and so reduces the temperature of the gas. In case the volume of the cylinder is diminished, the mole- ART. 362 CONDITION OF EQUILIBRIUM 397 cules will rebound from the moving piston with increased velocity, the velocity relative to the face again being the same after impact as before. The result of such compres- sion is, of course, to increase the mean kinetic energy per molecule and the temperature of the gas. The phenomena of adiabatic expansion and compression are thus fully explainable by the kinetic theory. 362. Condition of Equilibrium between Molecules of Different Masses. If a gas be conceived to consist of molecules of two different kinds (i.e., if it is a mixture of different gases) the molecules will pass among each other and occasionally molecules of one kind will, by collision or otherwise, exert force upon molecules of the other kind. Each time that force is exerted between two molecules of different kinds, they will exchange a portion of their kinetic energy. In general, the molecule having the greater kinetic energy will give up a portion of its energy to the molecule having less energy, so that as a result of the continued interchange of energy, we will find that the mean kinetic energy per molecule of the two different kinds of molecules will become equal, or in other words, the two constituents of the mixture will come to the same temperature. In the case of such mixtures, the mean velocities of the different classes of mole- cules will be different. In order that the temperature of the two constituents shall be the same, the mean value of the kinetic energy per molecule must be the same for the several constituents. In order to make this true, it is necessary that the mean square of the velocities of each kind of molecules shall be inversely proportional to the mass of a molecule of that kind, so that the lighter molecules in a mixture will have high velocities while the heavier ones will have low velocities. We have already seen in equation (7) Art. 357, that P F = MV 2 ', this equation may be \vritten PV-^V' (19) Substituting the value of P V from the characteristic equation of gases, we will have, = W R T, whence we deduce that vV 2 = V3