u. 
 
 . G/'/es. y.o/O. /&3***A o. 
 
 THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 OF CALIFORNIA 
 
 LOS ANGELES
 
 
 //-
 
 STEAM TURBINES
 
 Published by the 
 
 Me G raw- Hill Boot Company 
 
 Ne^v York 
 
 Successons to theBookDepartmervts of the 
 
 McGraw Publishing Company Hill Publishing Company 
 
 Publishers of Books for 
 
 Electrical World The Engineering and Mining Journal 
 
 Engineering Record Power and The Engineer 
 
 Electric Railway Journal American Machinist 
 
 Metallurgical and Chemical Engineering
 
 STEAM TURBINES 
 
 A SHORT TREATISE ON THEORY 
 
 DESIGN, AND FIELD OF 
 
 OPERATION 
 
 BY 
 
 JOSEPH WICKHAM ROE, M. E. 
 
 MEM. AM. SOC. MECH. ENGRS., MEM. AM. INST. MINING ENGRS. 
 
 ASSISTANT PROFESSOR OF MECHANICAL ENGINEERING, 
 
 SHEFFIELD SCIENTIFIC SCHOOL, YALE UNIVERSITY. 
 
 McGRAW-HILL BOOK COMPANY 
 
 239 WEST 39TH STREET, NEW YORK 
 
 6 BOUVERIE STREET, LONDON. E. C. 
 
 1911
 
 COPYRIGHT, 1911 
 
 BY THE 
 
 MCGRAW-HILL BOOK COMPANY 
 
 Printed and Electrotyped 
 
 by The Maple Press 
 
 York, Pa.
 
 Engineering 
 Library 
 
 TJ 
 
 PREFACE. 
 
 The purpose of this book is twofold, to provide, first, a text- 
 book suited to a short course on steam turbines in engineering 
 schools and, second, a book for the engineer on the principles 
 and general design of turbines without going into refined treat- 
 ment of the more difficult problems entering into their design. 
 
 At the end of each article is given a short list of references 
 where those wishing to pursue the subject will find it treated 
 most thoroughly. Other references are given among the prob- 
 lems to sources available to most students and it is suggested 
 that these be made subjects for short reports, thus extending the 
 reading of the student beyond the limits of the present text. 
 The writer wishes to thank Mr. Geo. A. Orrok of the New 
 York Edison Company, the engineers of the prominent turbine 
 manufacturers, for data and illustrations used, and especially 
 Mr. C. C. Perry of the Sheffield Scientific School for his help in 
 the preparation of the material. 
 
 JOSEPH W. ROE. 
 
 SHEFFIELD SCIENTIFIC SCHOOL, 
 
 YALE UNIVERSITY, 
 
 April, l. 1911. 
 
 713873
 
 TABLE OF CONTENTS. 
 
 CHAPTER I. EXPANSION OF STEAM. PAGE. 
 
 Art. 1. The Energy of a Jet 1 
 
 " 2. The Temperature-entropy Diagram 4 
 
 " 3. The Heat-entropy Diagram 7 
 
 " 4. The Velocity of a Jet 9 
 
 " 5. Weight of Steam Delivered and Impulsive Force . . 13 
 
 CHAPTER II. UTILIZATION OF KINETIC ENERGY IN STEAM. 
 
 Art. 6. Expanding Nozzles 16 
 
 " 7. Design of an Expanding Nozzle 22 
 
 " 8. Blade Forms and Blade Velocities 26 
 
 9. Conditions of Maximum Efficiency . 29 
 
 " 10. The Trajectory of the Steam . . : 35 
 
 CHAPTER III. CALCULATIONS OF TURBINE BLADING. 
 
 Art. 11. Single-stage Impulse Turbines 40 
 
 " 12. Multi-stage Impulse Turbines 44 
 
 " 13. Single Flow Impulse-reaction Turbines 54 
 
 " 14. Double Flow Impulse-reaction Turbines 66 
 
 CHAPTER IV. MECHANICAL PROBLEMS. 
 
 Art. 15. Centrifugal Strains 73 
 
 " 16. Bearings 78 
 
 " 17. Governing 82 
 
 CHAPTER V. COMPARISON OF TYPES. 
 
 Art. 18. Vertical Turbines 88 
 
 " 19. Tangential Flow Turbines 91 
 
 " 20. Multicellular Turbines ...... 94 
 
 " 21. Special Forms of Impulse-reaction Turbines ... 98 
 
 " 22. Low Pressure Turbines and Regenerators . . . . . 101 
 
 CHAPTER VI. CONDITIONS OF OPERATION. 
 
 Art. 23. Effect of Superheat 108 
 
 " 24. High Vacuums in Engines and Turbines 110 
 
 CHAPTER VII. THE POSITION AND FIELD OF THE STEAM TURBINE. 
 
 Art. 25. Relative Economy of Engines and Turbines . . . .116 
 
 " 26. General Comparison of Engines and Turbines. . 126 
 
 " 27. Relative Fields of Engines and Turbines 131 
 
 INDEX 137 
 
 vii
 
 STEAM TURBINES.
 
 STEAM TURBINES. 
 
 CHAPTER I. 
 
 THE FREE EXPANSION OF STEAM. 
 Art. i. The Energy of a Jet. 
 
 The power developed in a steam turbine is derived from one 
 or more jets of steam. The power available depends on the 
 kinetic energy of the steam available under the given conditions 
 of operation. 
 
 The total kinetic energy in a moving mass of weight W and 
 velocity V is 
 
 WV 2 
 
 (1) 
 
 where the body is brought to rest. Where the velocity is 
 reduced from V to V l the kinetic energy available in the change 
 is 
 
 Or, from the standpoint of the force of the jet we have Ft mV. 
 Taking the time as unity the impulsive force acting for one 
 second is 
 
 WV 
 
 F=mV = -- . (3) 
 
 9 
 
 If A = area of the jet and w= the weight per cubic foot of the 
 steam at the given pressure and dryness or superheat, the 
 weight delivered per second is W = wAV. Substituting, Eq. (3) 
 becomes 
 
 ' (4)
 
 2 STEAM TURBINES. 
 
 For any given pressure and dryness w is known. Both the 
 impulsive force and the kinetic energy, K, available become 
 determinate as soon as V is known. An important part of the 
 theory of turbines has for its object the determination of this 
 V for any given set of conditions. 
 
 Taking the weight of steam in Eq. (1) as unity we have, 
 since the value of 2g is a known constant, a definite relation 
 between K and 7 by which the velocity V may be calculated 
 when the energy available per pound of steam is known. 
 
 The energy of a gas such as steam may exist in two forms, heat 
 and kinetic energy. It may consist wholly of heat. In this 
 condition the gas is confined and under pressure from the energy 
 of its particles, due to heat. If allowed to do so it would expand 
 into a medium at lower pressure, doing work; but since it is 
 confined and at rest, this capacity for work is potential only and 
 analogous to that of a weight suspended and doing no work, but 
 capable of doing it if released. 
 
 Or, theoretically, having been allowed to expand under the 
 influence of its heat tension or pressure until all the heat had 
 been expended, the energy would be wholly kinetic. This condi- 
 tion, however, is unattainable, and is analogous to the energy of 
 the weight if it had fallen freely from its point of suspension to 
 the center of the earth. Practically, therefore, there is a third 
 or intermediate condition where the energy exists in both forms, 
 and the total energy of the steam is the sum of its heat energy 
 and the kinetic energy. As the weight can fall only to the sur- 
 face of the ground, so steam in expanding can not give up all its 
 heat, but can part with it only to a point corresponding to the 
 temperature of the medium into which it expands. 
 
 In the British system of units heat is measured in British 
 Thermal Units and energy in foot-pounds, the two being inter- 
 changeable at the ratio of 1 B.T.U = 777.5 foot-pounds. 1 From 
 the Law of Conservation of Energy the total energy in a pound 
 of steam during expansion remains a constant. Expressing 
 this in the form of an equation, 
 
 WV 2 WV^ 
 
 777. 5Sl+ -m.5H.+HJ. 
 
 i The heat values throughout this book are those given in Marks and Davis' "Steam 
 Tables and Diagrams."
 
 THE FREE EXPANSION OF STEAM. 3 
 
 where H^ \ and H 2 V 2 are the heat energies and steam velocity 
 for any two stages of the expansion. Remembering that W is 
 unity 
 
 y 2_ V 2 
 777.5 (H 1 -H 2 )=---^-. (5) 
 
 V 2 
 In the expansion of steam from a vessel --- may be neglected, 
 
 therefore Eq. (5) becomes 
 
 
 in which V is the theoretical velocity attained, and H l and H 2 the 
 total heat content in B. T. U. per pound of steam before and 
 after expansion. 
 
 Problems. 
 
 1. What is the impulsive force when five nozzles are each discharging 
 .96 Ib. of steam at a velocity of 3450 ft. per sec.? 
 
 2. What velocity must a pound of steam have to deliver 87,000 ft. Ibs. 
 of work per sec.? 
 
 3. What energy per Ib. will steam give up when slowed down from 
 2150 ft. per sec. to 1210 ft. per sec.? 
 
 4. What energy per Ib. of steam will be available for a decrease in 
 velocity from 3090 ft. per sec. to 2150? 
 
 5. What weight of steam must be delivered per sec. to give 60,000 
 ft. Ibs. of work per sec. when the velocities before and after ex- 
 pansion are 2500 and 1500 ft. per sec.? 
 
 6. What is the theoretical H. P. of a jet delivering 1.3 Ibs. of steam 
 per sec. at 3500 ft. per sec.? 
 
 7. What must be the initial velocity of steam which delivers in one 
 jet 40 H. P. per Ib. of steam delivered, the final velocity being 
 1600ft. per sec.? 
 
 8. What is the impulsive force in .092 Ib. of steam moving at 1330 ft. 
 per sec., also at 3680 ft. per. sec.? 
 
 9. How many H. P. are available in a heat drop of 42 B. T. U. per sec.? 
 10. What heat drop is required to generate a theoretical velocity of 
 
 3380ft. per sec.?
 
 4 STEAM TURBINES. 
 
 11. What is the H. P. per Ib. of steam of a jet where the heat drop is 
 235 B. T. U.? 
 
 12. What is the heat equivalent in B. T. U. per Ib. of the work done 
 when steam is reduced in velocity from 3400 ft. per sec. to 1300 
 ft. per sec.? 
 
 13. How many B. T. U.'s are the equivalent of a H. P. hr.? 
 
 References. 
 
 THOMAS: "Steam Turbines." 
 
 JUDE : " The Theory of the Steam Turbine." 
 
 Standard works on thermodynamics. 
 
 Art. 2. The Temperature -entropy Diagram. 
 
 The determination, then, of the theoretical steam velocities 
 which are to govern the design, depends on the heat drop in the 
 stage considered. This heat drop may be calculated analyt- 
 ically from steam tables, or determined more conveniently, and 
 with sufficient accuracy, from the entropy diagrams published 
 with steam tables or the works on turbine engineering. 
 
 J 
 
 FIG. 1. Temperature-entropy diagram. 
 
 In the temperature-entropy diagram for steam, the absolute 
 temperature of the water or steam is shown by the ordinate of a 
 point in a curve, and the total heat per pound by the projected 
 area underneath the curve. The corresponding abscissa repre- 
 sents a quantity known as the entropy. As engine and turbine
 
 THE FREE EXPANSION OF STEAM. 5 
 
 problems are concerned with certain changes in heat which 
 never involve the total contents, that portion only of the diagram 
 above the melting point of ice need be drawn. 
 
 The addition of a small amount of heat, dQ, at some temper- 
 ature T would be represented by the shaded slice, Fig. 1, or 
 
 TdE = dQ. (7) 
 
 If S be the mean specific heat during a change the heat added 
 is Q=S(T 1 -T 2 ), or for differentials, dQ=SdT. Substituting, 
 we have 
 
 (7a) 
 
 Integrating, the change of entropy for a rise in temperature 
 from T 2 to T v as from A to B, is 
 
 T 
 
 e . (8) 
 
 Equations (7) and (7a) represent the curve OB, the projected 
 area beneath this line showing the heat contents of water. 
 When heat is added as latent heat and goes wholly into changing 
 the condition, as during vaporization, the temperature remains 
 
 dQ 
 
 constant and Eq. (7) becomes - 7 -- = a constant, i.e., the entropy 
 
 dhi 
 
 and the heat vary directly and the curve is a horizontal straight 
 line represented by 
 
 As the latent heat varies for different temperatures the corre- 
 sponding horizontal lines, such as BC , will vary in length and a 
 curve, CI', drawn through their ends will be the locus of the 
 saturation points. After the water has been wholly converted 
 into steam, further addition of heat raises its temperature and 
 the equation of the curve resumes the form (8), with S as the 
 variable specific heat of superheated steam.
 
 6 STEAM TURBINES. 
 
 Expansion through an orifice or short nozzle is so rapid as prac- 
 tically to give the conditions of adiabatic expansion, in which 
 there is no exchange of heat between the steam and the walls 
 surrounding it. Such heat as is given up goes into external 
 work only, which is done at the expense of the internal energy of 
 the steam. For instance, let the steam be at the condition 
 indicated at C, that is, at the temperature T v and just dry and 
 saturated. If allowed to expand adiabatically to a lower tem- 
 perature !T 2 the vertical line CD" would indicate adiabatic expan- 
 sion, since any other line as CD' or CD" would have an area 
 under it indicating heat added to or subtracted from the steam, 
 as heat, during the expansion. The external work done, equal 
 to the heat energy represented by the area A BCD is accounted 
 for by the lowering of the quality of the steam, or the condensa- 
 tion of a portion. If the quality of the steam was originally 
 below the saturation point, as at E, then the quality at the 
 lower pressure will have some other value, as shown by the 
 position of F. If the steam were originally superheated, as 
 indicated at H, adiabatic expansion will reduce the amount of 
 superheat as at /, or if continued bring it to saturation as at /', 
 or if still further continued condense part of the steam as indi- 
 cated by the position of /. 
 
 Problems. 
 
 (Use standard steam tables, such as Marks and Davis'.) 
 
 1. What is the increase in entropy from water at 65 Fahr. to dry, 
 saturated steam at 320 Fahr.? 
 
 2. The entropy of evaporation at 360 Fahr. is 1 .0514. What is the 
 latent heat of evaporation for that point? 
 
 3. Referring to Fig. 1, under what conditions will steam expanding 
 adiabatically from Tj to T 2 have its quality raised, when will it 
 remain about the same, when will it be lowered? 
 
 4. What will be the final quality of steam expanded adiabatically from 
 the dry, saturated point, C, 140 Ibs. gauge pressure to 28 inches of 
 vacuum?/*, V,A ,177 
 
 5- Given steam at 170 Ibs. absolute and superheated 100 Fahr., at 
 what pressure will it be dry and saturated when expanded adiabat- 
 ically, at what pressure will its quality, be 90%? (Take the specific 
 heat of superheated steam at 0.6.) 
 
 6. Given steam at 160 Ibs. gauge pressure and 98 1/2% quality, what is
 
 THE FREE EXPANSION OF STEAM. 7 
 
 the quality or superheat at atmospheric pressure which corresponds 
 to the same total heat? 
 
 7. Given 1 Ib. of water at 70 Fahr., what will be its condition when 
 1148 B. T. U.'s have been added and its absolute pressure is 27 Ibs.? tf, : 
 
 8. What is the B. T. U. drop per Ib. for adiabatic expansion from" 
 150 Ibs. gauge pressure and 80 Fahr. superheat to a pressure cor- 
 responding to 28 1/2 inches of vacuum?- j-ll .^ 
 
 References. 
 
 THOMAS: "Steam Turbines." 
 
 JUDE: "The Theory of the Steam Turbine." 
 
 NEILSON: "The Steam Turbine." 
 
 MOYER: " Steam Turbines." 
 
 FRENCH: " Steam Turbines." 
 
 Art. 3 The Heat-entropy Diagram. 
 
 'Prof. Mollier has developed a heat diagram based upon the 
 temperature-entropy diagram, but more convenient to work with. 
 Copies of this chart, for both British and Continental units, are 
 published with a number of the standard works on steam turbines. 
 An excellent one is published with Marks and Davis' Steam Tables, 
 a part of which, on a reduced scale, is reproduced here. 1 
 
 In this chart the heat content of the steam at any given condi- 
 tion of pressure and dryness or superheat, appears as the ordi- 
 nate in a right-angled co-ordinate system, instead of an area as in 
 the temperature-entropy diagram, and the entropy appears as 
 the abscissa. Any condition of the steam may be expressed by 
 the position of a point in this plane. The points of equal pressures 
 being connected, there results the series of curves of equal 
 pressures running upward from left to right. Similarly, by 
 connecting points of constant dryness and constant super- 
 heat we have curves of constant quality and superheat. A 
 vertical line from an initial condition to the pressure line 
 of the final condition shows the heat drop due to adiabatic 
 expansion where there is no change in entropy, and the 
 heat change may be read off directly on the scale of the chart. 
 Horizontal lines indicate changes at constant heat or changes of 
 condition, and therefore give the change in quality for moist 
 
 1 The Marks and Davis Diagrams I, Total Heat-entropy Diagram and II, Tota 
 Heat-pressure Diagram, may be purchased at $0.40 net, from the publishers, Longmans, 
 Green, and Co., 4th Ave. and 30th St., New York City.
 
 8 STEAM TURBINES. 
 
 steam, or in temperature or superheat for superheated steam. 
 As the theoretical velocity developed in a nozzle is a function of 
 certain constants and the heat drop only (Eq. 6), an additional 
 scale may be plotted from which the velocity corresponding to 
 the heat change may be read off at once. A third scale of the 
 foot-pounds available per pound of steam is also added, in which 
 the values are 777.5 times the B. T. U. drops. 
 
 Problems. 
 
 1. What is final condition of dry steam expanded adiabatically from 
 150 Ibs. gauge to 1 Ib. absolute? J'l 7 
 
 2. What will be the quality, of a Ib. of steam at atmospheric pressure 
 which has the same total heat as steam at 50 Ibs. absolute and 95% 
 quality? <?/3 
 
 3. Let steam be expanded adiabatically from 170 Ibs. absolute and 
 220 superheat, What is its pressure when dr^ and saturated? 5* 
 At what pressure will it have a quality of 88%? j^ 
 
 4. If dry steam is expanded adiabatically from 100 Ibs. gauge pressure 
 what would be its final condition if the velocity obtained is 3600 
 ft. per sec.? g\ 5 Cff %&*' 
 
 5. Let steam be expanded from 140 Ibs. gauge and 100 superheat and 
 attain a velocity of 3500 ft. per sec. How many ft. Ibs. of work 
 per Ib. of steam are being carried away as lost heat in the exhaust? 
 
 6. Steam expands from 160 Ibs. gauge and 120 superheat to 1.5 Ibs. 
 absolute and 89% quality. What would be the quality if it had 
 expanded adiabatically to the same pressure?/ What is the cause 
 of the increase in quality? 
 
 7. A Ib. of steam at 130 Ibs. gauge pressure generates 350 H. P., what 
 is the quality at 1 Ib. absolute? What is the change in entropy? 
 
 8. How many ft, Ibs. of energy are available per Ib. in the adiabatic 
 expansion of dry steam from 150 Ibs. gauge to atmospheric pressure, 
 and also from atmospheric pressure to 1 Ib. absolute? 
 
 9. Let dry saturated steam be expanded adiabatically from 100 Ibs. 
 absolute to 1 Ib. absolute. How many B. T. U.'s are available 
 with an atmospheric exhaust? 
 
 10. With dry steam at 140 Ibs. gauge pressure and expanding to 1 Ib. 
 absolute, how many ft. Ibs. per Ib. would be lost for a discharge at 
 the saturation point over a discharge under pure adiabatic expan- 
 sion? 
 
 References. 
 MARKS AND DAVIS: "Steam Tables and Diagrams."
 
 THE FREE EXPANSION OF STEAM. 9 
 
 Art. 4. The Velocity of a Jet. 
 
 In calculating the heat drop, in order to get the velocity, H 1 
 is usually found directly from the initial conditions. H 2 , how- 
 ever, is not known immediately, as only one of the conditions, 
 usually the pressure, is directly given. The dryness or quality 
 of the steam at the lower pressure must be determined before 
 
 FIG. 2. Temperature-entropy diagram. 
 
 H 2 is known. Assuming first an adiabatic drop in pressure, we 
 will have the following equations, referring to the entropy 
 diagram, Fig. 2: 
 
 (9) 
 
 = 223 . 
 
 l -q;~ T(E' +xE v -E") 
 
 for moist or dry saturated steam, x being the quality, and 
 
 (9a) 
 
 for superheated steam, where 
 
 q 1 and q 2 total of the liquid at the initial and final 
 
 pressures, P t and P 2 , 
 L 1 latent heat of vaporization for P l 
 T t and T 2 = the absolute temperatures at initial and 
 
 final pressures, 
 T 3 = the absolute temperatures of the superheat, as 
 
 indicated in Fig. 2, 
 $ = the specific heat of superheated steam.
 
 10 STEAM TURBINES. 
 
 This last value has been the subject of extensive experiment, 
 and is still open to discussion. A working value, in use by 
 engineers engaged in handling superheated steam, is from .6 
 to 65. Variations in the specific heat are taken into account in 
 the heat-entropy chart. As the heat drop in the temperature- 
 entropy diagram, Fig. 2, is represented by the area ABEF, 
 and as the side AB approximates a straight line, the figure 
 may be assumed to be a trapezoid. The area then would 
 
 /BE+AF\ 
 be (T^-Tjl ----- - J. 
 
 With this assumption (9) reduces to 
 
 and (9a) to 
 
 . (10a) 
 
 E l in the case of initially moist steam is the entropy BE = xE v , 
 where x is the quality of the steam and E v the entropy of evapora- 
 tion. For dry saturated steam, E x becomes E v , x being 1. E 2 
 is the entropy AF or AD according as initial steam is moist or 
 dry. It may be scaled directly from the entropy diagrams or 
 found from steam tables by adding to E 1 the difference between 
 the entropy of the liquids at 7\ and T 2 . The error introduced 
 by using this trapezoidal approximation is only about 1%. 
 
 A nozzle will not, however, deliver steam at the full velocity 
 represented by the heat drop between the inlet and outlet 
 conditions. Whatever the contour of the nozzle, frictional 
 resistances are offered to the flow, and the steam must give up 
 some of its heat energy in overcoming them. The heat thus 
 used raises the temperature of the surrounding walls and of the 
 particles of the steam itself. As the temperature of the steam 
 falls during further expansion, this heat re-evaporates part of the 
 water of previous condensation and raises the quality of the 
 steam. If the frictional work be sufficient to maintain its heat 
 constant during the fall of temperature, there is of course no 
 heat drop during the expansion, and consequently from Eq. (6)
 
 THE FREE EXPANSION OF STEAM. 
 
 11 
 
 no velocity. Such is the case where the work of friction is all 
 spent in raising the internal energy of the steam as in a throttling 
 calorimeter, where the final velocity is practically zero. 
 
 Adiabatic and constant heat expansion are shown by the en- 
 tropy diagram, Fig. 3. With steam at condition E adiabatic ex- 
 pansion would be shown by the vertical drop EF, the heat 
 drop causing increase of velocity being represented by the area 
 ABEFA. An expansion at constant heat would occur along a 
 line EF', such that the total heat, shown by the area beneath 
 Amn would at all times be equal to that beneath ABE. At the 
 
 B/ 
 
 FIG. 3. Temperature-entropy diagram. 
 
 final temperature the total heat area beneath AF l being equal 
 to that below ABE, no heat drop would be shown and there 
 would consequently be no velocity. Actual expansion in 
 turbine nozzles occurs along some such curve as EK, between 
 the adiabatic and this constant heat line. The heat drop pro- 
 ducing kinetic energy is represented by the difference of total 
 heat areas beneath ABE and AK. Under adiabatic conditions 
 the area under AF subtracted from the total area under ABE, 
 gives the area corresponding to the available heat energy. 
 Under the actual conditions the area under AK must be sub- 
 tracted. The excess area under FK represents, then, the heat 
 which might have been applied to increasing the velocity of the 
 steam, but is lost energy due to the frictional resistances. In 
 dealing with the relative areas it should be borne in mind that the 
 scale of the ordinates and the abscissas are widely different. 
 If y be the percentage of the heat drop H^ H 2 which is so lost, 
 (H l H 2 ) (l y) will be the heat energy converted into kinetic
 
 12 STEAM TURBINES. 
 
 energy, and this expression may be substituted in equations 
 (6), (10), and (lOo) giving 
 
 - y) 
 
 (12a) 
 
 where E 1 and E 2 are the entropy changes for adiabatic expansion 
 as before. 
 
 The percentage of re-evaporation, or increase in the quality of 
 the steam, FK, is readily obtained. The lost heat, y(H l H 2 ), 
 is equal to X 2 L 2 , where L 2 is the latent heat of evaporation or 
 the area under AG, and X 2 is the percentage of FK to AG. 
 Therefore 
 
 In .turbine design y is usually determined by experiment for 
 the type of nozzle to be used. An average of the results of 
 many investigations gives about 10% as the value of y, which 
 corresponds to a velocity of about 95% of the theoretical 
 velocity. 
 
 Problems. 
 
 1. Let steam at 98 1/2% quality and 145 Ibs. gauge expand adiabatic- 
 ally to 1.5 Ibs. absolute, what is the velocity obtainable by Eq. 
 (9)? Check this by the heat-entropy chart. 
 
 2. What velocity is obtainable for an adiabatic expansion from 180 Ibs. 
 absolute and 120 superheat to 80 Ibs. absolute, and also from dry 
 steam 3 Ibs. absolute to 1 lb.? 
 
 3. What velocity is obtainable with an expansion of from 150 Ibs. 
 gauge and 60 superheat to atmospheric pressure, with an energy 
 loss of 20%? What is the condition of the exhaust? 
 
 4. Let dry steam be expanded from 140 Ibs. gauge to 2 Ibs. absolute. 
 What will be the quality of the steam when the energy loss during 
 expansion is 14%? 
 
 5. What is the velocity of steam expanded from 155 Ibs. gauge and 
 50 superheat to 1.5 Ibs. absolute with 15% energy loss? 
 
 6. What is H. P. per lb. of steam represented by the conditions of 
 Prob. 5?
 
 THE FREE EXPANSION OF STEAM. 13 
 
 7. What must be the initial conditions when steam expanded to 1 Ib. 
 absolute and 90% quality generates 370 theoretical H. P. per Ib. 
 of steam with an energy loss of 85 B. T. U.? 
 
 8. Construct a condition curve for the expansion of steam from 155 
 Ibs. absolute and 80 superheat to 1 . 5 Ibs. absolute, with a reheat- 
 ing loss of 15%. What is the condition of the steam at 100 Ibs., 
 50 Ibs., and atmospheric pressure? 
 
 9. What is the energy loss when the velocity loss is 6%? 
 
 References. 
 
 STODOLA: "The Steam Turbine." 
 THOMAS: " Steam Turbines." 
 JTJDE : " Theory of the Steam Turbine." 
 MOYER: " Steam Turbines." 
 FRENCH: " Steam Turbines." 
 
 Art. 5. Weight of Steam Delivered and Impulsive Force. 
 
 Both experiment and theory show that fur a given upper pres- 
 sure P! there exists a certain lower pressure p 2 called the critical 
 pressure, for which the quantity discharged becomes a maximum, 
 and that however far the final pressure be lowered the quantity 
 delivered is not materially increased . The final velocity and weight 
 discharged will depend upon the final pressure only when that 
 pressure is higher than the "critical pressure" (about .SSpJ. 
 There exists in an expansion nozzle for final pressures lower than 
 this critical pressure, a zone near the inner end where the velocity 
 and weight of flow are the same whatever the lower pressure., 
 Beyond this point further expansion to the final pressure may 
 take place, with a marked increase of velocity, but the quantity 
 delivered will not be increased. While the final velocity attained 
 depends on the final conditions, the quantity discharged depends 
 solely on the critical pressure, provided the final pressure is less 
 than the critical pressure. This pressure varies somewhat with 
 different gases, as shown below. 
 
 Gas 
 
 Critical Pressure 
 
 Dry air 
 
 Superheated steam. . . 
 Dry saturated steam 
 
 .526 Pl 
 .546 Pl 
 .577 Pl 
 
 Moist steam j . 582 Pj 
 
 The value for steam is usually taken at I .58
 
 14 . , STEAM TURBINES. 
 
 It can also be shown that whatever the initial pressure, the 
 critical velocity of the steam in the throat created by the drop 
 in pressure to .58 p v is about the same, and that for that and 
 all lower final pressures the theoretical velocity in the throat is 
 about 1450 feet per second. 
 
 To determine, then, the weight of flow, only the critical 
 velocity and the area of the orifice, or, in the expanding nozzles, 
 of the throat, can be considered. The weight delivered is 
 
 144 v 
 
 where A = the area of the orifice, or least cross section, in square 
 inches., and v= the volume in cubic feet per pound at the critical 
 pressure . 58 p r Substituting for V the value given in Eq. (10) we 
 have 
 
 (Bi+BW'j-Tj, (14o) 
 
 E 2 and T z being taken for the critical pressure, and not the 
 final pressure. 
 
 The available energy per pound of steam multiplied by the 
 pounds of steam per H. P. hour is equal to 33000X60. There- 
 
 33000X60 
 
 fore the pounds of steam per H. P. hour or the 
 
 777. o(H j H 2 ) 
 
 2545 
 
 theoretical steam rate per H. P. hour = . (15) 
 
 Hi-Ht 
 
 This must be increased by the percentage of mechanical losses, 
 such as windage, friction, etc., to obtain the commercial rating. 
 From Eq. (3) the impulsive force, F, may be determined by 
 substituting the values of V and W found in Eq. (10) and (14a), 
 remembering the E 2 and T 2 in Eq. (10) apply to the final pressure, 
 while in Eq. (14a) they apply, together with v, to the critical 
 pressure. A simple formula, developed by Mr. George Wilson, 
 for determining the reaction of orifices flowing into atmospheric 
 pressure, while largely empirical, agrees very closely with 
 experimental results. The reaction = 1 . 23 p 1 -l4.7 pounds 
 per square inch of orifice. This applies, of course, only to non- 
 condensing turbines.
 
 THE FREE EXPANSION OF STEAM. 15 
 
 Problems. 
 
 1. What is the theoretical steam rate of a turbine having a heat drop 
 of 235 B. T. U. per Ib. of steam? , t C^ 8 
 
 2. What heat drop must steam have to give a theoretical steam rate of 
 18 Ibs. per H. P. hour? 
 
 3. A 200 H. P. turbine having eight nozzles has a heat drop of 250 
 B. T. U. per Ib. of steam. What must be the throat area of nozzle 
 to pass the required weight per sec. when the initial pressure = 150 
 Ibs. gauge. 
 
 4. What is the reaction of an orifice .35 sq. inch in area discharging 
 from 100 Ibs. gauge pressure into the atmosphere? 
 
 5. What throat diameter is required in a nozzle to give a reaction of 
 - 12 Ibs. when expanding from dry steam at 120 Ibs. absolute to 
 
 atmospheric pressure? , 07 3T' 
 
 6. What area of throat is required in a nozzle to discharge . 12 Ibs. of 
 steam per sec. when the specific volume is 5 . 1 cu. ft.? - ' 
 
 7. Steam at 150 Ibs. absolute is expanded with an energy loss of 5% 
 at the throat, what area is required to discharge . 1 Ib. per sec.?. ." 
 
 8. What is the impulsive force of the jet in the throat for conditions 
 of Prob. 7? ' i 
 
 9. What is the impulsive force of the jet if the expansion of Prob. 7 
 is continued down to 1 . 5 Ibs. absolute with a total energy loss of 
 10%? f , y 
 
 References. 
 
 THOMAS: " Steam Turbines." 
 MOVER: " Steam Turbines." 
 FRENCH: "Steam Turbines."
 
 CHAPTER II. 
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 
 Art. 6. Expanding Nozzles. 
 
 When expanding nozzles are used, the pressure hi the throat, 
 a, can not be less than . 58 P lt but having passed this point, 
 there is nothing to preclude further expansion down to the 
 pressure of the surrounding medium. This further expansion 
 increases the velocity of the steam, but unless the flow is con- 
 centrated in one direction the energy will be dissipated, and for 
 any useful purposes lost. The function of the divergent nozzle 
 used in turbine design is to direct the jet issuing from the throat 
 in a definite direction so that the kinetic energy generated 
 may be made available. There is no more energy in the flow 
 froni an expanding nozzle than from a simple orifice, but if 
 
 FIG. 4. Expanding nozzle. 
 
 properly proportioned the nozzle allows the steam to expand 
 from the critical pressure to the final pressure with a minimum 
 of vibration, and renders the kinetic energy of the jet available 
 along some definite line of action. 
 
 The proper proportions for expanding nozzles have been the 
 subject of extensive experiments. The most notable results 
 are those of Rosenhain, Stodola, Rateau, and Gutermuth, and 
 the material brought out in these investigations is so great that 
 little more can be done here than to point out some of the 
 general results. 
 
 For short nozzles, whether rounded at the entrance, conver- 
 16
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 17 
 
 gent, or straight, there is a sudden drop of pressure just beyond 
 the throat or entrance, to a pressure below that of the discharge 
 chamber. The steam returns to the 
 pressure of the exhaust medium in a 
 series of oscillations roughly propor- 
 tionate to the depression, and de- 
 creasing, as a damped vibration, 
 until at perhaps 1 or 1 1/2 times the 
 length of the nozzle the pressure has 
 settled down to that of the lower 
 medium. It is the function of a well 
 designed divergent nozzle to reduce 
 these oscillations to a minimum. 
 These vibrations are clearly shown in 
 Fig. 5, taken from Stodola's experi- 
 ments. Fig. 6 shows the effect of 
 the divergent nozzle, where it is seen 
 that there are practically no oscilla- 
 tions of pressure within the nozzle 
 after the one created at the throat 
 has died out. If the final pressure, 
 beyond the nozzle, is either above or 
 below that corresponding to the ex- 
 pansion within the nozzle, oscillations 
 will be set up in the exhaust space. 
 These are shown clearly from the ex- 
 periments of Dr. C. E. Lucke, Fig. 7, 1 
 which were made with a De Laval 
 nozzle, the best known for giving 
 complete expansion. In this nozzle 
 the divergent portion is conical. 
 Parenty has deduced mathematically 
 that the most efficient curve is that 
 of an ellipse with the focus in the 
 throat. Experiments seem also to 
 indicate that the best form for the divergent part is to have it 
 slightly concave, and some turbines have adopted this form. 
 But for manufacturing reasons they are usually made conical, 
 as the increase in efficiency is only slight. 
 
 ' A. S. M. E., Vol. XXVI., page 134. 
 2 
 
 FIG. 5. Expansion curves.
 
 18 STEAM TURBINES. 
 
 The form recommended by Rosenhain had the inner corner 
 but slightly rounded, and a straight divergent taper beyond, of 
 about 1 in 10 or 1 in 12. A greater efficiency appears to be obtain- 
 able with a nozzle which under-expands rather than one which 
 over-expands, as the loss of energy increases rapidly with over- 
 expansion. With a well proportioned nozzle a velocity efficiency 
 
 FIG. 6. Pressure curves in an expansion nozzle. 
 
 of 95% may be relied on. Fig. 8 shows full size the contour 
 of a De Laval nozzle for a non-condensing turbine. 
 
 Mr. Strickland Kneass, of Wm. Sellers and Co., has made an 
 extensive investigation into the discharge of steam through 
 nozzles and arrived at a form differing quite markedly from the 
 De Laval nozzle, but \^hich has shown an equally high if not 
 higher efficiency. Fig. 9 shows a section of some of the 
 nozzles tested and gives curves of the variations in pressure and
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 19 
 
 velocity for steam at initial pressures of 20, 30, 60, 90, and 120 
 pounds. 
 
 Taking the 1 in 10 tube, No. 2, as a basis, various tapers were 
 
 y/tfflfyty. 
 
 Distances from throat 
 FIG. 7. Pressure curves showing over expansion. 
 
 tried. The angle of divergence, as we have already been led to 
 expect, had little or no effect on the inlet half of the tube. The 
 tube was gradually shortened also from the outlet end with the 
 
 FIG. 8. Section of a De Laval nozzle non-condensing. 
 
 same result. The divergent curve of No. 5 was calculated to 
 give uniform acceleration and to avoid the losses due to the 
 changes of velocity, shown in the conical portion of Nos. 3 and 4,
 
 20 
 
 STEAM TURBINES. 
 
 and which were characteristic of all the straight tapered forms. 
 This form, No. 5, gave the best results. It is interesting to note 
 that while Rosenhain and others advocate an only slightly 
 rounded inlet (see also'Fig. 8), Mr. Kneass obtained better results 
 
 No. J. Cylindrical No. 2 Taper, 1 In 10 No.3 Taper, 1 in 6 Nb.4 Taper, 1 In 5 No.5 Special Curve 
 
 \s 
 
 FIG. 9. Kneass' experiments on nozzles. 
 
 with well rounded inlets and a taper of 1 to 6. The best efficiency 
 obtained was from a nozzle proportioned for 30 pounds initial 
 pressure and atmospheric exhaust. The results were as follows: 
 
 Gauge 
 Pressure 
 
 Actual 
 Velocity 
 
 Theoretical 
 Velocity 
 
 Difference 
 
 Per Cent, 
 of Loss 
 
 120 
 
 2690 
 
 2820 
 
 130 
 
 .046 
 
 90 
 
 2550 
 
 2650 
 
 100 
 
 .038 
 
 60 
 
 2290 
 
 2400 
 
 110 
 
 .045 
 
 30 
 
 1970 
 
 2000 
 
 30 
 
 .015 
 
 15 
 
 1400 
 
 1500 
 
 100 
 
 .066 
 
 
 1 
 

 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 21 
 
 The velocity loss, except at the lowest pressure, is within 0.5% 
 and at the pressure for which the nozzle was designed, 30 pounds, 
 there was but 1.5% loss. This test would indicate that an ex- 
 panding nozzle should be designed for a pressure under, rather 
 than over, the average to be encountered. The energy loss from 
 the above, being proportional to the square of the velocity, varies 
 from 3% to 13% with an average of about 10% as previously 
 stated. 
 
 FIG. 10. Nozzle on Kerr turbine. 
 
 A form of nozzle similar to No. 5 has been adopted in the Kerr 
 turbine. In this turbine there is multi- stage expansion and con- 
 sequently only a small pressure drop in any one set of nozzles. 
 Fig. 10 shows a longitudinal section of this nozzle. 
 
 Problems. 
 
 1. Report on tests and conclusions of Sibley and Kemble in paper 
 " Efficiency Tests of Steam-turbine " Nozzles. Trans. A. S. M. E., 
 vol. xxxi, p. 617. 
 
 2. Report on the tests of Borsody and Cairncross. Reported in 
 Transactions of A. S. M. E., vol. xxvi, p. 114. 
 
 References. 
 
 STODOLA: " The Steam Turbine." 
 
 THOMAS: " Steam Turbines." 
 
 RATEAU: "Flow of Steam through Nozzles." 
 
 MOYER: " Steam Turbines." 
 
 JUDE : " Theory of the Steam Turbine." 
 
 BORSODY: AND CAIRNCROSS: "Pressures and Temperatures in Free 
 
 Expansion," Trans. A. S. M. E., vol. xxvi. 
 SIBLEY AND KEMBLE: "Efficiency Tests of Nozzles," A. S. M. E., vol.
 
 22 STEAM TURBINES. 
 
 Art. 7. Design of an Expanding Nozzle. 
 
 The following example in the design of an expanding nozzle, 
 worked out first by the use of the steam tables and entropy dia- 
 gram, will be used also to illustrate the use of the heat-entropy 
 diagram. 
 
 Let the conditions be as follows: 
 
 Initial steam pressure, = 165 pounds absolute 
 
 Initial dryness of steam, =98 1/2 % 
 
 Final steam pressure, = 1 pound absolute 
 
 Loss of energy during expansion, y =15% 
 
 Weight of steam discharged per second = . 092 pound 
 
 Let it be required to find the diameter of a conical nozzle and 
 the condition of the steam at the points where the pressures are 
 96, 75, 60, 45, 30, 15, and 1 pound absolute per square inch. The 
 first of these pressures, 96 pounds, is . 58 of the initial pressure, and 
 is therefore the " critical pressure " in the throat. The first seven 
 lines in the following table give the detailed operations in finding 
 the adiabatic heat drop. The letters in the second column refer 
 to Fig. 3. Lines 8 to 12 are the operations to determine the 
 quality of the steam at the various pressures. With this known, 
 the volume of steam to be delivered per second may be calcu- 
 lated. From this the areas and corresponding diameters required 
 may easily be obtained. 
 
 Let it be given that the divergent portion 5f the nozzle is to 
 be 4 inches long. From the results tabulated the nozzle may be 
 drawn and the curves of pressures and velocities plotted as 
 shown in Fig. 11. Values for 5 pounds and 21/2 pounds 
 absolute are interpolated to assist in drawing the curves. The 
 pressure and velocity for any point in the nozzle may be readily 
 found from the curves. For instance for the section, aa, project 
 downward cutting the two curves. The pressure curve will be 
 cut at 15 pounds and the velocity curve at 2710 feet per second, 
 as referred to their respective scales. 
 
 The operations from 1 to 12, requiring considerable time and 
 care, may be arrived at in a few moments by the use of the heat- 
 entropy diagram. Fig. 12 reproduces part of it for clearness. 
 From the point A, giving the initial condition of the steam, 165
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 23 
 
 
 * S 
 8 8 
 
 CO IN iH 
 
 rH IN O5 
 
 
 <N rt 50 _ rt (N 05 O 
 
 JO 5 3 g ^ O 
 
 K TO 
 
 C5 5 N rt n 
 
 1-1 oo 5 w rt 
 
 |J 
 
 II i 
 
 Sti 
 
 5 ll- 
 
 ii i J x -s x 
 
 03 H C3 . * ** T! ^ ' 
 
 jiij * i*;^i 
 
 " M1M -a f-s-s 5 -3 
 
 III a ? 
 
 ill o g 
 
 ^ >. > > <^
 
 24 
 
 STEAM TURBINES. 
 
 pounds pressure and . 985 dryness, drop a perpendicular to B on 
 the line of the given final pressure, 1 pound. The distance AB, 
 laid off on the heat scale gives 319 B. T. U., the heat drop for 
 adiabatic expansion, corresponding with the calculated value in 
 line 6 of the table. But 15% of the heat drop is lost in friction. 
 Laying off Bb' = . 15 of AB, we have Ab' as the actual heat drop. 
 Projecting b' horizontally until it crosses the 1 pound pressure 
 
 1" 2" 3' 
 
 FIG. 11. Curves for expanding nozzle. 
 
 line as at b", we have, reading from the quality lines, .813 as the 
 final dryness, which agrees with the calculated value line 12. 
 
 To ascertain the condition at any intermediate pressures, with 
 B as a center and Bb' as a radius, draw the arc b'c. Draw a 
 tangent to the are b'c through A. From the points d, e, etc., 
 where AB cuts the pressure lines in question, draw arcs tangent 
 to Ac. Project the points d' , e' , where the arcs cut AB, hori- 
 zontally over to the points d", e", on their respective pressure
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 25 
 
 lines. These points referred to the quality lines give the 
 dryness. A "quality curve/' Ab", may be drawn through 
 d", e", etc., from which the dryness for any intermediate pressure 
 may be read off at once. The qualities thus found will agree 
 with the values as calculated within limits of error justified by 
 the nature of the problem. It may be noted here that this qual- 
 ity curve may be laid off almost as readily for a varying friction 
 
 Fio. 12. Condition curve for expanding nozzle. 
 
 loss as for a constant one. This is of value in calculations for 
 multistage machines where the friction losses increase as the 
 steam expands. 
 
 Problems. 
 
 I. Design an expanding nozzle for the following conditions: Initial 
 steam pressure = 120 Ibs. gauge; superheat =40 Fahr. ; atmospheric 
 discharge pressure ; energy loss, 16% ; weight of steam delivered = 
 .11 Ib. per sec. ; length of nozzle =3 ins.
 
 26 
 
 STEAM TURBINES. 
 
 2. Design a nozzle for same conditions as Prob. 1, except that dis- 
 charge pressure is 1 .5 Ibs. absolute and length =4 ins. 
 
 3. Calculate the H. P. available in jet at throat of nozzle, Prob. 1, and 
 also after expansion to atmospheric discharge pressure. 
 
 4. Calculate the H. P. available at throat and exit of nozzle in Prob. 2. 
 
 5. If the expanding portion of the nozzle in Prob. 2 is 4 inches long, 
 what are the pressure and velocity at points 1/2 inch and 2 1/2 
 inches from the throat? 
 
 
 References. 
 
 STODOLA: "The Steam Turbine." 
 THOMAS: "Steam Turbines." 
 MOYER: "Steam Turbines." 
 
 Art. 8. BLADE FORMS AND BLADE VELOCITIES. 
 
 The velocities which enter into the problem of turbine design 
 are: 
 
 The absolute velocity of the jet as it enters the blades. 
 
 The velocity of the moving blades. 
 
 The relative velocity of the jet and the blades. 
 
 The absolute velocity of the 
 jet as it leaves the blades. 
 
 The ideal condition in all 
 turbines, whether steam or 
 water driven, is that the driv- 
 ing fluid " enter without shock 
 and leave without velocity." 
 Let V, above, be the abso- 
 lute velocity of the entering 
 steam, and u the blade veloc- 
 ity. W, the relative velocity, 
 is found, both in magnitude 
 and direction, from the ve- 
 
 FIG. 13. Velocity diagram. , . . , T7 . 
 
 locity triangle V, u, and W. 
 
 The angle /? determines the direction of the back of the blade 
 on the entering side. The curved surface of the blade de- 
 flects the jet, discharging it backward with a velocity W 1} 
 equal to W, less a certain loss due to friction. This friction can 
 not be determined theoretically, but may be assumed from results 
 of experiments and experience in turbine design. These indicate 
 that W l varies from . 8 to . 95 of W, according to conditions, . 92 
 being a fair average value for the single stage turbine. The angle
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 27 
 
 /?' is ordinarily made equal to /? for convenience in manufacture 
 and to reduce end thrust. Having W in magnitude and direc- 
 tion, the final absolute velocity 7 t is readily obtained by com- 
 bining it with the bucket velocity u. From equation (2) the energy 
 
 yz _y 2 
 per pound of steam developed in buckets is and the theo- 
 
 2 # 
 retical efficiency is 
 
 Fig. 14 shows a convenient method of determining the form 
 of the bucket, where entrance and exit angles are equal. 
 
 Lay off u, the bucket velocity, horizontally. Draw V to the 
 same scale, making the angle a. In the De Laval wheel this 
 angle is 20. Closing the triangle we have the relative velocity 
 
 e, 
 f Pitch-^ 
 
 FIG. 14. Determination of blade sectioas. 
 
 W in direction and magnitude. Draw ab parallel to u and lay 
 off /?' = /? on the exit side. Take c and e equidistant from ab and 
 the width of the blade apart. Lay off cc' and ee' equal to the 
 pitch of the blades. The face of the bucket may be drawn as the 
 arc of a circle about the intersection, /, of the perpendiculars cf 
 and ef and the center line ab. 1 The back of the blade is formed 
 by two lines parallel to be and be connected by an arc with /as the 
 center. 
 
 The best width ce and pitch cc' are empirical and determined 
 by experience, as no formulae for them have been developed. 
 Moyer says, "for turbines of less than 100 H. P., the width of the 
 
 1 A well known German rule is to make the radius equal to twice the pitch times sine /?, or 
 r =2p sine )9.
 
 28 STEAM TURBINES. 
 
 blades is often made about I", increasing to about 1.5" in tur- 
 bines of 1000 H. P." "The most efficient blade pitch appears to 
 be between the limits of 1/2" and 1". Between these two values 
 the efficiency of blades made according to conventional designs 
 is practically constant. The usual blade pitches are 5/8, 3/4, and 
 7/8 inch." 
 
 It is more important that the backs of thq vanes should be 
 parallel to the entering steam than the faces, for steam striking 
 the backs is deflected outward, retarding the wheel and causing 
 loss. If it strikes the face the energy of deflection goes into useful 
 work in the wheel. In the spacing of the blades there must be 
 enough free area to provide for the unobstructed passage of the 
 steam at the large volume corresponding to the exhaust side of 
 the blade, and it should be as near uniform in section as con- 
 ditions will permit. It must be borne in mind, too, that the 
 opening of a round inclined nozzle is an ellipse, and the greater 
 part of the steam is discharged through these openings near the 
 middle of the nozzle. 
 
 Problems. 
 
 1. If steam issues from a nozzle with a velocity of 3400 ft. per sec. at 
 an angle a. =20 and the blade velocity u =1200 ft. per sec., what 
 are the relative velocity W and blade angle /?? 
 
 2. Assume blade angles /? and /? t as equal, what is the final absolute 
 exit velocity neglecting steam friction in the blading? 
 
 3. What is the energy per Ib. of steam available for the conditions of 
 Probs. 1 and 2? What is the efficiency? 
 
 4. Given 7=3400 ft. per sec. a =20, w=1200 ft. per sec., and an 
 energy loss of 20% in passage through the blading, what is the 
 final velocity of exit F x ? 
 
 5. Determine the energy absorbed by the wheel per Ib. of steam and 
 the efficiency for conditions of Prob. 4. 
 
 6. Draw a cross section of the blading for conditions of Prob. 4. 
 What length of blade could be used with a nozzle .8 inch exit 
 diameter? 
 
 7. How many r. p. m. should a 42-inch diam. wheel run for a nozzle 
 velocity of 2300 ft. and a =22 1/2 and /? =27. 
 
 8. With a blade velocity u =400 ft. per sec., a nozzle velocity of 1720 
 ft. per sec., and a =42, what will be the absolute angle of exit of the 
 steam for a symmetrical blade? 
 
 9. Report on article on "Principles of Steam Turbine Buckets." 
 Power, March 17, 1908, p. 391
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 29 
 
 References. 
 
 STODOLA: "The Steam Turbine." 
 THOMAS: " Steam Turbines." 
 MOYER: " Steam Turbines." 
 JUDE: "Theory of the Steam Turbine." 
 NEILSON: " The Steam Turbine." 
 
 Art. 9. Conditions of Maximum Efficiency. 
 
 Let Fig. 15 be the velocity diagram for the entrance and 
 exit velocities, where the relative velocity W is supposed to 
 remain constant. 
 
 FIG. 15. Velocity diagram. 
 
 From trigonometry 
 
 FIG. 16. Velocity diagram. 
 
 V 1 2 = W 2 + u 2 -2uW cos 
 V 2 - VS = + 2u W (cos p 
 V 1 2 = V 2 -2u W (cos p + 
 
 cos 
 
 subtracting, 
 (17) 
 
 Y 2 V 2 
 
 The efficiency of the bucket, - , Eq. (16), will be highest 
 
 when Vi 2 is least. V l 2 will be least, V 2 being constant, for the 
 maximum value of the second term in Eq. (17). * As in 
 hydraulic problems the ideal condition is given by complete 
 reversal where cos /? and cos /? t are each positive and unity. 
 
 FIRST CASE. Where p, & and V are fixed. 
 
 Since the above quantities are fixed it is clear from Eq. (17) 
 that YI is least where uW is greatest. In Fig. 16 the area of 
 
 abxtrn, 
 the triangle abc = bc.%ac sin p = lab.cm, therefore =
 
 30 
 
 STEAM TURBINES. 
 
 oc.oc = W.u. But ab = F, and sin /? are constant, therefore, 
 comparing with Eq. (17), F t 2 is least when cm is maximum. 
 The length ab and the angle acb are fixed, therefore the locus of 
 the possible positions of the intersection c with reference to ab is 
 an arc acb and cm is maximum when ac = cb, or when u W. We 
 have then 
 
 F 
 U= ^3 (18) 
 
 and 
 
 (19) 
 
 Taking the relative velocities TF and W \ as equal, the efficiency, 
 
 F 2 - F^ 2w. TF(cos + cos ft) 
 
 ^ becomes - ^L_ 
 
 If, in addition, /? and ft are also equal 
 
 FIG. 17. Velocity diagram. 
 
 Since W cos p= V cos a-u, the efficiency in terms of a is 
 
 (20) 
 
 SECOND CASE. Where V and a are fixed, and ft and ft are equal 
 but not determined. 
 
 Eq. (17) above becomes V l 2 = V 2 -4uWcos^, V, 2 ^ V 2 -4u.cd.
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 31 
 
 V l is least when u.cd is maximum, bd, the sum of u and cd is 
 constant and = V cos a. Therefore, u.cd is maximum for u = cd, or 
 
 V cos 
 
 (21) 
 
 and 
 
 tan 
 
 ad ad ad 
 
 1 = = = 2 = 2 tan a. 
 dc bd bd 
 
 Also, since W = W l} ec = ac and the triangle cef can easily be 
 shown to be similar and equal to the triangle acd. Therefore 
 cf= ad or V l =V sin a. 
 
 V 2 -V 2 V 2 -V 2 sin 2 a 
 The efficiency 2 becomes then = 
 
 V 2 (I -sin 2 a) 
 
 2 or simply =cos 2 a (22) 
 
 FIG. 18. Velocity diagram. 
 
 THIRD CASE. When V, a, and ft are fixed. The triangle abc 
 is fixed. W and u are therefore determinate. Cos /? u then, is 
 the only variable on the right hand side of Eq. (17), and V l is 
 least for ft = 0. 
 
 In the foregoing, losses in the relative velocity W, due to fric- 
 tion, have been neglected. If these be considered, V 2 = W 2 + 
 u 2 + 2uW cos p as before, but Vf becomes V 1 2 =W 1 
 2uW l cos ft, where W t =yW.
 
 32 STEAM TURBINES. 
 
 The energy developed is 
 
 72 _ V 2 w*-WS + 2u(W c 
 
 The general expression for the efficiency 
 V 2 -V 1 2 _W 2 -W 1 2 + 2u (W cos 
 
 l cos ft) 
 
 y* F 2 
 
 For Case II where /3 = ft it becomes 
 
 TF 2 - W* + 2w. cos p (W + JFj) 
 
 (23) 
 
 It frequently happens that the best value of u must be sacri- 
 ficed for safety or for cheapness of construction, or there may 
 be offsetting gains in mechanical efficiency by adopting a 
 
 FIG. 19. Velocity diagram. 
 
 slower speed. Take as an example, a De Laval nozzle, coming 
 under Case II, delivering steam at 3680 feet per second at an 
 
 angle, a = 20. Then u = y- = - . 94 - 1730 feet per sec- 
 ond. This would give a value for the relative velocity 
 
 w = X/3680 2 + 1730 2 - 2 co8~26~3680 . 1730 = 2130 feet, 
 
 and a blade angle, p = tan i 2 tan 20=- tan' 1 . 728 = 36. Experi- 
 ence has shown that the blade velocity should not exceed 1400 
 feet per second. If the actual speed be 1250 feet per second 
 the value for the relative velocity is
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 33 
 
 W = A/3680 2 + 1250 2 - 2 cos 20 .3680 .1250 = 2540 
 and since sin /3 = ~ -_ - - , the blade angle = 
 3680 sin 20 
 
 FIG. 20. Velocity diagram. 
 
 In the De Laval turbine a nozzle angle of 20 has been estab- 
 lished for all sizes. The angles /? and /3 X are equal, varying from 
 30 or 32 up to 36. 
 
 /? and /? t can not be equal to zero, unless the plane of the rever- 
 sal of the steam makes an angle with the line of motion. This 
 is done in some turbines, as the Stumpf and Terry machines. 
 
 FIG. 21. Velocity diagram tangential type. 
 
 The introduction of this new angle partially offsets the advan- 
 tage of complete reversal, as will be seen in considering Fig. 21. 
 If V and u be represented by ab and ac the velocity, u, can be 
 resolved into two components, u cos a = ad, and u sin a = cd. 
 The component cd will be impressed on the entering jet giving it 
 the direction ab' so that W is the relative velocity of entrance, not
 
 34 STEAM TURBINES. 
 
 cb or ef. The complete reversal of the jet gives a relative exit 
 velocity of W, equal to W, and an absolute exit velocity 
 of V 1} as shown. 
 
 Neilson shows that V 1 is minimum for u = -- . For this 
 
 F 2 (l -cos'a.) 
 value 7, 2 = 
 
 3 cos 2 a+l 
 
 The third of the principal forms of buckets used in single- 
 expansion turbines is the Pelton type, which lends itself to use 
 
 FIG. 22. Pelton type of blade. 
 
 with steam as well as water. A complete reversal of the steam 
 
 y 
 jet and a value of u = - would give a theoretical efficiency of 100%. 
 
 It is necessary, of course, to give the steam some exit velocity 
 to clear the wheel. This velocity, V 1} can be determined graph- 
 ically as in Fig. 22, or analytically by the equation 
 
 V* = W 2 + u*-'2 W ucos ft. Since W=V-u 
 
 = (V-u) 2 + u 2 -2u (V-u) cos ft, 
 = V 2 -2u (V-u) (1+cos ft). 
 
 The theoretical efficiency as before = 
 
 _2u W (1+cos /9) 
 
 (25)
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 35 
 
 Problems. 
 
 1. Given V =2420 ft. per sec., /?. =45 and 0, =40, what is the best 
 value for the blade velocity and for the nozzle angle? Neglect 
 steam friction. 
 
 2. What is the blade efficiency for the conditions of Prob. 1. 
 
 3. Given a steam velocity of 2250 ft. per sec. and a nozzle angle of 
 22, what is the best blade velocity, neglecting steam friction? 
 What is the efficiency of the blading? 
 
 4. With symmetrical blading what nozzle angle should be used when 
 the steam velocity is 2700 ft. per sec. and the blade velocity 1430 
 ft. to get an efficiency of 87%? 
 
 5. What angles a and /? should be used for a DeLaval nozzle and blade 
 to give 88 1/2% efficiency with an entrance velocity of 3550 ft. per 
 sec.? What blade velocity does this call for? 
 
 6. What is the power developed per Ib. of steam for the conditions of 
 Prob. 5? 
 
 7. Find the power developed in a DeLaval blade with V =3550 as in 
 Prob. 5., u limited to 1240 ft. per sec., a =20. 
 
 8. Find the power developed under the conditions of Prob. 7 if in 
 addition there is a velocity loss of 10% in passage through the 
 blades; what is the blade efficiency under these conditions? 
 
 9. Show that for maximum efficiency, V and u are at right angles. 
 10. Prove that "dilution of the jet" or lowering the velocity of the 
 
 steam by having mixed with a heavier fluid, as water, is a less 
 efficient way of reducing speeds than by lowering the velocity. 1 
 
 References. 
 
 STODOLA: "The Steam Turbine." 
 
 NEILSON: "The Steam Turbine." 
 
 THOMAS: "Steam Turbines." 
 
 JUDE: "Theory of the Steam Turbine." 
 
 MOYER: "Steam Turbines." 
 
 RATEAU: "Method of Calculating Steam Turbines," London Engi- 
 neering, Dec. 10, 1909, p. 804. 
 
 BRILING: "Energy Losses in Turbine Buckets," Zeitschrift d. v. 
 Deut. Ing., Feb. 12, 1910. 
 
 Art. 10 The Trajectory Of The Steam. 
 
 The absolute direction of the steam at any point may be deter- 
 mined by combining the velocity u of the vane with that of the 
 steam as it moves relatively to the vane. Neglecting frictional 
 losses, this would have a magnitude W, and a direction tangent 
 
 "See French, Steam Turbines, p. 63.
 
 36 
 
 STEAM TURBINES. 
 
 to the vane surface at the point in question. By taking a suc- 
 cession of points the absolute directions chould be found and the 
 envelope of these would give an approximate trajectory. The 
 error in this method is cumulative, however, and a better way is 
 as follows: Let W be the relative velocity at entrance, and u the 
 vane velocity as heretofore. If the inner vane surface be semi- 
 circular the time required to move from 
 
 A to B will be . The distance forward 
 
 covered in the time will be u 
 
 W 
 
 Lay- 
 
 ing this off along the path of B we have 
 the end of the trajectory. For any in- 
 termediate point, as C, the time required 
 
 arc AC 
 will be and the distance forward 
 
 arc AC 
 covered by C will be CC t = ==- u. 
 
 The path will depend on the size and 
 shape of the vane and the relative 
 velocities u and W. If, as is usual, 
 the vane surface is only a portion of a 
 semicircle, the method is not altered and 
 the distance CC l for any point C is laid 
 
 distance AC 
 off along its path equal to 
 
 u, and so on for any number of points needed to determine 
 the curve. 
 
 If, however, the relative velocity W be reduced by friction to W l 
 during the passage through the vane it will lengthen out the 
 trajectory. Just at what rate the retardation occurs would be 
 difficult to determine, but it may be assumed to be uniform. If 
 W and W l be the relative velocities at entrance and exit the loss 
 from A to B=WW 1 , and assuming this loss as uniform the 
 
 AC 
 velocity at C = W- t (W ' WJ and the time required to move 
 
 Fio. 23. Trajectory of the 
 steam. 
 
 from A to C 
 
 AB 
 
 AC 
 ave.rel. vel. 
 
 AC 
 
 AC
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 37 
 
 The point corresponding to C on the trajectory would then lie 
 on its path a distance forward 
 
 AC 
 
 
 A succession of points, as before, will determine the complete 
 trajectory. 
 
 Below are given the trajectories for a blade of the De Laval 
 
 form, for values of = . 35, . 4, . 45, . 5, . 55, and . 6, and a fric- 
 tional loss of . 08. 
 
 FIG. 24. Trajectory curves. 
 
 The cross section of the passage between the vanes should be as 
 nearly uniform as possible. Where the steam fills the passage and 
 the backs of the blades differ in form from the faces, there maybe 
 a marked difference in the trajectories of steam particles, which 
 means eddies and inevitable loss of energy. 
 
 Fig. 25 shows a difference in the paths of particles mov- 
 ing along the fronts and backs of the blades, which is to be
 
 38 STEAM TURBINES. 
 
 guarded against as far as possible in designing turbine blades. 
 In impulse turbines the expansion occurs in the nozzles or fixed 
 vanes and there is no drop in pressure as the steam goes through 
 the buckets. This renders the determination 1 of the trajectory 
 easy, but in reaction turbines the moving passages are themselves 
 nozzles, and the steam velocity increases sharply in passing 
 through them. The determination of the trajectory under these 
 conditions becomes very involved. Approximations have been 
 
 Trajectory for Trajectory for 
 
 backatoc. face adc. 
 
 FIG. 25. Trajectory at front and back of blade. 
 
 made by assuming that the relative velocity increases in some 
 regular manner. Having made some such assumptions trajec- 
 tories may be plotted by the method outlined, but as they are at 
 best guess work and of necessity differ throughout the entire 
 length of the rotor they are of little value. The methods out- 
 lined above of course apply to the Pelton type of bucket as well 
 as to the side entrance type. 
 
 Problems. 
 
 1. With a steam velocity of 2200 and a blade velocity of 800 ft. per 
 sec. and semicircular blade as in Fig. 23, how far will the blade 
 travel during the passage of the steam, assuming no friction loss? 
 
 2. Given nozzle and blade velocities of 3300 ft. and 1200 ft. per sec., a 
 nozzle angle of 20, a blade pitch of 5/8 in. and a width of 1 in., 
 how far has the blade moved when the steam crosses the center line, 
 and how far at exit?
 
 UTILIZATION OF KINETIC ENERGY IN STEAM. 39 
 
 3. Assuming the W and blade face of Prob. 2, plot the trajectory for 
 u = .3, .4, and .5 of W. 
 
 4. Given V =3400 ft. and u =1220 ft. per sec., a =20 and a pitch of 
 3/4 in., draw a section of the blading and plot the trajectories of 
 the steam moving along the face and back of the blade (see 
 Fig. 25). 
 
 References. 
 
 JUDE: "Theory of the Steam Turbine." 
 STODOLA: "The Steam Turbine."
 
 CHAPTER III. 
 CALCULATIONS OF TURBINE BLADING. 
 
 Art. ii. Single-stage Impulse Turbines. 
 
 The simplest form of successful turbine is the single-stage 
 impulse turbine. In this all the expansion occurs in one set of 
 nozzles, where the heat energy availablejs converted into kinetic 
 energy and directed against a single row of moving vanes. 
 
 As the steam velocity varies with the heat drop and the vane 
 velocity with that of the incoming steam, the speed of the rotat- 
 ing vanes in the case of single expansion is very high, from 1,000 
 to 1,400 feet per second, or about half the velocity of a modern 
 high powered rifle bullet. De Laval frankly accepted these speeds 
 and developed a machine capable of withstanding the strains 
 produced. Some idea of the problems involved may be had 
 from the fact that in the 300-horse-power turbines the blades, 
 weighing only 1/28 of a pound each, but running with a velocity 
 of 1380 feet per second on a 15-inch radius, develop a centrifugal 
 force of 3/4 of a ton. It called for engineering ability of a high 
 order, and greatest care in the details of design and manufac- 
 ture, for not only was a built up rotor required capable of running 
 from 10,000 to 30,000 R.P.M., according to the size, but the 
 velocities developed had to be reduced through gearing to ones 
 which could be used. An efficient and practical machine has 
 been developed, however, which runs with gear velocities of 100 
 feet per second with but little wear, no vibration, and high 
 efficiency. 
 
 The relation between the pressures and velocities during the 
 passage of the steam through an impulse turbine of the De Laval 
 type is shown schematically in Fig. 26. The boiler pressure 
 drops in a single expansion to the exhaust pressure before the 
 steam enters the vanes. The wheel therefore has equal pressure 
 on both sides. The velocity V of the steam is maximum as it 
 enters the vanes and is nearly all absorbed in the passage through 
 
 40
 
 CALCULATIONS OF TURBINE BLADING. 
 
 41 
 
 them. The steam enters the exhaust chamber with the low 
 velocity v, sufficient only to clear the wheel. 
 
 As an example of calculation for the blading of a turbine of 
 this type let the jsteam conditions be the same as for the example 
 on page 22, namely, 
 
 Initial steam pressure, 
 Initial dryness 
 Final steam pressure 
 
 150 pounds gauge 
 981/2 % 
 1 pound absolute 
 
 Boiler Pressure 
 
 Velocity in 
 Steam Pipe 
 
 Exhaust 
 chamber 
 
 Condenser Pressure" 
 
 Fia. 26. Scheme of single stage impulse turbine. 
 
 In addition let the 
 Output 
 
 Revolutions per minute of wheel = 
 Blade velocity be limited to 
 Number of nozzles 
 Angle of nozzles 
 
 110 H. P. 
 13000 
 1250 feet per second 
 
 6 
 20 
 
 Angle of entrance and exit of blades to be equal. 
 
 As already pointed out in Art. 8 the design of the blading, 
 and in fact of the whole turbine, is materially affected by the 
 frictional losses in the nozzles and blades. In determining the 
 proportions for a given case assumptions must be made for these, 
 based on experience. Stodola gives the following values for the 
 various losses. 1 
 
 1 Steam Turbines, 2nd ed., p. 224.
 
 42 
 
 STEAM TURBINES. 
 
 Losses in the nozzle 
 Losses in the blades 
 Losses at exit 
 Total loss 
 
 = 15% of the available energy 
 = 21% of the available energy 
 = 4.6% of the- available energy 
 = 40.6% of the available energy 
 
 From the given conditions of steam and exhaust the theoretical 
 heat drop available is 319 B. T. U. But assuming a nozzle loss of 
 15%, only 319X- 85 = 271 B. T. U. will be transformed into 
 kinetic energy. From Eq. (6) we have 7 = 223.8^/271 = 
 3680 feet per second. (See problem in Art. 7.) 
 
 3680 X 94 
 From Eq. (21) u= =1730 feet per second for 
 
 maximum efficiency. For mechanical reasons u will be limited 
 to 1250 feet per second as given in the initial conditions. The 
 
 FIG. 27. Velocity diagram. 
 
 21 
 energy loss in the blades is 21% of the total, or '- =24.7% of 
 
 .85 
 
 that delivered to the blades by the nozzles. If 2540 feet per 
 second be the relative velocity at entrance, as shown by the 
 velocity diagram, Fig. 27, the relative velocity at exit will be 
 such that the kinetic energy is 24 . 7 % less, or 
 
 2540 2 W* 
 
 x.753= - 1 -. Hence 
 
 W l = A/2540 2 X .753 = 2200 feet per second. 
 
 The diagram shows that the blade angles are 30 and the final 
 velocity F 1 = 1280 feet per second. Comparison of Fig. 27 with
 
 CALCULATIONS OF TURBINE BLADING. 43 
 
 Figs. 19 and 20 shows how friction and mechanical limitations 
 modify the theoretical conditions. 
 
 Comparing reported tests of similar turbines, 18 pounds per 
 B. H. P. hour may be assumed for the. steam rate on which to .base 
 
 1 8 V 1 1 
 the nozzle areas. Then = .55 pounds of steam must be 
 
 oOUU 
 
 delivered per second by the six nozzles or . 092 pounds for each 
 nozzle. The proportions of a nozzle for these conditions have 
 already been worked out in Art. 7 and are shown in Fig. 11. 
 13000 R. P. M. have been assumed for the rotor shaft, and 1250 
 
 feet per second for u, therefore - - = 5 . 75 feet is the cir- 
 
 loUUU 
 
 cumference of the blade circle, which corresponds to a pitch 
 diameter of 22 inches. From Art. 8 the pitch may be assumed 
 as approximately 5/8 inch, which gives us 110 blades. Since 
 the exit diameter of the nozzle, Fig. 11, is .99 inches we may 
 make the blades, say, 11/8 inches high. 
 
 Problems. 
 
 -A i. Given the steam conditions of Prob. 1., Art. 7, namely: 
 
 Steam pressure =120 Ibs. gauge. 
 
 Superheat = 40 F. 
 
 Exhaust at atmospheric pressure 
 
 Output = 100 K. W. 
 
 R. P. M. of wheel =12000. 
 
 Blade velocity = 1200 ft. per sec. 
 
 Number of nozzles =8. 
 
 Angle of nozzles =20. 
 
 Blades symmetrical. 
 
 Design nozzles and blading for a single stage impulse turbine 
 assuming a steam rate of 50 Ibs. of steam per K. W. hr. 
 
 2. Design nozzles and blading for a condensing turbine, conditions as 
 in Prob. 1, except exhaust pressure =1.5 Ibs. absolute. What 
 changes of design are involved ? Assume a steam rate of 26 Ibs. per 
 K. W. hr. 
 
 3. Design nozzles and blading for a single stage impulse turbine. 
 Steam pressure 15 Ibs. absolute; exhaust pressure 1 Ib. absolute; 
 quality of steam at admission = 88%; blade velocity = 1200 ft. 
 per sec. Take steam rate at 42 Ibs. per K. W. hr. 
 
 4. Report on the construction and efficiency of the reduction gearing 
 of the DeLaval steam turbine.
 
 44 
 
 STEAM TURBINES. 
 References. 
 
 STODOLA: " The Steam Turbine." 
 NEILSON: "The Steam Turbine." 
 THOMAS: " Steam Turbines." 
 LEA AND MEDEN: Paper, "DeLa- 
 vol. xxv. 
 
 Steam Turbines," A. S. M. E. 
 
 Art. 12. Multi-stage Impulse Turbines. 
 
 As seen in the last article a single-stage impulse turbine must 
 run at a very high velocity and be geared down. 
 
 There are two ways by which the velocity of an impulse tur- 
 bine may be reduced, by subdividing the heat drop in a series of 
 
 FIG. 28. Scheme of impulse turbine with single pressure stage 
 and several velocity stages. 
 
 expansions, and by having the steam impinge on two or more rows 
 of buckets after expansion. The shaft velocity can thus be 
 reduced to a point where the turbine can be directly connected 
 to a generator, blower, or centrifugal pump. Such turbines are 
 more complex and theoretically less efficient than the single- 
 stage machine. This is offset, however, by the advantages of 
 direct connection and lower speed. The De Laval type of single-
 
 CALCULATIONS OF TURBINE BLADING. 
 
 45 
 
 stage turbine finds its limit at about 500 H. P. Beyond this 
 the strains become too great and the problem of speed reduction 
 too troublesome. In the multi-stage type, however, there seems 
 to be almost no limitation of the power which can be developed 
 by a single machine. Curtis turbines of this type are in use 
 developing 20,000 K. W., and larger units might be used were 
 they commercially desirable. 
 
 The field of the multi-stage turbine is much wider than that of 
 the single-stage, and it constitutes the second of the main divisions 
 into which turbines may be separated. 
 
 Fig. 28 illustrates the action of the original Curtis and the 
 Riedler turbines. Complete expansion occurs as before in a 
 
 Fia. 29. Scheme of Curtis turbine, multi-pressure, multi-velocity stage. 
 
 single set of nozzles, and the steam enters the first row of blades 
 at high velocity as in the previous case. The steam leaves this 
 row, however, with considerable velocity, is redirected by a set of 
 stationary guide vanes and impinges on the next row, and so on 
 to the exhaust chamber. The drops in steam velocity occur in 
 the passage through the moving blades. The stationary vanes 
 are merely guides, and the velocity during the passage through 
 them is substantially constant, as shown. The increase of 
 length in the successive rows of stationary blades is to allow 
 for the decrease in velocity, not for increase in volume. Theo- 
 retically the exhaust pressure with its corresponding volume is 
 reached at the nozzle, and all the rows of blades are driven by
 
 46 STEAM TURBINES. 
 
 kinetic energy, revolve in a vacuum with the least possible resist- 
 ance, and the wheels are balanced for pressures. This is a single- 
 pressure, multi-velocity stage type and is still used on the smaller 
 Curtis turbines up to about 35 K.W. 
 
 As now built the Curtis turbines have the pressure drop divided 
 into two or more " pressure stages." Steam is partially expanded 
 in a set of nozzles to some lower pressure and passes through a num- 
 ber of rows of moving blades as at a, Fig. 29, constituting one 
 stage where its kinetic energy is absorbed. It is then expanded 
 again and goes through another series of blades, or second stage, b. 
 The number of stages and of rows in each stage varies with the 
 
 FIG. 30. Scheme of multicellular turbine, multi-pressure, single- velocity stage. 
 
 conditions. As before, the wheels are balanced, and there is no 
 end thrust. The pressure throughout each stage is constant, the 
 drops occurring in the expanding nozzles at the begin- 
 ning of each stage. This may be described as a multi-pressure, 
 multi-velocity stage machine. 
 
 This idea of breaking up the pressure drop is carried to the 
 limit in the "multi-cellular" turbines, Fig. 30, such as the 
 Rateau, Zoelly, Kerr, and Wilkinson machines. Here a set of ex- 
 pansion nozzles after each row of blades replaces the fixed 
 guide vanes, and accelerates the steam to a certain velocity, 
 which is absorbed in the following running wheel. The multi- 
 cellular turbine is therefore a multi-pressure, single-velocity 
 tage machine. A turbine has been patented 1 which is similar 
 to Fig. 30 except that, while the velocity drop is about as usual, 
 
 'U. S. Patent, J. F. M. Patitz, Oct. 4, 1910.
 
 CALCULATIONS OF TURBINE BLADING. 
 
 47 
 
 both velocities V andFj are high i.e., the broken line in Fig. 30 
 is raised as a whole. The energy available in a single stage 
 varies with V 2 V ^, and is much greater for a given drop when 
 both velocities are high. It is hoped by this means to reduce 
 greatly the number of stages, but this will be partially offset by 
 greater steam friction. See Probs. 3 and 4, p. 3. 
 
 In all of these forms there will be noticed the characteristic 
 which defines impulse turbines, that there is no fall of pressure in 
 the moving blades. Expansion occurs only in fixed passages or 
 nozzles, and the moving blades are free from end thrust. 
 
 FIG. 31. Velocity diagram for two stages. 
 
 The determination of the velocities in the multi- velocity stage 
 turbine is an extension of the method already outlined. The final 
 velocity, V lt at exit from the first row, Fig. 31, is deflected and 
 becomes the initial velocity for the second row of blades, and so 
 on for the whole number of rows. When the rows of buckets 
 have the same mean diameter, as is usual, u has the same value 
 for each row. The diagram may be arranged conveniently and 
 more compactly by extending the line of the vane velocity as in 
 Fig. 32, and laying off a succession of lengths, each equal to u, 
 and connecting each with the point a, as shown. With an initial 
 velocity of 2430 feet per second, a blade velocity of 400 feet per 
 second, and a nozzle angle of 22 1/2, the exit velocity from 
 the second row of moving blades is 1130 feet per second, and the
 
 48 STEAM TURBINES. 
 
 blade angle 42. Proper allowance for friction, however, 
 materially affects the design and should, as before, be taken into 
 account. Fig. 33 shows how this may be done, and gives the 
 diagram where friction in the entering nozzle has reduced the 
 velocity, V, to 2320 feet per second, and in each succeeding row 
 a friction loss of 10% is assumed. Comparison of the blade sec- 
 tion as determined by the two diagrams shows a marked differ- 
 ence. If the radii of the successive rows on the shaft are not 
 
 FIG. 32. Velocity diagram for Curtis turbine, no allowance for steam friction. 
 
 equal, the length of u should be made to increase directly as the 
 diameter. In general, the friction loss is not constant through the 
 successive stages, but increases from 3% or 4% to perhaps 10% 
 with increasing presence of water in the steam. Proper values can 
 be assigned only from experience. The method of finding the 
 velocities in Fig. 33 is applicable for an increasing friction loss 
 as well as for a constant one. 
 
 As an illustration of calculations for blading in a multi-stage 
 impulse turbine, let the following conditions be given:
 
 CALCULATIONS OF TURBINE BLADING. 
 
 49 
 
 Initial steam pressure 
 
 Initial superheat 
 
 Final pressure 
 
 Assume a blade velocity u 
 
 Assume nozzle angles 
 
 = 175 pounds absolute 
 = 140Fahr. 
 = 1 pound absolute 
 = 400 feet per second 
 = 22 1/2 
 
 Assume 10% energy loss in the nozzles and 10% velocity 
 loss in each row of vanes. Let the turbine be of the Curtis type 
 with three stages and two rows of moving blades in each stage. 
 
 FIG. 33. Velocity diagram for Curtis turbine with allowance for steam "friction. 
 
 For convenience part of the heat chart is reproduced in Fig. 
 34. The initial condition of the steam is given by the intersection 
 of the 175-pound pressure line and the 140 superheat line. A 
 vertical line dropped to the 1 pound line gives 357 B. T. U. as the 
 total heat drop for pure adiabatic expansion. Dividing this 
 drop as nearly equally as possible at AC, CD, and DB, we have 
 the pressure ranges for the first three stages. 
 
 First, 175 pounds to 45 pounds absolute. 
 Second, 45 pounds to 8 pounds absolute. 
 Third, 8 pounds to 1 pound absolute.
 
 50 
 
 STEAM TURBINES. 
 
 Deducting CC' = 10% of AC for the assumed heat loss in the ex- 
 panding nozzle, we have AC', which, referred to the velocity 
 scale, gives 2320 feet per second initial velocity. As u and a 
 are given, we may draw the velocity diagram, allowing for the 
 10% velocity loss in each row. This is given in Fig. 33, where 
 
 FIG. 34. Condition curve, Curtis turbine. 
 
 the final velocity is found to be 673 feet per second. The blade 
 sections thus determined are given in the same figure. 
 
 From Eq. (3.) the force per pound of steam acting in the line 
 
 W 
 of motion, due to entrance, is V cos a and that due to the 
 
 . TP, ' 
 
 exit is - F/ cos /?'. Remembering that W here is unity the 
 
 total force acting on the first row per pound of steam is
 
 CALCULATIONS OF TURBINE BLADING. 51 
 
 - and the work done is this expression multi- 
 
 plied by the blade velocity, u, or the 
 
 Work done in the first row per second. per pound of steam = 
 
 U - (Vcosa-Vicosp). (26) 
 
 9 
 
 A similar expression gives the work done in the second row of 
 moving blades. The velocities required may be scaled from the 
 velocity diagrams. 
 
 The actual energy per pound of steam which has gone into work 
 during passage through the stage is thus found to be 56540 
 foot-pounds or in its heat equivalent, 72.8 B.T.U. This is laid 
 off on the heat drop at AE in Fig. 34 and the remainder EC, in 
 this case about 40% of AC, is still in the steam as heat energy. 
 Since the steam is now at a pressure of 45 pounds absolute, 
 and has a total heat corresponding to the ordinate of E, the con- 
 dition of the steam at the beginning of the second stage is found 
 by projecting E horizontally until it meets the 45 pound line as 
 at F. From the position of F it is seen that the steam, instead of 
 being 98% quality, is superheated about GO 9 Fahr. Dropping 
 a vertical from F to the 8 pound line shows an adiabatic heat 
 drop of 126 B. T. U., which, with 10% allowance for losses, gives 
 a velocity of 2380 feet per second. Laying out the diagram as 
 before, we have an exit velocity of 710 feet for the second stage. 
 The work for this stage is found, by the previous method, to be 
 59,150 foot-pounds per pound of steam, and the corresponding 
 actual heat drop, 76 B. T. U. Applying this to the heat chart as 
 before, we find that the steam enters the. third or last stage with 
 a quality of .986. The adiabatic heat drop for the last stage is 
 129 B. T. U., and the velocity, allowing far losses, is 2400 feet 
 per second. The energy developed in this stage is 59,600 foot- 
 pounds per pound, and the corresponding heat drop, 76 . 7 B. T. U. 
 From this last we can obtain the final condition of the steam at 
 /, where it is found to have a dryness of .947%. 
 
 Adding the work of the three stages, we have 
 First stage ................. ..... 56,540 
 
 Second stage .................... 59,150 
 
 Third stage ..................... 59,600 
 
 Total work per pound of steam = 175,290
 
 52 
 
 STEAM TURBINES.
 
 CALCULATIONS OF TURBINE BLADING. 53 
 
 1,980,000 
 
 The theoretical steam rate = = 11.3 pounds per 
 
 175,290 
 
 H. P. hour. Allowing 8% for mechanical friction, windage, etc., 
 
 11 3 
 
 this becomes ' =12.3 pounds. 
 . 92 
 
 If the generator efficiency be taken at 95% we have a steam 
 rate of 13 pounds per E. H. P. hour, or 17.5 pounds per K. W. 
 hour, on the basis of a power factor of unity. 
 
 As in Fig. 12, a quality curve may be drawn through the 
 points A, F, H, and I, which will give the condition of the steam 
 for any point during the expansion. With this determined, and 
 with the H. P. to be developed, and the steam rate as found above, 
 we have the basis for the calculation of the lengths of the blades. 
 
 Problems. 
 
 1. Make diagrams and calculations for a Curtiss turbine with 5 pres- 
 sure stages, each of 2 velocity stages. 
 
 Initial steam pressure = 155 Ibs. abs. 
 
 Superheat =75 F. 
 
 Final pressure =28 in. vac. 
 
 Assumed blade velocity =425 ft. per. sec. 
 
 Nozzle angle =22. 
 
 Velocity loss in each nozzle 5%. 
 
 Velocity loss in each row of blades 10%. 
 
 Calculate the nozzle area and blading for a 500 K. W. turbine, the 
 mechanical and generator friction being taken at the values given 
 on p. 117. 
 
 2. Make diagrams and calculations for a L. P. Curtis turbine, the con- 
 ditions being those of Prob. 1, except that the initial pressure is 
 15 Ibs. absolute and there are two pressure stages, each with two 
 velocity stages. The nozzle angles to be 25. 
 
 3. Report on the Small Curtis Turbine. See paper of G. A. Orrok, 
 Trans. A. S. M. E., vol. xxxi, p. 263. 
 
 4. Report on a Comparison of the Rateau or multicellular, and the 
 Curtis Principles of Design. Power, Dec. 20, 1910, p. 2218, and 
 Jan. 3 and 10, 1911, pp. 19 and 64. 
 
 References. 
 
 STODOLA: " The Steam Turbine." 
 THOMAS: " Steam Turbines." 
 EMMET: "The Steam Turbine in Modern Engineering," Trans. A. S. 
 
 M. E., vol. xxv. 
 See also references in the problems.
 
 54 STEAM TURBINES. 
 
 Art. 13. Single Flow Impulse -reaction Turbine. 
 
 An impulse turbine as indicated in Art. 12 is one in which 
 expansion occurs only in the fixed passages or nozzles. 
 
 A reaction turbine is one in which the energy is derived from 
 the reaction of steam issuing from openings or nozzles in the mov- 
 ing wheel. No pure reaction turbine is being built at this time. 
 A number were built in this country many years ago by Avery, 
 but they have long since been abandoned. Theoretically, there 
 is no reason why a pure reaction turbine might not be built, but 
 the velocities involved are so high as to render the type impracti- 
 
 B oiler Press. 
 
 I 
 
 Velocity 
 
 FIG. 36. Scheme of impulse- reaction turbine. 
 
 cal. A combination of the impulse and reaction principles has, 
 however, led to one of the largest and most important types of 
 turbines yet developed. 
 
 Figs. 55 and 67 show sectional elevations of two Parsons or 
 impulse-reaction turbines, both single-flow, i.e., the steam 
 enters at the end and flows axially in one direction. Fig. 36, 
 corresponding to Figs. 23 to 26, illustrates their operation. 
 The general form of the buckets is shown in Fig. 37, in which it 
 is seen that the curve at the entering end of the moving vane acts 
 as in impulse turbines, to absorb the kinetic energy discharged 
 from the fixed nozzles. The long straight portion at the exit 
 end of the moving blades forms a nozzle which restores the 
 velocity just absorbed and adds the power of the reaction of 
 exit to that of the impulse first received. In this type there is 
 an almost uninterrupted lowering of the pressure. If there were
 
 CALCULATIONS OF TURBINE BLADING. 
 
 55 
 
 Moving blades 
 
 no motion in the rotor there would be a corresponding rise in the 
 steam velocity, as shown in the curved line, Fig. 36. In fact, the 
 long passage between the rotor and the casing is essentially an 
 enlarged nozzle, its sectional area increasing steadily, and con- 
 forming roughly to that which would be given an expanding 
 nozzle. 
 
 The impulse-reaction turbine allows the lowest velocities which 
 have been attained with high economy. Its construction is 
 much more complicated than 
 the simple De Laval wheel, but 
 it has been successful in a very 
 wide range of service. 
 
 In the impulse-reaction dia- 
 gram, Fig. 37, the fixed vanes 
 beyond the first row of moving 
 blades receive the steam at a 
 velocity, V 1} using the same 
 notation as on page 29. The 
 steam, in passing through the 
 fixed vanes, expands, and the 
 velocity increases to V. With 
 respect to the following row of 
 moving blades, the steam enters at the velocity W. In passage 
 through the moving blades there is further expansion, and the 
 steam leaves them at a high velocity, W v The total work done 
 
 Fixed Vanes 
 
 in the moving blades is : First, the energy 
 
 29 
 
 per pound 
 
 of steam produced in the guide blades and expended upon 
 the moving vanes; second, the reaction accompanying the 
 increase of steam velocity in the moving blade from W to 
 
 W lf which is equal to - 
 
 
 per pound of steam used. The 
 
 guide blades and moving vanes usually have the same form and 
 angles, consequently these two expressions are equal, and the 
 total work is divided equally between impulse and reaction. 
 This type of turbine is subject to end thrust which is balanced 
 by pistons on the rotor as shown in Figs. 55 and 67. 
 
 Before the vanes can be designed in this type, the heat drop 
 in the various stages must be determined, and for this the follow- 
 ing data and assumptions are required:
 
 56 
 
 STEAM TURBINES. 
 
 1. The initial steam pressure, with dryness or superheat. 
 
 2. The exhaust pressure. 
 
 3. The absolute velocity, V, of steam as it leaves guide blades. 
 This varies progressively through the turbine. 
 
 4. Friction losses of the steam in passing through the turbine. 
 
 5. The exit angles of fixed and moving blades. 
 
 6. The peripheral velocity of the blades for the various cylin- 
 ders or steps. 
 
 The exit angles are made the same for both guide vanes and 
 rotating blades, ordinarily between 20 and 30. The smaller 
 angles than these, while apparently increasing the power, lead 
 to contracted passages and increased friction. On the other 
 hand, with too great angles the power for each stage decreases, 
 requiring too many stages, and increasing the size of the turbine. 
 The peripheral velocity u (item 6 above) at the H. P. stage 
 varies from 100 to 135 feet per second and increases as the size of 
 the rotor increases in the later stages. Table I, from a paper 
 of E. M. Speakman, gives some basis for selecting the vane 
 velocities. 
 
 Table I. 
 
 PARSONS TURBINE PRACTICE. 
 Electrical Work. 
 
 
 Peripheral Vane Speed 
 
 
 
 Rated Capacity 
 
 
 Number of 
 Rows 
 
 Revolutions 
 Per Minute 
 
 First 
 
 Last 
 
 
 Expansion 
 
 Expansion 
 
 
 
 5000 K. W. 
 
 135 
 
 330 
 
 70 
 
 750 
 
 3500 K. W. 
 
 138 
 
 280 
 
 75 
 
 1200 
 
 2500 K. W. 
 
 125 
 
 300 
 
 84 
 
 1360 
 
 1500 K. W. 
 
 125 
 
 360 
 
 72 
 
 1500 
 
 1000 K. W. 
 
 125 
 
 250 
 
 80 
 
 1800 
 
 750 K. W. 
 
 125 
 
 260 
 
 77 
 
 2000 
 
 500 K. W. 
 
 120 
 
 285 
 
 60 
 
 3000 
 
 250 K. W. 
 
 100 
 
 210 
 
 72 
 
 3000 
 
 75 K. W. 
 
 100 
 
 200 
 
 48 
 
 4000
 
 CALCULATIONS OF TURBINE BLADING. 
 
 Marine Work. 
 
 57 
 
 Type of Vessel 
 
 Peripheral Vane Speed 
 
 Mean 
 Ratio of ^ 
 
 No. of 
 
 Shafts 
 
 In H. P. 
 
 In L. P. 
 
 High speed mail steamer 
 Intermediate mail steamer 
 Channel steamers 
 
 70-80 
 80-90 
 90-105 
 85-100 
 105-120 
 110-130 
 
 110-130 
 110-135 
 120-150 
 115-135 
 130-160 
 160-210 
 
 .45-. 5 
 .47-. 5 
 .37-. 47 
 .48-. 52 
 .47-. 5 
 .47-. 51 
 
 4 
 3 or 4 
 3 
 4 
 3 or 4 
 3 or 4 
 
 Battleships and cruisers. 
 Small cruisers 
 Torpedo craft 
 
 The steam velocity (item 3) varies from 2 to 3.5 times the 
 blade velocities. When it would rise above this in the pro- 
 gressive expansion along the rotor, the diameter of the rotor is 
 increased, beginning a new step or drum. 
 
 The heat drop in any stage (i.e., one row of fixed vanes and one 
 row of moving blades) may be found readily by the following 
 
 .Example of calculation for "Stage Dropj'-First Stage A 
 Aa=Aa below =V= 200 'per sec. 
 Ab=Ab =n=120' " " 
 In diagram bf =170, by scaling 
 
 FIG. 38.- Velocity curves and heat drops, single flow impulse-reaction turbine. 
 
 simple graphical construction, Fig. 38. In the velocity tri- 
 angle formed by V, W, and u, produce u and drop a perpendic- 
 ular aa' upon it from a. With a', the base of this perpendicular, 
 as a center, and Aa f as a radius, describe the arc afp. Drop a
 
 58 STEAM TURBINES. 
 
 perpendicular from b, cutting the arc at /. The work done in foot- 
 pounds per pound of steam in the stage is W , where bfis 
 
 y 
 measured to the same velocity scale as u and V r 
 
 The proof of this is as follows: 
 
 The separate velocity diagrams in Fig. 33 may be combined 
 as shown, and where the work is divided equally between impulse 
 and reaction the figures will be symmetrical with respect to aa'. 
 The velocities of exit from the fixed and moving blades are W 
 and Vi, and from Eq. (26) the work is done 
 
 u(V cosa+ViCos /3) u(Aa'+a'o) 
 
 But bf, being the perpendicular from /to the hypothenuse of the 
 right-angled triangle a, f, p, inscribed in a semicircle, is the mean 
 proportional between the segments ab and bp, therefore 
 
 bf 2 AbXbp and since bp = ao, 
 = Ab(Aa'-\-a'o) 
 = u(V cos a+V^os $ 
 
 9 
 The heat drop producing the work will be 
 
 -mfa (-m) 
 
 If the heat drops in the various stages were equal, the number 
 of stages could be determined at once by dividing the total heat 
 drop from inlet to condenser by the stage drop assumed. The 
 stage drops, however, vary, those nearest the condenser being 
 much greater than the earlier ones. A method of determining 
 these, outlined by Prof. Stodola, will be used in working out a 
 definite case. The conditions will be taken as follows: 
 
 Normal capacity =2000 K. W. 
 
 Overload capacity, without by-pass, =2400 K. W. 
 
 Initial pressure = 175 pounds absolute 
 
 Superheat = 50 
 
 Condenser pressure = l pou nd absolute
 
 CALCULATIONS OF TURBINE BLADING. 59 
 
 R. P. M. =3,600 
 
 Number of drums = 4 
 
 Loss due to steam friction 28% 
 
 Loss due to leakage = 6% 
 
 Loss due to windage, bearings, etc., = 15% 
 
 Energy in exhaust = 3% 
 
 Total losses in addition to steam friction = 24%. 
 
 Efficiency of generator 94% 
 
 We must first assume blade velocities. From reference to 
 Table I on page 56 these may be taken as 
 
 it = 120 feet for first stage, increasing to 
 w = 320 feet at exhaust end. 
 
 Assume also exit angles for all blades and vanes =24, and a 
 clear area through the blades = 1/3 of the cross section of the 
 opening. 
 
 Lay off, as in the lower part of Fig. 38, a horizontal base AB 
 to represent the length of the rotor. Let the steam velocity in 
 the first stage be 200 feet per second, and in the final stage be 
 950 feet, these values being based on experience. The curve 
 of steam velocities must be assumed. It follows approximately 
 a hyperbolic curve except toward the exhaust end, where it 
 rises rapidly. The curve here drawn is about as followed in 
 practice. 
 
 The velocity w=12Q feet per second, for the first cylinder, is 
 laid off at the left, and the velocity 320 feet, for the last cylinder, 
 is laid off at the right. The most advantageous ratio between 
 
 v 
 
 the steam and blade velocities is from 2 to 3 and it should vary 
 
 u 
 
 between about the same limits on each drum. It is customary 
 also to make the ratio between the successive drum diameters 
 substantially constant. The blade velocities, on this basis, come 
 to 120, 165, 225, and 320 feet per second. 
 
 Moyer gives an empirical formula for determining the number 
 of stages: 
 
 (28)
 
 60 STEAM TURBINES. 
 
 where C is a constant which varies from 1,500,000 for marine tur- 
 bines to 2,600,000 for electric generator service, and u is the mean 
 blade velocity in feet per second of the cylinder considered. The 
 n found is the number of rows required if the blade speed for 
 the whole turbine were u. As the cylinder considered develops 
 a certain fraction only of the total power, the number of rows 
 required for that cylinder will be that fraction of the n found 
 in the formula. 
 
 It can be seen from the wide range in the constant that reliance 
 on this formula calls for experience on the part of the designer 
 with the working conditions and their relation to the constant 
 used. It may be used to great advantage by any one, however, as 
 giving a good approximation for the number of blades on each 
 drum or cylinder. Let us assume that the power developed by 
 the various cylinders shall be approximately 1/6, 1/5, 1/4, and 
 3/8 of the total. 
 
 Then, taking C at 2,500,000, for 
 
 2500000 
 1st cylinder, ^ = -.1/6=30 stages 
 
 2500000 
 
 2nd cylinder, n 2 = - -- .1/5 = 18 stages 
 loo 
 
 2500000 
 
 3rd cylinder, n 3 = 00 ^ .1/4 = 12 stages 
 22o 
 
 2500000 
 4th cylinder, n t = - ~ . 3 /8 = 6 stages 
 
 Total 66 stages. 
 
 The stages are spaced off uniformly on AB and the drum lengths 
 located tentatively as at cd, ef, and gh. 
 
 The heat drop which would occur in a stage located at any 
 point may be determined by the graphical method of Fig. 38. 
 Having taken a sufficient number of these points, and plotted 
 the corresponding heat drops, we get the broken curve marked 
 "stage drops," the breaks being as shown in dotted lines. The 
 average ordinate of this curve gives the average of the heat 
 drops for all the stages, which, in this case, =3.58 B. T. U. This 
 average drop, divided into the total heat drop from inlet to 
 exhaust, will give the total number of stages. The total heat
 
 CALCULATIONS OF TURBINE BLADING. 
 
 61 
 
 drop, determined from the steam-entropy tables, or from the 
 heat-entropy chart (see Fig. 40) is found to be 338 B. T. U., for 
 pure adiabatic expansion, but there is a loss of energy in the 
 steam of y = 28 % ; therefore 338 X ( 1 - 28) = 338 X . 72 = 243 
 B. T. U. Actual heat drop per pound of steam. 
 
 Curve of Net Voll per Ib. of Steam, 
 FIG. 39. Pressure and volume curves, single-flow, impulse-reaction turbine. 
 
 The number of stages then will be the 
 Total heat drop 243 B. T. U. 
 
 =68 instead of 66. 
 
 Average stage drop 3 . 58 B. T. U. 
 
 The 68 stages may be laid off on the base AB and the cylinders, 
 which have up to this point been divided only tentatively, may 
 be readjusted, as shown in full lines. The division made here is 
 as follows: 
 
 
 
 Heat Drop, as Scaled 
 from Curve 
 
 First cylinder 
 
 32 stages 
 
 43 
 
 Second cylinder 
 
 . 18 stages 
 
 54 
 
 Third cylinder 
 Fourth cylinder 
 
 11 stages 
 7 stages 
 
 64 
 
 82 
 
 Total 
 
 68 stages 
 
 243 
 
 

 
 62 STEAM TURBINES. 
 
 The progressive heat drop through the turbine may be shown 
 in a curve (see Fig. 39) in which the ordinates represent the 
 progressive sum of the heat drops from A. The last ordinate 
 should check with the total net heat drop 243 B. T. U. 
 
 By the initial conditions there are further losses amounting 
 to 24% of the actual heat drop. Therefore, 243x76% = 185 
 B. T. U. per pound of steam, are available for power. Then 
 
 1980000 
 
 - =13.8 pounds of steam per B. H. P. 
 
 185X777.5 
 Since the efficiency of the generator = 94%, 
 
 13.8X1.36 
 
 = 20 pounds = steam per K. W. hour. 
 
 . i/4 
 
 2000 X 20 
 
 =11.1 pounds steam per second for normal load. 
 
 3600 
 
 The steam rate may rise slightly for overloads, but hardly 
 enough to change the rate inside of 20% overload; we have 
 
 20 X 2400 
 
 therefore =13.4 pounds steam per second for overload 
 
 3600 
 
 conditions. Where a by-pass valve is used, as in Fig. 55, the 
 steam rate should be further raised for the blading beyond it. 
 
 There remains the determination of the steam volume under 
 the given conditions, and of the dimensions of the blades and 
 vanes. The condition of the steam may be taken from 
 Fig. 40, which is taken from the heat chart. A, as before, 
 indicates the initial conditions. The vertical drop to B on the 
 1 pound line gives a quality of 79.2%. But the 28% energy 
 loss raises the quality of the exhaust to 88.5%. The condition 
 curve gives the quality of the steam for any intermediate 
 pressure. 
 
 The heat drop for any point, read off from the curve of total 
 drops, Fig. 39, and applied to Fig. 40 by measuring down from 
 A and projecting over to the quality curve AD, gives the pres- 
 sure and condition corresponding to the pressure. Curves of 
 pressure and volume of Fig. 39 may thus be derived. 
 
 The blade lengths may be derived as follows: From Eq. (14) 
 the area of the steam passage required, in square inches, = 
 
 weight^fjteam per second X vol. per pound X 144 
 steam velocity in feet per second.
 
 CALCULATIONS OF TURBINE BLADING. 63 
 
 and the length of blade required to give the necessary area 
 (assuming the blades as occupying 1/3 of the clear passageway, 
 and the blade angle = 24) is 
 
 Area X 1.5 1.5 A 
 
 ~ 
 
 7rXmean blade dia. sin 24 
 
 FIG. 40. Condition curve, single-flow impulse-reaction turbine. 
 
 Combining these equations and reducing, 
 
 . 5 _ 1 7 1 . 5 v 
 AxVd ~~ Vd ' 
 
 For the normal load, 2000 K.W.,TF=11. 1 pounds (p. 62). 
 For the overload, 2400 K. W.,W = 13.4 pounds (p. 62) .
 
 64 STEAM TURBINES. 
 
 The mean blade diameter, d, for the various cylinders, is 
 determined from the values of u, Fig. 38, and the initial con- 
 dition of 3,600 R. P. M., or 60 revolutions per second. 
 
 u = 6QXxXd, from which 
 
 120 
 
 For first cylinder d = - = .635'= 7 5/8 ins. mean dia. 
 .toy 
 
 For second cylinder d = -= .875' = 10 1/2 ins. mean dia, 
 
 loc/ 
 
 095 
 
 For third cylinder d = = 1. 19' = 14 1/4 ins. mean dia. 
 
 ic?y 
 
 320 
 For fourth cylinder d = = 1.7' =20 1/2 ins. mean dia. 
 
 lOc/ 
 
 For a slower R. P. M. or higher blade velocities the mean blade 
 diameters would of course be correspondingly larger. 
 
 Taking V from the curve V, Fig. 38, and volumes from 
 Fig. 39, and with the values for w and d above, the lengths of 
 the various blades may be determined. For manufacturing 
 reasons the lengths, instead of increasing progressively along the 
 rotor, are stepped into groups as shown in Fig. 44. 
 
 Problems. 
 
 1. Make diagrams and calculations for the blading of a single flow 
 Parsons turbine, having four drums. 
 
 Capacity, rated, 1000 K. W. 
 
 Capacity at opening of by-pass valve, 1300 K. W. 
 Initial pressure, 150 gauge. 
 
 Superheat, 50 F. 
 
 Exhaust pressure, 28 1/2 in. vac. 
 
 R. P. M., 3600. 
 
 Exit blade angles, 25. 
 
 Steam velocities, 250 ft. to 1000 ft. 
 
 Blade velocities, 150 ft. to 350 ft. 
 
 Losses and generator efficiency, as given on p. 62. 
 
 2. Make diagrams and calculations for the blading of a single flow 
 L. P. turbine of Parsons type. 
 
 Initial steam pressure, 16 Ibs. absolute. 
 
 Quality, 95%. 
 
 Exhaust, 28 1/2 vacuum. 
 
 R. P. M., 3600. 
 Exit blade angles, 28.
 
 CALCULATIONS OF TURBINE BLADING.
 
 66 STEAM TURBINES. 
 
 Assume same steam and blade velocities as for the low pressure 
 stages of Prob. 1. 
 
 3. Report on the Avery turbine, interesting as being a pure reaction 
 turbine and probably the first commercial one. See American 
 Machinist, Nov. 9, 1905, p. 631. 
 
 4. Report on the article on Blading Calculation, Power, Aug. 9, 1910, 
 p. 1412. 
 
 5. Report on article on Construction Details of a Reaction Turbine, 
 Power, May 19, 1908, p. 761. 
 
 6. Report on article on the Internal Losses in a Parsons Turbine, by 
 Prof. A. G. Christie. Power, Aug. 24, 1909, p. 299. 
 
 References. 
 
 STODOLA: "The Steam Turbine." 
 
 THOMAS: "Steam Turbines." 
 
 MOYER: "Steam Turbines." 
 
 HODGKINSON: Paper, A. S. M. E., vol. xxv. 
 
 PARSONS: Paper, Inst. Naval Arch. (London), May, 1904. 
 
 See also references in the following problems. 
 
 Art. 14. Double Flow Impulse -reaction Turbines. 
 
 On account of the drop in pressure through the moving blades 
 in the Parsons turbine steam must be admitted around the entire 
 circumference, which leads to very short blades in the high- 
 pressure stages, and for the same reason the clearance over the 
 ends of the blades must be very small. Leakage is further 
 minimized by using only small pressure drops, which increases 
 the number of H. P. stages, lengthens the rotor, and introduces 
 trouble from expansion which in the larger sizes becomes serious. 
 While the heat drop per stage is less at the H. P. end of the rotor 
 than at the L. P. end, the pressure drop is greater. This, coupled 
 with the fact that the end clearances over the short H. P. blades 
 must inevitably give a greater percentage of leakage, makes the 
 H. P. end of a Parsons turbine its least efficient portion. The 
 pure reaction type, where the blades are pressure balanced and 
 admission may be had through a portion only of the blade circle, 
 is more efficient in the high-pressure ranges than the reaction 
 type, but in the later stages where water is present in the steam 
 it is less efficient. 
 
 These considerations have led to the combination of the two 
 types in one machine, utilizing the advantages of both, Steam
 
 CALCULATIONS OF TURBINE BLADING. 
 
 67
 
 68 
 
 STEAM TURBINES. 
 
 is admitted through nozzles to a multi-stage impulse wheel and 
 expanded to about atmospheric pressure. The rest of the ex- 
 pansion takes place in fixed and moving blades of impulse- 
 reaction type. The reaction portion is divided in the latest 
 form and steam flows axially in both directions from the impulse 
 wheel. Fig. 42 shows a Westinghouse turbine of this design 
 where the central impulse wheel is clearly seen, with the reaction 
 portions on each side. Fig. 43 is a sectional elevation of the 
 same turbine and shows clearly the course of the steam as it 
 leaves the impulse wheel and is divided into two streams flowing 
 in opposite directions. This arrangement automatically balances 
 
 [Exhaust h- Exhaust 
 
 FIG. 43. Section of 10,000-K. W. Westinghouse double-flow turbine. 
 
 the end thrust of the reaction blades and eliminates the balancing 
 pistons necessary in the single-flow type. Besides a symmetrical 
 casing, with smaller exhaust connections it materially shortens 
 the distance between the bearings. Fig. 44 shows two rotors, 
 both for 2000-K.W. Westinghouse machines, the upper one of 
 the double-flow combined type and the lower the old single-flow 
 type. 
 
 Double-flow turbines are found most desirable in the larger 
 sizes, but for comparison with the previous problem of a single-flow 
 turbine, let the same conditions be assumed for one of this type. 
 Let the steam be expanded in a set of nozzles from inlet pressure 
 to 25 pounds absolute and pass through two velocity stages of 
 an impulse wheel of the Curtis type as shown in stage a, Fig. 29. 
 Let the remainder of the expansion to 1 pound absolute take 
 place in two sets of Parsons blading as in Fig. 42. Let the
 
 CALCULATIONS OF TURBINE BLADING. 69 
 
 osses in the impulse element, due to disc and blade friction, 
 leakage, etc., be assumed as 40%, the energy so lost reappearing 
 in the increased quality of the steam. The friction losses in the 
 low-pressure blading will be taken at 28% as before. 
 
 Fig. 45 gives the expansion diagram for these conditions. 
 The net drop available for the impulse stage is 91.2 B. T. U. 
 and for the low-pressure stages 142.8 B. T. U. It will be seen 
 from last article that the number of stages in the low-pressure 
 
 FIG. 44. Comparison of single- and double-flow Westinghouse rotors 3600 and 1800 
 R. P. M.^ame H. P. 
 
 blading depends on the available heat drop, the steam and blade 
 velocities and the exit angles. Dividing the flow does not affect 
 the number of stages on each side. It merely halves the length 
 of the blades, an advantage in the last few stages where in the 
 single-flow machines the length is excessive. Greater blade 
 angles may be used to advantage in low-pressure stages than in 
 high-pressure ones without unduly increasing the number of 
 stages, and 30 will be used instead of 24 as before. 
 
 Let the blading be carried on two drums or cylinders running 
 at 225 and 320 feet per second and the steam velocity increase 
 from 400 feet per second to 950. This gives the same conditions 
 as for the last two drums in Fig. 38. 
 
 If 3/8 of the total work be carried by the impulse wheel, 1/4
 
 70 
 
 STEAM TURBINES. 
 
 by the smaller drums, and 3/8 by the larger ones, the application 
 of formula (27) gives 13 stages and 9 stages for the ^ first and 
 second drums, respectively. Laying these off tentatively and 
 proceeding as in Fig. 35 we find the mean stage drop to be 
 6.8B. T. U. (Fig. 46). Then 
 
 = 21 = number of stages. 
 
 6.8 
 
 FIG. 45. Condition curve, double-flow turbine. 
 
 Re-adjusting we may take 13 for the first cylinders and 8 for 
 the second. The stage drops are laid off in Fig. 45, those from 
 B to C being on the first cylinder, and those from C to D on the 
 second. The pressures and conditions are found directly and 
 the blade lengths determined as in the last article, which will 
 be those for a single-flow turbine of 21 rows. In the present
 
 CALCULATIONS OF TURBINE BLADING. 
 
 71 
 
 one there will be two complete sets of blades of 21 stages each, 
 each set of blading one-half the length required for the single- 
 flow. Curves of pressures and net volumes per pound of steam 
 are shown in Fig. 46. 
 
 It must be remembered that in this and the foregoing articles 
 certain constants, velocities and friction coefficients have been 
 
 Vssumed Curve_ofSteamVeloci 
 Curve of StagePv 
 
 B C 
 
 FIG. 46. Velocity curves and heat drops, double-flow turbine. 
 
 more or less arbitrarily assumed. Accurate values for these 
 can be assumed only after wide experience and from intimate 
 knowledge of working conditions. Such information on the 
 choice of values as is available may be found in the standard 
 works on turbines referred to at the end of this article. 
 
 Problems. 
 
 \ / 1. Calculate the blading and draw diagrams for a double-flow 
 turbine similar to Fig. 43. 
 
 Capacity, 2000 K. W. 
 
 Initial steam pressure, 160 Ibs. gauge. 
 
 Superheat, 60. 
 
 Exhaust pressure, 28 ins. vac. 
 
 Impulse wheel to have two velocity stages and to carry expansion 
 down to 20 Ibs. absolute, with reheating losses of 40%.
 
 72 STEAM TURBINES. 
 
 2. Make diagrams and blade calculations for a turbine for conditions 
 similar to Prob. 1. The first pressure stage to be a two-stage 
 Curtis wheel expanding to 25 Ibs. absolute. The remainder of the 
 expansion to take place in a series of wheels of Rateau or multi- 
 cellular type (Fig. 30) . Consult J. A. Moyer, Steam Turbines, p. 86. 
 
 3. Report on the Westinghouse double flow turbine described in 
 Power, June 16, 1908, p. 931. 
 
 4. Report on the construction and test of a 10,000-K. W. double-flow, 
 impulse-reaction turbine, described in paper by Naphtaly, Trans. 
 A. S. M. E., vol. xxxii, Dec., 1910. (Shown in Fig. 43.) 
 
 5. Report on the Melms-Pfenninger turbine (Curtis-Parsons), described 
 in Lond. Engineering, July 9, 1909, p. 39, and Power, Sept., 1907, 
 p. 643. 
 
 References. 
 
 MOYER: " Steam Turbines." 
 STODOLA: "The Steam Turbine." 
 
 NAPHTALY: "Test of 10000-K. W. Turbine," Trans. A. S. M. E., Dec., 
 1910.
 
 CHAPTER IV. 
 MECHANICAL PROBLEMS. 
 
 The problems already considered have dealt with the using 
 of steam at the high velocities of turbine practice. These 
 involve problems of a purely mechanical nature, among which 
 are provision for centrifugal strains due to speeds of 3,000 to 
 30,000 R. P. M., the balancing of the shafts, bearings suitable 
 for such speeds, and close and rapid regulation under varying 
 loads. 
 
 Art. 15. Centrifugal Strains. 
 
 A thorough consideration of this subject involves extended 
 and complex analysis. Some only of its phases will be touched 
 on here. 
 
 As the velocities in the De Laval turbine are much higher 
 than in any other, it is in this turbine that the interesting be- 
 havior of a disc rotating at high velocities is most marked. 
 
 If a flexible shaft carry a round disc, one side of which is 
 slightly heavier than the other, the center of gravity will lie at 
 one side of the geometrical center, as in Fig. 47 "a". If they 
 are rotated rapidly the unbalanced centrifugal force of the heavy 
 side will deflect the shaft toward the heavy side, and cause the 
 geometrical center of the disc to describe a circle as at "b". This 
 action increases with the speed up to a certain point called the 
 "critical speed," when the vibration becomes momentarily 
 excessive. On further increase of speed they settle down and 
 will run quietly, however much the speed be increased. At 
 this critical speed the axis of rotation shifts from the center of 
 the path of the geometric center, o, to the center of gravity of 
 the wheel, as shown in Fig. 47 "c". 
 
 It can be shown that the deflection is 
 e 
 
 v= ^ 
 
 '-fe 
 
 73
 
 74 
 
 STEAM TURBINES. 
 
 where e is the eccentricity of the center of gravity and V c the 
 critical velocity referred to. The greater the velocity V, 
 the smaller y becomes, approaching the value y = e, until the 
 wheel bursts. In the De Laval practice the critical speed is 
 from 1/8 to 1/5 of the normal R. P. M. 
 
 FIG. 47. Action of the flexible shaft. 
 
 For cylindrical rings where the radial thickness is small, the 
 tensional stress due to the centrifugal force is equal to 
 
 12 w 
 
 (29) 
 
 where S = stress in pounds per square inch. 
 w = weight per cubic inch of material. 
 v = linear velocity of ring in feet per second
 
 MECHANICAL PROBLEMS. 
 
 75 
 
 Calculation of the stresses in discs rotating at very high speeds 
 is difficult. They vary with the weight of the material and the 
 square of the speed. Fortunately the materials available have 
 been so improved that a factor of safety can be used, sufficient 
 
 FIG. 48. Large and small De Laval wheels. 
 
 to cover any uncertainty as to the centrifugal strains. Two 
 facts are shown clearly by both theory and experiment. 
 
 First. The stresses are greater nearer the center than near 
 the rim. 
 
 Second. The stress in the nave of a bored disc is greater than 
 in a solid disc. A small hole may even double the strains.
 
 76 STEAM TURBINES. 
 
 These principles have been recognized in the design of the 
 disc in the De Laval turbine shown in Fig. 48. The profile is 
 a form of logarithmic curve asymptotic to the central axis of 
 the disc. In the smaller turbines the flexible shaft runs through 
 the disc, but in the larger ones the shafts are flanged to the sides, 
 to avoid piercing the disc. The curved lines added near the 
 center of the large wheel show the theoretical form, to which 
 the attachments are tangent. Wheels of this form, when 
 tested to destruction, would burst through the center into 
 large pieces, and it is stated that these pieces have been 
 driven through a steel wheel case 2 inches thick. This menace 
 is obviated, however, by turning grooves, A, A, which reduce 
 the thickness of the wheel close to the periphery, decreasing 
 the strength of the wheel at this point so that the stresses 
 here are about 50% higher than in the rest of the wheel. The 
 factor of safety at this point being about 5, the rim of the wheel 
 will tear off at a little over twice the normal speed, breaking up 
 into small fragments, which are unable to damage the wheel 
 case. When the rim lets go, the blades which are the impelling 
 force of the wheel go with it, the centrifugal forces are at once 
 much reduced, and the wheel is unbalanced. The heavy hub 
 which projects into the casing at B with but small clearance 
 comes into contact with the sides and acts as a brake, bringing 
 the wheel to rest in a few revolutions. Discs of rolled plate are 
 not used for a single-stage machine, as streaks or lines of weak- 
 ness, due to "piping," difficult to detect, may become elements 
 of danger. 
 
 In connection with the improvement in materials referred to, 
 it may be noted that Krupp and Co. of Essen, Germany, have 
 for this use a special nickel steel of 125,800 pounds tensile 
 strength, 92,300 pounds elastic limit, and 12% elongation. 
 They have recently produced nickel steel of even higher strength 
 but of less elongation. The following figures are taken from 
 their published tables:
 
 MECHANICAL PROBLEMS. 
 
 77 
 
 Ult. Tensile Strength, 
 Pounds per Sq. Inch 
 
 Elastic Limit, 
 Pounds per Sq. Inch 
 
 255,600 
 
 7. 
 
 136,320 
 
 Measured 
 
 252,760 
 
 5.5 
 
 153,360 
 
 on .472 inch 
 
 251,340 
 
 6. 
 
 210,160 
 
 diam. bar, 
 
 258,440 
 
 4.1 
 
 227,200 
 
 3 . 937 between 
 
 211,580 
 
 6.8 
 
 187,440 
 
 points. 
 
 310,980 
 
 (?)' 
 
 213,000 
 
 
 Broke in center punch mark. 
 
 FIG. 49. Section of rotor, five-stage Curtis turbine. 
 
 These elastic limits are erratic, but the results are remarkable. 
 It is a question whether such hard material is practical but discs
 
 78 STEAM TURBINES. 
 
 are used which show under test 134,900 pounds tensile strength, 
 14% elongation, and 106,630 pounds elastic limit.. 
 
 In multi-stage impulse turbines where the velocity is about 
 half that of the single-stage type, the question of centrifugal 
 strains is not so difficult. In the Curtis turbine the wheels are 
 built up of castings and plates. The blades are milled in a 
 sectional blade ring bolted to the discs at the edge. Fig. 49 
 shows the detail of this construction. 
 
 In turbines of the Parsons type the velocities are still further 
 reduced (see table, p. 56). The principle adopted by Mr. Parsons 
 was to have the drum and shaft stiff, balanced as closely as pos- 
 sible, and carried in a bearing which would provide sufficient 
 lateral motion to allow the shaft to find its own center. 
 
 Problems. 
 
 i. Report on the conclusions of paper on "Critical Speed Calculations." 
 by S. H. Weaver, Jour. A. S. M. E., vol. xxxii, June, 1910. 
 
 References. 
 
 STODOLA: " The Steam Turbine" (especially 4th ed.). 
 JUDE: "Theory of the Steam Turbine." 
 MOYER: "Steam Turbines." 
 J. M. NEWTON: "Design and Construction of High Speed Turbine 
 
 Rotors," London Engineering, July 8 and 15, 1910. 
 WEAVER: "Critical Speed Calculation," Jour. A. S. M. E., June, 
 
 1910. 
 
 Art. 1 6. Bearings. 
 
 The earlier form of bearing used by Parsons is shown in Fig. 
 50, where the space between the shaft and the journal wall was 
 taken up by two sets of rings. Those of one set fitted the shaft 
 closely, and had play between their outer ' diameters and the 
 journal wall. Those of the other set, which alternated with 
 these, fitted the journal box tightly, and were loose on the shaft. 
 They were held in contact by a side spring. A lateral movement 
 of .005 inch or more was thus provided. This arrangement, while 
 satisfactory, has been superseded by one (Fig. 51) in which there 
 is a nest of bronze sleeves concentric with the shaft, each having 
 about . 002 inch play on the diameter. Holes are bored through 
 them to permit the lubricating oil to reach the inner sleeves and 
 shaft. Side play is thus provided as before, but with a much
 
 MECHANICAL PROBLEMS. 
 
 79 
 
 simpler construction. In the large machines, running below 
 1200 R. P. M., the flexible bearing is dispensed with and solid 
 self -oiling bearings are used. 
 
 In the vertical Curtis turbine the problem has been to design 
 
 FIG. 50. Old Parsons shaft packing. 
 
 a step bearing which would carry the entire weight of the shaft, 
 wheels, and the field. The end of the shaft carries a cast iron 
 block, which runs upon a similar block in the bearing. Oil or 
 water is forced through the pipe ^l,Fig. 52, into the recessed 
 portion between the bearing faces, and circulates out and 
 
 FIG. 51. Later Parsons shaft packing. 
 
 upward, through the journal, leaving the bearing at the top 13. 
 The entire weight of the moving parts is thus carried on the 
 film of lubricant between the blocks a and 6. The pressure of 
 the lubricant is from 150 pounds to 900 pounds per square inch, 
 according to the size.
 
 80 
 
 STEAM TURBINES. 
 Problems. 
 
 1. Report on the principles of labyrinth packings, see Power, Sept. 
 1908, p. 401. 
 
 2. Report on the general principles of the labyrinth packing, i 
 Lond. Engineering, Jan. 10, 1908, p. 35. 
 
 FIG. 52. Step bearing of a Curtis vertical turbine. 
 
 References. 
 
 STODOLA: "The Steam Turbine" (4th ed.). 
 
 JUDE : " Theory of the Steam Turbine." 
 
 For theory of the labyrinth packing see London Engineering, Jan. 10, 
 
 1908, p. 35, also "Power," Sept. 8, 1908, p. 401. 
 Revue de Mechanique, Nov., 1910.
 
 MECHANICAL PROBLEMS.
 
 82 STEAM TURBINES. 
 
 Art. 17. Governing. 
 
 There are three types of turbine governors in general use: 
 
 First, balanced throttling valves. 
 
 Second, multiple closing or relay valves. 
 
 Third, intermittent admission. 
 
 The well known turbines present examples of all three of these 
 classes. A fourth method of control is used in conjunction with 
 the third as supplementary to it. It consists of means for 
 admitting H. P. steam directly to the later stages by means of a 
 by-pass valve, in order to provide for heavy overload conditions. 
 
 Throttling Type. 
 
 As applied on the DeLaval turbine, this governor has a spring- 
 actuated double-beat valve, controlled by a spring and weight 
 governor located at one end of one of the gear shafts where the 
 speed has been reduced 10 to 1. Even here the speed is from 
 1,000 to 3,000 R. P. M. This high velocity alters the weight 
 arms materially from the well known shape, and they take 
 the form of semi-cylindrical leaves, D, turning about the knife 
 edges, and closely enfold the controlling spring. The governing 
 mechanism has a further control in addition to that of the 
 throttle. If the balanced valve fails to govern and the speed 
 continues to rise, the tappit, P, comes into contact with an 
 independent valve, operating a butterfly valve, V, in the ex- 
 haust passage and raising the back pressure. This immediately 
 puts a brake on the wheel and prevents any further accelera- 
 tion of speed. The effectiveness of this action may be shown by 
 the fact that a 150 H. P. turbine, with nozzles designed for 150 
 pounds gauge pressure, and 26 inches vacuum, if operated on a 
 back pressure equivalent to an atmospheric exhaust, will slow 
 down and can not be brought up to full speed even with the 
 entire load removed. 
 
 The controlling mechanisms of the De Laval, Kerr, Zoelly, and 
 a large number of other turbines follow these general lines. 
 
 Multiple or Relay Control. 
 
 In the smaller sizes of Curtis turbines governing is effected by 
 throttling, as already described. In the larger sizes the speed is 
 controlled by the opening and closing of small valves admit-
 
 MECHANICAL PROBLEMS. 
 
 83 
 
 1. Govenor. 
 
 2. Steam Chest. 
 
 Nozzle 
 
 Moving Blades 
 Stationary Blades 
 Moving Blades 
 
 Stationary Blades 
 Movmg Blades 
 
 1 I J, 
 
 Fro. 54. Relay control of Curtis turbine.
 
 STEAM TURBINES.
 
 MECHANICAL PROBLEMS. 
 
 85 
 
 ting to the separate nozzle sections, as shown in the lower part of 
 Fig. 54, which is a schematic section of the casing 2 above, the 
 number in action depending upon the load. These nozzle 
 valves are operated from the governor mechanism, 1, at the top 
 of the unit, and are designed to be fully open or shut, like a 
 pop-safety valve, in order to prevent cutting of the seats by 
 wire drawing. The control of the nozzle valves by the governor 
 has been effected by means of positive mechanical connections, 
 electrical connections, and hydraulic cylinders. The last has 
 been found most satisfactory, and is used on the later machines. 
 This method of control by multiple valves gives excellent 
 economy, as the steam is used at an almost constant thermo- 
 dynamic efficiency, whatever the load. 
 
 Intermittent Control. 
 
 The general arrangement of the controlling mechanism is 
 shown on the general section of a Westinghouse turbine, Fig. 55. 
 
 FIG. 56. Governing mechanism of the Westinghouse turbine. 
 
 Admission is through a single double-beat valve controlled by 
 a steam-operated piston above it, Fig. 56. A heavy spring 
 above the piston tends to hold the valve to its seat. Steam is
 
 86 
 
 STEAM TURBINES. 
 
 admitted to the piston B through the annular clearance X, around 
 the valve steam and exhausts through a controlling valve 
 A, which is actuated by the governor. The governor is of the 
 bell-crank type, the horizontal arms bearing against an ad- 
 justable spiral spring. E and D are fixed fulcrums, F, a 
 floating one, moving up and down with the governor sleeve. 
 C is an oscillating lever driven by worm gearing and an eccentric, 
 from the main turbine shaft. The motion of C is communicated 
 to the pilot valve, A, and thence to the main valve, admitting 
 steam to the turbine in gusts. The distance that the valve A 
 opens as it moves up and down, and consequently the time it 
 
 & 1BO 
 
 SI 125 
 
 fi 75 
 5 '0 
 
 26 
 
 Atmos- 
 pheric^ 
 
 Absolute 
 Zero 
 
 8 
 2210 O 
 
 FIG. 57. Pulsation diagram, Westinghouse turbine. 
 
 remains open, is controlled through F by the position of the 
 governor. At light loads the main valve opens for only short 
 periods and remains closed for the greater part of the stroke of A. 
 As the load increases the valve remains open longer, until finally 
 a practically continuous pressure is maintained in the H. P. end 
 of the turbine. The effect of the governor on the initial pressures 
 is shown in Fig. 57. The fourth method of control, that of 
 providing for overloads by admission of steam to later stages is 
 also shown in Fig. 55 where a secondary admission valve V s is 
 provided, to admit high pressure steam to the second drum of 
 the turbine for overloads. It is not opened and closed regularly, 
 as the main one is, but is controlled by another pilot valve con- 
 nected directly with the governor sleeve. Another device for 
 accomplishing the same thing, used by Brown, Bovari, and Co. 
 in Europe, opens by-pass valves to the later stages as the pres-
 
 MECHANICAL PROBLEMS. 87 
 
 sure rises in the H. P. chamber. It is obvious that steam 
 admitted directly to the later stages is not used to the greatest 
 advantage, but as overload conditions are intermittent the loss 
 in steam economy is admissible. 
 
 A comparison of tests of turbines using the three methods of 
 governing 1 shows that from the standpoint of steam consump- 
 tion under light loads the multiple valve control is most economi- 
 cal, intermittent admission next and throttling valve last. The 
 throttling governor is, however, the simplest and is used almost 
 universally on small units. 
 
 Problems. 
 
 1. Look up and report on the various methods of operating the multiple 
 nozzle valve on the Curtis turbine, see Bulletins of the General 
 Electric Co. 
 
 2. Report on the regulation of the Rateau low pressure turbine, de- 
 scribed in Power, May 10, 1910, p. 845. 
 
 References. 
 
 STODOLA: "The Steam Turbine" (4th ed.). 
 JUDE : " Theory of the Steam Turbine." 
 MOVER: " Steam Turbines." 
 Revue de Mechanique, Oct., 1910. 
 
 1 Mechanical Engineer, Jan. 20, 1906.
 
 CHAPTER V. 
 COMPARISON OF TYPES. 
 
 Art. 1 8. Vertical Turbines. 
 
 Up to the introduction of the Curtis turbines no one seems to 
 have thought of arranging the shaft to run vertically, influenced, 
 perhaps, by the accustomed position of the reciprocating engines. 
 The builders of this turbine adopted this position and still 
 adhere to it for their large units. Its use is limited to self con- 
 tained generating sets. The following reasons are advanced in 
 its favor. 
 
 1. Accurate control of the relative position of its parts by 
 means of the adjustable step bearing. (Fig. 52.) 
 
 2. Symmetry of design. 
 
 3. All bearings relieved from side strain and lateral wear. 
 
 4. Friction practically eliminated. 
 
 5. A short shaft, free from deflection. 
 
 6. Small floor space. 
 
 7. Small foundations. 
 
 The arrangement, shown in Fig. 54, unquestionably has advan- 
 tages. That it reduces friction to a minimum is shown by the fact 
 that unless a brake is applied a 5,000-K. W. unit will run for four or 
 five hours after steam has been shut off. The elaborate step bear- 
 ing necessitated, with its system of high pressure, forced lubrica- 
 tion is one of the chief objections, and though little trouble seems 
 to have developed from this source, it is an object of constant 
 watching. The generator is located above the turbine, ex- 
 posed to the heat arising from it, and to steam leaking past 
 the glands. While the vertical position offers convenient access 
 for inspection and minor repairs, it is inconvenient in case of 
 overhauling. In the horizontal type the turbine and generator 
 may be overhauled independently, and work can be done simul- 
 taneously on both ends. In the vertical, the machine has to be 
 taken apart from the top down, and the discs stripped off one 
 by one. 
 
 88
 
 COMPARISON OF TYPES. 
 
 89 
 
 An interesting example of the vertical type was built in Berlin 
 by the Allgemeine Electricitats Gesellschaft or "A. E.G.," com- 
 bining the features of the Curtis turbine with those of the Reidler- 
 Stumpf . A section of this turbine is shown in Fig. 58. The weight 
 of the moving parts was carried by a thrust bearing (B) between 
 the generator and turbine, and a jet condenser was located at 
 
 FIG. 58. Section of old A. E. G. turbine. 
 
 the lower end of the shaft. The steam exhausted into the 
 passage E, where it was condensed by water sprayed in from the 
 side. The condensed water drained into a centrifugal pump on 
 the end of the main turbine shaft. This arrangement is said to 
 have given a high vacuum, and proven very satisfactory. The 
 A. E.G. have, however, discontinued this vertical type and now
 
 90 
 
 STEAM TURBINES. 
 
 FIG. 59. 100 H. P. Terry steam turbine, opened.
 
 COMPARISON OF TYPES. 
 
 91 
 
 build for their larger sizes a horizontal machine illustrated in Art. 
 20. This has a Curtis single-pressure, multi-velocity stage wheel 
 and a low pressure end with a number of pressure stages, each 
 having a single velocity stage. A section of this turbine is shown 
 in Fig. 66. 
 
 Problems. 
 
 i. Report of paper, Emmet, "Steam Turbine in Modern Engineering," 
 Trans. A. S. M. E., vol. xxv., p. 1041. 
 
 References. 
 
 STODOLA : ' ' The Steam Turbine. ' ' 
 THOMAS: " Steam Turbines." 
 JUDE : " Theory of the Steam Turbine." 
 FRENCH: " Steam Turbines." 
 
 EMMET: Paper, "Steam Turbine in Modern Engineering," Trans. A. S. 
 M. E., vol. xxv. 
 
 Art. 19. Tangential Flow Turbines. 
 
 The Reidler turbine is one of the few turbines which use tan- 
 gential jets. The buckets for tangential wheels may have two 
 forms, those which curve in one plane only, as the Reidler 
 
 FIG. 60. Bucket arrangement, Terry turbine. 
 
 and Terry turbines, with the jet divided or not, or they may 
 be of the Pelton type, which curve in all directions. Prof. 
 Rateau and Zoelly both experimented extensively with the 
 divided bucket, but have abandoned it in favor of multicellular 
 machines with axial flow. In the Reidler-Stumpf machines,
 
 STEAM TURBINES. 
 
 however, it has been developed with success, and these have 
 used it in units of 2,000 K. W. and over, having four or more 
 stages. 
 
 The Terry turbine, Fig. 59, is manufactured in this country. In 
 this, undivided tangential jets are used. The steam is expanded 
 in one or more nozzles to exhaust pressure and enters at A, 
 Fig. 60, is deflected to one side, and compounded on a single wheel 
 by looping back into buckets B, in the casing, and returned from 
 these into succeeding buckets in the single row on the wheel. 
 
 FIG. 61. Nozzle arrangement of Reidler-Stumpf Turbine. 
 
 This reversal is accomplished four or five times, a portion of the 
 steam escaping at each loop, through the exhaust openings, C. 
 Some of the dimensions of one of these turbines are: 
 
 Diameter of wheel 
 Number of buckets 
 Width of buckets 
 Pitch of buckets 
 R. P. M. 
 Peripheral velocity 
 
 = 2 feet. 
 
 = 70. 
 
 =2 1/2 inches. 
 
 = 1 inch. 
 
 = 2600. 
 
 = 270 feet per second. 
 
 It developed 30 H. P. with 145 pounds steam pressure on 32 
 pounds steam per H. P. hour. Remarkable economy is not 
 claimed for this type but it gives a compact and simple turbine
 
 COMPARISON OF TYPES. 
 
 93 
 
 with low cost and running at moderate speeds. In the Reidler 
 turbines the return loops are made in separate sets of buckets, 
 as shown in Fig. 61. 
 
 FIG. 62. Section of Kerr turbine. 
 
 The Kerr turbine, developed by Mr. C. V. Kerr, uses buckets 
 of the Pelton divided-flow type, mounted on discs. It is of 
 the multicellular type shown in Fig. 30. The buckets are drop 
 forgings, finished on the inside. The stages are repeating 
 
 FIG. 63. Rotor of Kerr steam turbine. 
 
 sections with the nozzles increasing in number, as rendered 
 necessary by the expansion of the steam. The design shows 
 careful consideration of the manufacturing problems involved, 
 and adaptability for commercial production. The speed of
 
 94 STEAM TURBINES. 
 
 the Terry and Kerr turbines is from 1200 to 3,000 R. P. M., 
 and they are used direct connected for blowers, pumps, and 
 generators, also for belt driving. The governors are of the 
 throttling type, closely resembling the De Laval. 
 
 Problems. 
 
 1. Report on the Terry turbine, see Power, Nov. 1907, p. 801, and 
 paper of Orrok, A. S. M. E., vol. xxxi, p. 263. 
 
 2. Report on the Kerr turbine as described in paper of G. A. Orrok, 
 Trans. A. S. M. E., vol. xxxi, p. 263, also Am. Machinist, Mar. 21, 
 1907, p. 415. 
 
 3. Report on Sturtevant steam turbine, see paper of G. A. Orrok, 
 A. S. M. E., vol. xxxi, p. 263. 
 
 4. Report on the Dake steam turbine. See Power, December, 1907, 
 p. 886, and paper of Orrok, A. S. M. E., vol. xxxi, p. 263. 
 
 5. Report on the Bliss turbine as described in paper of G. A. Orrok, 
 A. S. M. E., vol. xxxi, p. 263, and Power, August 10, 1909, p. 250. 
 
 6. Report on the Richards turbine described in the American Machin- 
 ist, November 16, 1905, p. 660. 
 
 References. 
 
 STODOLA: "The Steam Turbine." 
 JUDE : " Theory of the Steam Turbine." 
 See also references in the following problems. 
 
 Art. 20. Multicellular Turbines. 
 
 As mentioned before, Prof. Rateau's investigations led him 
 into a multicellular type of machine having many pressure stages, 
 each with a single velocity stage, which has been brought to a 
 high degree of perfection in France and is one of the best known 
 of the European turbines. It is also one of the few turbines 
 which have been applied to Marine Service. Fig. 64 shows a 
 section of a L. P. Rateau turbine as manufactured in the U. S. 
 The H. P. machines are practically the same except for the num- 
 ber of stages. 
 
 The pressure and velocity changes are those shown in Fig. 30. 
 The running joints are on the shaft, where for a given clearance 
 there is a minimum of leakage. So many rotating discs would 
 appear to offer large steam friction loss, but tests of turbines up to 
 1,000 and 2,000 H. P. show a friction of only from 2 to 4%, or
 
 COMPARISON OF TYPES. 
 
 95 
 
 about the same as drum turbines of the Parsons type. The 
 expansion nozzles are inserted in openings in the fixed diaphragms. 
 In the high-pressure stages they occupy but a small portion of 
 the circumference, but extend farther around as the pressure 
 falls and the volume increases. The nozzles or vanes in each 
 successive diaphragm are set around in angular advance of the 
 preceding one, corresponding to the trajectory of the steam, 
 so that the steam as it leaves the moving blades is opposite the 
 openings of the next expansion set. An advantage in this 
 type is that the clearance around the blades may be very large, 
 
 FIG. 64. Section of Rateau low-pressure turbine. 
 
 running from 1/16 to 1/4 of an inch; in fact the builders do not 
 trouble about giving it any precise value. The only small clear- 
 ances are at the hubs, where friction is less to be feared. The 
 diaphragm bushings are of soft material with little attempt at 
 clearances, for the machine when started wears a sufficient play 
 to turn without touching. 
 
 The Zoelly turbine has been mentioned as having originally 
 had tangential flow instead of axial flow. The old form had a 
 wheel with long spokes milled on their faces for two grooves, which 
 gave them a Pelton form where the jet impinged upon them.
 
 96 
 
 STEAM TURBINES.
 
 COMPARISON OF TYPES. 
 
 97 
 
 With the change to side admission the long spokes were aban- 
 doned, and as now built the Zoelly is a multicellular turbine 
 differing from the Rateau only in its construction and details. 
 It has been very successful and is widely known in Europe. 
 
 FIG. 66. Section of A. E. G. horizontal turbine. 
 
 As stated in Art. 18, the Algemeine Electricitats Gesellschaft 
 are building a turbine combining a Curtis single-pressure, multi- 
 velocity stage wheel, in which the steam is expanded to about
 
 98 STEAM TURBINES. 
 
 atmospheric pressure, and a multicellular low-pressure end, 
 making a Curtis-Rateau machine analogous to the Curtis-Parsons 
 described in Art. 14. The Bergmann turbine is also of this type. 
 Both are being built in large sizes. 
 
 Problems. 
 
 1. Report on the A. E. G. turbine described in Lond. Engineering, 
 May 20, 1910, p. 639. Also Power, Feb. 7, 1911. 
 
 2. Report on the Rateau turbine as described and illustrated in Lond. 
 Engineering, May 15, 1908, p. 639. 
 
 3. Report on the Zoelly turbine as described and illustrated in Lond. 
 Engineering, July 3, 1908, p. 1. 
 
 4. Report on multicellular turbine described in U. S. Patent issued to 
 J. F. M. Patitz, October 4, 1910. No. 971,555. 
 
 References. 
 
 STODOLA: "The Steam Turbine" (4th ed.). 
 
 RATEAU: Paper, "Different Applications of SteamTurbines," Trans. 
 
 A. S. M. E., vol. xxv. 
 JUDE: "Theory of the Steam Turbine." 
 REY: Paper, "Rateau Steam Turbine and its Applications," Journal 
 
 Am. Soc. Naval Eng., Nov., 1905. 
 See also references in the problems. 
 
 Art. 21. Special Forms of Impulse -reaction Turbine. 
 
 The Allis-Chalmers turbine shown in Fig. 67 is a single-flow 
 machine of the Parsons type differing from the Westinghouse 
 only in the method of balancing, blading, and in various details. 
 
 In the typical single-flow Parsons turbine the end thrust is 
 carried by the pistons P t , P 2 , and P 3 shown in Fig. 55. In the 
 large sizes the large low-pressure piston, P 3 , distorts under pres- 
 sure and repeated heating and cooling, so that it has been 
 necessary to give them clearances which permit leakage of steam. 
 In the Allis turbine this large balancing piston is replaced by a 
 smaller one, a, at the low-pressure end of the rotor where it is 
 practically free from distortion, and nearly the whole area is 
 effective. In the later forms of Westinghouse machines the 
 balancing is accomplished by the double flow, as already described. 
 In the blading, the ends are riveted to a channel-shaped shroud 
 ring, B, Fig. 68, stiffening them against vibration. The openings
 
 COMPARISON OF TYPES. 
 
 99
 
 100 
 
 STEAM TURBINES. 
 
 for the blade tips are stamped in the ring, accurately spacing 
 the blades. The shape of the ring forms a natural baffle, 
 and the clearance may be smaller than in previous practice. 
 Only the thin edges of the channel can touch the casing, and if 
 they do, they wear free without any material heating. The 
 
 FIG. 68. BJading of Allis-Chalmera turbine. 
 
 shroud ring itself is not new, as both the Rateau and Zoelly 
 have used them, but the gain from its use is greater in reaction 
 turbines than in these types. 
 
 Problems. 
 
 1. Look up and report on the early history of steam turbines, see 
 Neilson, French or Gentsch. 
 
 2. Look up the Elektra turbine described in Power, April 6, 1909, p. 
 635. Compare with the new type of small Westinghouse turbine. 
 
 3. Report on the Wilkinson turbine and small type of Westinghouse 
 turbine. 
 
 4. Report on the Eyermann turbine, a turbine having combine radial 
 and axial flow. See Power, November 24, 1908, p. 855.
 
 COMPARISON OF TYPES. 
 
 101 
 
 References. 
 
 STODOLA: "The Steam Turbine" (4th ed. illustrates and describes 
 
 all the turbines of any prominence). 
 JUDE: "Theory of the Steam Turbine." 
 
 GENTZCH: "Steam Turbines." Translated by A. R. Liddell. 
 SOZNOWZKI: "Turbines a Vapeur," Paris, 1897. 
 (The last two are valuable for the history of steam turbines.) 
 See also references in the problems. 
 
 Art. 22. Low-pressure Turbines and Regenerators. 
 
 Reference to the pressure-temperature curve, Fig. 69, or to 
 the heat chart, shows that the heat drop on which the available 
 energy depends is greatest at the low pressures. A reciprocating 
 
 Absolute Pressures 
 70 80 90 100 110 120 130 MO 160 180 170 ISO 
 
 FIG. 69. Pressure-temperature curve. 
 
 engine is most efficient at the higher pressures, down to about 
 that of the atmosphere. The turbine is most effective in utilizing 
 the lower vacuums, as excessive expansion in an engine entails
 
 102 STEAM TURBINES. 
 
 prohibitive sizes of L. P. cylinders, and, with the wide range of 
 power available below atmospheric pressure, it can be coupled 
 with a reciprocating engine to great advantage. In fact, the 
 economy of such a combined unit where the engine exhausts into 
 a low-pressure turbine, is higher than when the entire pres- 
 sure range from boiler to condenser is utilized in an engine or a 
 turbine alone, and the installation of combined units of this kind 
 is coming more and more into use. For marine service there is a 
 further advantage of superior maneuvering power and economy 
 at slow speeds over turbines alone, and the new White Star 
 steamers Oceanic and Titanic are being equipped with engines 
 and exhaust turbines. For power station work the total economy 
 of a combined unit of new engines and new turbines, taking 
 into account all running expenses, fixed charges, etc., is not so 
 high as for a H. P. turbine plant alone. It furnishes, however, a 
 valuable means of utilizing existing reciprocating plants and 
 bringing them up to the highest efficiency. Where a good engine 
 plant already exists its capacity may be increased more econom- 
 ically by the addition of exhaust turbines than by replacing the 
 engines with H. P. turbines. 
 
 The conditions of operation for exhaust turbines fall under two 
 classes: 
 
 First, where the steam supply is substantially constant or 
 varies with the turbine load. 
 
 Second, where it is widely fluctuating or intermittent and is 
 independent of the turbine load. 
 
 In the first class fall marine engines and those for power station 
 service. A conspicuous example of the successful installation of 
 exhaust turbines for the latter service is found in the Fifty-ninth 
 Street Station of the Interborough Rapid Transit Co., N. Y. 
 City. 
 
 This station was equipped with 7500-K. W. compound Corliss 
 condensing engines direct connected to generators, each unit 
 having two 42-inch H. P. and two 86-inch L. P. cylinders, all of 
 GO-inch stroke, and an average steam rate of 17 to 18 pounds 
 per K. W. hour. After consideration of various means of pro- 
 viding additional power, exhaust turbines were installed on 
 three units to determine their desirability for the remaining sets. 
 They were 3-stage vertical Curtis turbines, of 7500 K. W. maxi- 
 mum rating, each having 6 fixed nozzles, and 6 operated by hand
 
 COMPARISON OF TYPES. 103 
 
 so as to control the division of load between the engine and its 
 exhaust turbine. An overspeed governor operating a 40-inch 
 butterfly valve on the steam line connecting the separator and 
 the turbine, and an 8-inch vacuum breaker on the condenser 
 were the only forms of governor used. 
 
 Mr. Stott summarizes the results of the tests as follows: 
 
 "a. An increase of 100% in maximum capacity of plant. 
 
 "b. An increase of 146% in economic capacity of plant. 
 
 "c. A saving of approximately 85% of the condensed steam 
 for return to the boilers. 
 
 "d. An average improvement in economy of 13% over the 
 best H. P. turbine results. 
 
 "e. An average improvement in economy of 25% (between 
 limits of 7500 K. W. and 15000 K. W.) over the results obtained 
 by the engine units alone. 
 
 "f. An average unit thermal efficiency between the limits of 
 6500 K. W. and 15500 K. W. of 20.6%." 
 
 The steam rate of the engines alone was from 17 to 18 pounds 
 per K. W. hour, of the exhaust turbines, 26 1/2 to 28 pounds, 
 and of the combined unit ,13 to 14 pounds. 
 
 In an installation of this character where the load on the 
 turbine is electrically connected with that of the engine, the 
 turbine load rises and falls with the steam supply and no governor 
 is required. When running at very light loads, where a turbine 
 is inefficient, it is found economical to cut it out, and run the 
 engine alone, condensing. Where the supply of steam from the 
 engine is liable to long-continued interruptions, live steam can 
 be admitted through a reducing valve from an independent 
 source, the exhaust turbine thus drawing its supply from two 
 sources. 
 
 The second class of installations, where there is intermittent 
 steam supply, comprises rolling mills, forging plants, mine hoists, 
 and other non-condensing engines. Such engines use great 
 quantities of steam under widely varying loads, often with little 
 or no expansion. Prof. Rateau has given much attention to the 
 application of low-pressure turbines to such exhausts, and to 
 equalize the supply from these constantly varying sources he has 
 developed the steam regenerator or heat accumulator, shown in 
 Figs. 70 and 71. The engine exhaust at about atmospheric 
 pressure is condensed in the regenerator when it arrives in large
 
 104 
 
 STEAM TURBINES. 
 
 quantities, and revaporized when the excess ceases. The con- 
 densation and re-evaporation of the steam follow the fluctuations 
 of pressure as the supply exceeds or falls short of that required 
 by the turbine. 
 
 \Perforations In Mixing Tube for 
 distributing Steam into the Water 
 
 FIG. 70. Side view of Rateau regenerator. 
 
 The regenerator takes a form like a tubeless horizontal 
 boiler (Fig. 70) where the water is kept in forced circulation 
 by the injection of steam. It is necessary to provide a relief 
 valve to carry off any surplus steam, an automatic expansion 
 valve, as in the previous case, to supply steam directly to 
 
 Extension of Mixing Tubes 
 above Water Level Leadiug 
 steam in Regeuera 
 Manifold 
 
 Water Level 
 Baffle Plate 
 
 Perforations in 
 Narrowed Portion 
 of Mixing Tube 
 for Distribution 
 of Steam in the 
 Water. 
 
 FIG. 71. Cross-section of Rateau regenerator. 
 
 the turbine should the main engine be shut down for any 
 length of time, and check valves to protect the regenerator and 
 main engine when the turbine is running direct. 
 The steam flow from the regenerator to the turbine is constant
 
 COMPARISON OF TYPES. 105 
 
 compared to that from the engine to the regenerator and is, of 
 course, substantially equal to the average rate of engine exhaust. 
 Let T be the maximum time, in minutes, of stoppage of the 
 engine, during which the regenerator must supply the turbines 
 alone. Let R be the total steam consumption of the turbine in 
 pounds per minute, L the mean latent heat at the regenerator 
 pressures (usually to 4 pounds gauge), t the allowed temper- 
 ature drop of the water. Then 
 
 (30) 
 
 is the weight of water required to run the turbine T minutes 
 with an allowed fall in temperature, and consequently pressure. 
 This difference in pressure is not over 3 pounds, at the outside. 
 The capacity to absorb the engine exhaust, however, deter- 
 mines the amount of water required, rather than the question 
 of the turbine supply. A regenerator may be called on to 
 absorb fluxes of steam five times as great as the more uniform 
 flow to the turbine and they may be thrown on it almost instantly 
 and must be cared for. If S be the maximum pounds of steam 
 the regenerator will be called on to absorb, L the mean latent 
 heat of the engine exhaust, and 12.4 B. T. U. the difference in 
 temperature between and 4 pounds gauge pressure, then the 
 water required is 
 
 ' (3D 
 
 . . 
 
 which will usually be found greatly in excess of the w above. 
 
 Proper values of T, S, and the mean engine exhaust are 
 determined only by careful investigation for each installation. 
 The form of regenerator shown in Fig. 71 has shown the greatest 
 capacity for absorbing the steam. Two regenerators of an older 
 type installed at the Bruay Mines in France to utilize the exhaust 
 of a hoisting engine and drive a 300 H. P. Rateau generator set 
 have been in successful service since 1902. With supply pressures 
 ranging from 12 to 14.5 pounds absolute, and condenser pressures 
 from 2 . 13 to 2 . 62 pounds absolute, the plant showed a steam con- 
 sumption of from 37 . 4 to 45 . 2 pounds per E. H. P. hour. A great 
 number of regenerators and L. P. turbines are now in successful
 
 106 STEAM TURBINES. 
 
 use in Europe and in this country, some of them exceeding 
 3000 H. P. of turbine capacity. 
 
 Where there are long periods, as for instance over night, when 
 the exhaust steam supply is not available, a high-pressure turbine 
 has been coupled with the low-pressure one, the low-pressure tur- 
 bine being so proportioned that it can carry the entire load, but 
 if its steam supply fails regulating valves controlled by the speed 
 and the pressure in the regenerator, cut in the high-pressure 
 turbine, and kept up the output. The load may be carried 
 
 FIG. 72. Rateau mixed-flow turbine. 
 
 entirely by either turbine, or distributed between them, as the 
 momentary conditions require. Any exhaust steam used in the 
 H. P. turbine passes through the L. P. one, and the group is thus 
 working at the best' economy possible. Running entirely on the 
 H. P. machine, with steam at 110 pounds gauge pressure, one of 
 the combined units has been found to give an economy of about 
 18 pounds of steam per E. H. P. hour, and running entirely on 
 the L. P., with steam at atmospheric pressure, it gave about 36. 
 The two turbines are now combined in one to form a "mixed- 
 flow" turbine as shown in Fig. 72, a much more compact 
 arrangement.
 
 COMPARISON OF TYPES. 107 
 
 Problems. 
 
 1. Report on the article on compounding piston engines with turbines, 
 by Prof. Rateau, Power, October, 1907, p. 693. 
 
 2. Report on paper on Exhaust Turbines and Regenerators, by R. F. 
 Halliwell, given in Lond. Engineering, February 5, 1909, p. 197. 
 
 3. Report on low pressure steam turbine as referred to in article by 
 R. M. Neilson, Power, July 6, 1909, p. 1. 
 
 4. Report on article by C. H. Smoot, on Regenerators. Power, 
 November 8, 1910., p. 1979. 
 
 5. Report on article, L. P. Turbines, by C. H. Smoot, Power, June 22, 
 1909, p. 1100. 
 
 6. Report on investigation into L. P. turbines for the Cambridge 
 Elect. Light Co. by Prof. Hollis, see Power, November 10, 1908, 
 p. 787. 
 
 7. Report on the Brush-Parsons double-flow exhaust turbine, de- 
 scribed in Lond. Engineering, July 1, 1910, p. 2. 
 
 8. Report on English and German experience with L. P. turbines as 
 described by Gradenwitz in Engineering Magazine, vol. xxxiv, p. 278. 
 
 9. Report on the test of engines and exhaust turbines at 59th street 
 Interborough Station, see paper by Stott and Pigott, Trans. 
 A. S. M. E., March, 1910, see also Power, December 14, 1909, p. 985. 
 
 References. 
 
 STODOLA: " The Steam Turbine." 
 
 MOYER: "Steam Turbines." 
 
 RATEAU: Paper, "Different Applications of Steam Turbines," Trans. 
 
 A. S. M. E., vol. xxv. 
 
 RATEAU: Article, Power, Oct., 1907, p. 693. 
 
 BUELEIGH: Paper on Exhaust Turbines, Power, Oct., 17, 1908, p. 828. 
 HALLIWELL: Paper on Exhaust Turbines, London Engineering, Feb. 5, 
 
 1909. 
 STOTT AND PIGOTT: Paper, "Test of a L. P. Turbine," Trans. A. S. 
 
 M. E., 1910. See also Power, Dec. 14, 1909, p. 985. 
 SMOOT: Articles, Power, June 22, 1909, p. 1100, and Nov. 8, 1910, 
 
 p. 1979. 
 See also references in the problems.
 
 CHAPTER VI. 
 
 CONDITIONS OF OPERATION. 
 Art. 23. Effect of Superheat. 
 
 As with reciprocating engines, there is a gain in the economy 
 of turbines by the use of superheated steam, but how much is 
 gained can not be fully determined until the specific heat of 
 superheated steam is definitely known. 
 
 While this has been the subject of repeated and extensive 
 experiments from the time of Regnault to the present, the proper 
 values have not been agreed upon. Grindley in England; 
 Greissman, Lorenz and Knoblauch, Linde and Klebe in Germany, 
 and Carpenter and Jones in America, have all done important 
 work in this direction, but the results are contradictory and 
 have not definitely settled how the specific heat varies with the 
 pressure and temperature changes. Modern experiments show 
 that the value .4805 of Regnault is too low. Apparently the 
 specific heat increases with increase of pressure, but decreases 
 with increase of superheat. This conclusion is indicated by 
 Lorenz, and is sustained by Knoblauch, Linde, and Klebe. 
 Mr. Emmett has deduced from a series of experiments made in 
 a Curtis turbine at a pressure of 155 pounds that it varies 
 from about . 53 to .77 for temperatures of 360 to 620 Fahr. 
 The usual practice is to take it as constant and at from . 6 to . 65. 
 The bearing of the specific heat on the theoretical economy of 
 the turbine using superheated steam is well shown by calcula- 
 tions made on a De Laval turbine. By taking first the water 
 rate consumption as a basis for calculating, the gain was found 
 to be 8. 1 per cent. Then on the basis of the heat units in the 
 steam the gain was found to be, for 
 
 Specific Heat 
 
 Gain 
 
 .48 
 
 4.8% 
 
 .6 
 
 4 % 
 
 S 
 
 2.7% 
 
 108
 
 CONDITIONS OP OPERATION. 
 
 109 
 
 In the diagram following are given the average of a number 
 of steam consumptions for various degrees of superheat, up to 
 200. These are based on tests of Parsons, Curtis, Zoelly, and 
 Brown- Boveri turbines, and of such high grade engines as had 
 records of tests under same conditions. The lines for the turbines 
 are more reliable than for the engines, being based on a larger 
 
 I 19 
 
 3 
 
 60 80 loo' iao 
 
 Degrees of Superheat 
 FIG. 73. Effect of superheat. 
 
 180' SCO 1 
 
 number of tests. According to these curves the gain in economy 
 is greater for engines than for turbines. The curves for the 
 turbines would confirm the statement made by Mr. Parsons and 
 by Messrs. Dean and Main that the gain in economy is about 
 1% for every 10 "of superheat, up to about 150 or 180 Fahr. 
 The gain from superheat in turbine practice comes chiefly from 
 the reduced steam friction in the blades and passages. Refer- 
 ence to Fig. 40 shows that there may be 10% or 15% of water 
 in the steam in the later stages. Superheating reduces the con-
 
 110 STEAM TURBINES. 
 
 densation and by lessening the water going through the blades, 
 materially decreases the steam friction. It is claimed that a 
 turbine can operate under much higher superheat than an 
 engine. Doubtless this is true, but it remains to be shown that 
 there is any advantage in the high superheats the turbine may 
 be made to stand. The best practice indicates that a moderate 
 superheat, of 50 to 100 is of advantage. Beyond this the 
 results are not wholly favorable, for while the steam rate can be 
 lowered it is done at the expense of extra fuel required for the 
 high superheats. 
 
 References. 
 
 STODOLA: "The Steam Turbine." 
 
 JUDE: '' Theory of the Steam Turbine." 
 
 MOYER: "Steam Turbines." 
 
 FRENCH: " Steam Turbines." 
 
 MARKS AND DAVIS: "Steam Tables and Diagrams." 
 
 Trans, of A. S. M. E., 1905 to 1910. 
 
 Art. 24. Relative Effects of High Vacuums in Reciprocating 
 Engines and Turbines. 
 
 The turbine gains relatively more than the steam engine as the 
 vacuum is pushed toward its limit. In fact, this is one of the chief 
 elements in its success in competition with the older form. The 
 advantage in economy, under equal conditions, is usually in 
 favor of the steam engine for vacuums lower than 26 inches or 
 2 pounds absolute. For higher vacuums the turbine gains rap- 
 idly. General practice has set the economical vacuum for recip- 
 rocating engines at 26 inches to 27 inches. Most of the turbine 
 practice at the present time is based on 28 inches to 28 1/2 inches 
 of vacuum. 
 
 The reasons why the turbine shows this greater benefit for the 
 higher vacuums are: 
 
 First. The low temperatures of the exhaust pressure 
 can not reach back into the hotter parts of the machine, as 
 in a L. P. engine cylinder, which is alternately exposed to wide 
 differences of temperature. 
 
 Second. If expansion is carried too far in the steam engine, 
 the L. P. cylinder valves and passages become abnormally large, 
 absorb power, and neutralize any thermodynamic gains. A
 
 CONDITIONS OF OPERATION. Ill 
 
 compound engine with a cylinder ratio of 4 to 1, using steam at 
 150 pounds, might expand say 15 times. A turbine presents no 
 difficulties to an expansion ratio of 100 to 110 or down to a 
 pressure of 1 pound absolute. To carry this expansion in a 
 compound engine calls for a cylinder ratio of 33 to 1, which is 
 obviously prohibitive. 
 
 Since the expansion of the engine is limited to the L. P. termi- 
 nal, c, Fig. 74, the only gain in a higher vacuum is the lowering 
 of the back pressure, represented by the area e, d, f, g. 
 
 FIG. 74. Pressure-volume curve for engines and turbines. 
 
 Since expansion can be carried down within a turbine to the 
 lowest condenser pressures, the turbines can utilize the large 
 triangular expansion area to h, in addition to all that the engine 
 gains. 
 
 Theoretically the gain increases very rapidly for the rarer 
 vacuums, but with the turbine, as with the engine, there is a 
 practical limit, though not reached so soon, beyond which the 
 cost, maintenance, and power required for the condensing 
 apparatus offset the theoretical gains. As already stated, the 
 limit is 28 to 28 1/2 inches, but its value for any given set of condi- 
 tions is a question of engineering economics. Into it enter the 
 following: 
 
 1. The steam consumption of 
 
 (a) turbine, 
 
 (b) auxiliaries. 
 
 2. The use-factor, or the ratio of the actual output to the 
 rated output. 
 
 3. The cost of the coal, as fired. 
 
 4. Cost of injection water.
 
 112 
 
 STEAM TURBINES. 
 
 5. Fixed charges, on the condensing plant, covering 
 
 (a) Interest on cost. 
 
 (b) Interest on cost of masonry, space occupied, etc. 
 
 (c) Depreciation and repairs. 
 
 (d) Insurance, taxes, etc. 
 
 The method of determining the economical back pressure may 
 be illustrated by an assumed case. Let 
 
 Capacity of turbine = 1,500 K. W. 
 
 Use-factor (2) =15%. 
 
 Cost of coal (3) = $3 . 50 per ton, fired. 
 
 Suppose fixed charges (5) = 10%. 
 
 Average boiler evaporation = 7 pounds per pound of coal. 
 
 p 
 o 
 
 Lss 
 
 x 
 I 
 
 X 
 
 
 
 83 
 
 53 
 
 Vacanma 
 
 FIG. 75. -Approx. relation of water rate and vacuum. 
 
 Let the cost of condensing apparatus, based on injection 
 water of 70 Fahr., obtained from estimates of builders for several 
 different back pressures, be as follows: The plant for 28 1/2 
 inches and 29 inches would be the same as for 28 inches, except 
 for an increase in the size of the dry vacuum pump. These 
 vacuums are obtainable only with injection water of 60 Fahr. 
 for 28 1/2 inches, and 45-50 for 29 inches.
 
 CONDITIONS OF OPERATION. 
 
 113 
 
 Inches of 
 Vacuum 
 
 Cost of 
 Condensing 
 Plant 
 
 Increase 
 in Cost 
 
 Increase in 
 Annual Charge 
 Based on 10% 
 
 26 
 
 $6000. 
 
 
 
 26* 
 
 6900. 
 
 $900. 
 
 $90. 
 
 27 
 
 7500. 
 
 600. 
 
 60. 
 
 27* 
 
 8000. 
 
 500. 
 
 50. 
 
 28 
 
 9500. 
 
 1500. 
 
 150. 
 
 28* 
 
 10000. 
 
 500. 
 
 50. 
 
 Let the guaranteed steam consumption of the turbine be 21 
 pounds per K. W. hour, at 28 inches vacuum. The steam rates 
 for varying vacuums may be interpolated from Fig. 75, which is 
 based on some Westinghouse tests. The steam consumption of 
 the auxiliaries may be based on their estimated H. P., and a 
 steam consumption of 1 1/2 times that of the turbine. 
 
 The total steam consumption then would be 
 
 - 
 
 Steam Consumption 
 
 Vacuum 
 
 
 Inches 
 
 
 
 
 
 Turbine 
 
 Auxiliaries 
 
 Total 
 
 1 
 
 2 
 
 3 
 
 4 
 
 26 
 
 23.4 
 
 3.4 % 
 
 24.2 
 
 26* 
 
 22.8 
 
 4. % 
 
 23.7 
 
 27 
 
 22.2 
 
 5.25% 
 
 23.3 
 
 27* 
 
 21.6 
 
 6.9 % 
 
 23.1 
 
 28 
 
 20.9 
 
 9. % 
 
 22.8 
 
 28* 
 
 20.2 
 
 12. % 
 
 22.6 
 
 The yearly running cost = X const. Where 
 E 
 
 A =K. W. capacity of the unit. 
 
 5 = Total consumption (Coll. 4 last table). 
 
 (7 = Power factor. 
 
 D Cost of coal, fired. 
 
 E = Average boiler evaporation per pound.
 
 114 
 
 STEAM TURBINES. 
 
 hours per year 8760 
 Constant = = -=3.92. 
 
 pounds per ton 2240 
 
 Calculating the yearly cost with the various consumptions, 
 and tabulating, we have : 
 
 Inches of 
 Vacuum 
 
 Cost of Steam 
 per Year 
 
 Saving 
 
 26 
 
 440X24.2 =$10648 
 
 
 26J 
 
 440X23.7 = 10428 
 
 $220. 
 
 27 
 
 440X23.3 = 10252 
 
 176. 
 
 27J 
 
 440X23.1 = 10164 
 
 88. 
 
 28 
 
 440X22.8 = 10032 
 
 132. 
 
 28J 
 
 440X22.6 = 9944 
 
 188. 
 
 Comparing these savings per year with the increase in the annual 
 charge as the vacuum varies, we see that the gain changes to a 
 loss at just under 28 inches. We see, too, that if an ample supply 
 of cold injection water is available, it would pay to carry 28 1/2 
 
 Fia.J76. Parsons Augmentor. 
 
 inches where the temperatures will permit. This method would 
 call for a vacuum somewhat too low, if anything, for the steam 
 used in the auxiliaries is not all lost, as a large part of the heat 
 in it is regained in heating the feed water.
 
 CONDITIONS OF OPERATION. 115 
 
 Higher vacuums than 28 inches are carried in high-class power 
 
 tations. Some condenser plants have even been installed under 
 
 a guarantee to maintain a working vacuum within 3/4 inch 
 
 of the barometer. Whether such a high vacuum is profitable 
 
 remains to be shown by experience. 
 
 Mr. Parsons has invented a device, Fig. 76, which has been 
 widely used in Europe, but for some reason has been little used in 
 this country. He places the air pump, proportioned for about 26 
 inches vacuum, below the main condenser, and connects this by 
 an inverted siphon, forming an air seal. Between the air pump and 
 condenser, as a by-pass connection, is a steam ejector connection, 
 A, delivering through a small surface condenser B, about 1/20 
 the size of the main one, into the air pump suction beyond the 
 siphon. This ejector draws nearly all the residual air and 
 vapor from the main condenser and increases the vacuum to 
 27 1/2 inches or 28 inches, without the increase in size of main 
 condenser and air pump demanded by the ordinary arrangement. 
 Mr. Parsons states that the live steam required by the ejector is 
 about 1 1/2% of that used by the main turbine at full load, and 
 is materially less than that required to drive the larger air pump, 
 which would regularly be provided for the higher vacuum. 
 
 Problems. 
 
 i. Report on paper of G. I. Rockwood on "Condensers for Steam 
 Turbines," Trans. A. S. M. E., vol. xxvi, p. 383. 
 
 References. 
 
 STODOLA: " The Steam Turbine." 
 JUDE: "Theory of the Steam Turbine." 
 
 ROCKWOOD: Paper, "Condensers for Steam Turbines." Trans. A. S. 
 M. E., vol. xxvi. p. 383.
 
 CHAPTER VII. 
 
 POSITION AND FIELD OF THE STEAM TURBINE. 
 Art. 25. Relative Economy of Engines and Turbines. 
 
 The heat equivalent of a H. P. hour is 
 33000 + 60 
 
 If H t and H 2 are the total heats per pound of steam before and 
 after adiabatic expansion to the exhaust pressure, and W the 
 weight of steam per H. P. hour as tested, then 
 
 <*.-*.> e-~ 
 
 or the available heat drop X% utilized = B. T. U. utilized per 
 pound 
 
 2545 
 
 This "potential efficiency," P, which has been variously named 
 by different authorities, gives a comparison between the heat 
 actually utilized by the motor, and that available under its 
 operating conditions. It applies equally to reciprocating 
 engines, and to turbines, and can be used as a .basis of compari- 
 son, provided the water rate can be brought to the same basis. 
 The almost universal basis used in determining the economy of 
 the reciprocating engine is the steam rate per indicated H. P. 
 hour. No indicator has been devised for turbines, and it 
 would be difficult to show the internal power developed. 
 While some device might show the energy of the jet of steam 
 from the nozzle, it would be practically impossible to register 
 definitely the energy given up to the blades in a multi-stage 
 turbine, where there are losses from eddies, friction, etc. Engi- 
 116
 
 POSITION AND FIELD OF THE STEAM TURBINE. 117 
 
 neers, however, are so familiar with economies based on indicated 
 H. P. that comparisons are often made by reducing the 
 steam consumption of the turbine to the basis of the I. H. P. of 
 a reciprocating engine having the same electrical output or 
 brake H. P., as the case may be. Where it is possible there is a 
 growing practice of basing the steam rate on the K. W. hours 
 or electrical H. P., which requires no assumptions, especially as 
 the bulk of turbine work outside of the marine service is in 
 direct connected electrical units. 
 
 Comparisons based on I. H. P. must take into account the 
 efficiency of the generators, turbines, and engines. The efficiencies 
 of engine-driven generators for alternating currents on sizes 
 from 500 to 5,000 K. W. will range from 87 1/2% at 1/4 load up 
 to 96% at 1 1/4 load. For direct current generators, 100 K. W. 
 to 3,000 K. W., it will range from 89% at 1/4 load to 94% at 
 full load. The generator efficiency with the De Laval units is 
 somewhat lower, as the electrical work is divided between twin 
 generators. Their efficiency may be taken at from 88% at 1/2 
 load to 91% at full load, for direct current, and at 86% at 1/2 
 load to 92% at full load. 
 
 The following generator efficiencies are reported in various 
 tests. 
 
 
 Capacity 
 
 
 
 Load 
 
 
 
 
 K. W. 
 
 i 
 
 i 
 
 1 
 
 Full 
 
 H 
 
 Westinghouse 
 
 1 250 
 
 86 
 
 93 
 
 
 96 
 
 
 Westinghouse 
 Allis-Chalmers 
 Curtis 
 
 400 
 5,500 
 
 
 94.6 
 
 97 
 96 
 
 95.7 
 97.9 
 
 96.6 
 98.3 
 97 5 
 
 98.5 
 
 
 
 
 
 
 
 
 In comparing with engines a value of 95% may fairly be 
 assumed. The mechanical efficiency of reciprocating engines 
 has^been^exhaustively investigated, and the friction losses 
 appear to be nearly constant for all loads. The efficiency con- 
 sequently falls off rapidly for light loads. A summary of various 
 modern engines as given by French is as follows :
 
 118 STEAM TURBINES. 
 
 Mechanical Efficiency of Engines at or near Rating. 
 
 Engine 
 
 Efficiency, % 
 
 Engine 
 alone 
 
 Engine and 
 Generator 
 
 
 96.5to97.5 
 94.5 
 91 
 94 
 87 to 93 
 90 
 
 92 to 94 
 90 
 
 Large horizontal Corliss, compound 
 
 
 High speed, simple 
 Small and medium, hor. compound 
 
 
 The mechanical efficiency for turbines, as it involves the com- 
 parison of the brake H. P. with the indeterminate internal 
 power developed by the steam, can only be assumed. This 
 factor is taken from 90% to 95%. For large units the higher 
 figure is probably nearer correct. These values give a combined 
 efficiency of 85% to 93% for a turbine generating unit, which 
 may be used in reducing K. W. output to an I. H. P. basis, for 
 comparison with reciprocating plants. The following tables, 
 from a paper by Mr. C. V. Kerr before the A. S. M. E., 1 give 
 means of comparing reciprocating engines and turbines on the 
 basis of their potential efficiencies. 
 
 1 Trans. A. S. M. E., vol. xxv., 1904.
 
 POSITION AND FIELD OF THE STEAM TURBINE 119 
 
 o >o >o co .p . . . *^ 
 
 SCO <Nt^ 00--H O t> i-4 <0 
 
 t* t~ CO COlO CO^t-t* 
 
 II 
 
 O 50 rH rH 
 
 -H CO * O 
 
 CD -< -^ t* 
 
 CO CO 03 CO 
 
 w 
 
 O U5 * 
 
 5 ^ 00 CO t^ b- 
 
 UP 
 
 fc,' 00 O 00 OOOfflO^ 
 
 2 S 
 
 i I I ; 1 
 
 i jil: I 
 
 ; li s l! 
 
 : 
 .3 -a
 
 120 
 
 STEAM TURBINES. 
 
 ' "> S o a o a 
 
 **\ |J 14 
 
 5 
 
 If ri 
 
 ill 
 
 <! 8 
 
 o 
 
 -^ J2 
 
 g 8 
 
 itf:| 
 
 -, .a H 2L Jo da 
 
 lit 
 
 O CO O O b- <N 00 00 CM 
 
 O CM rH o 
 
 ^ r o w oo # <o 
 
 O5 lOOiOOOO CO XO 
 
 00 t-lCCIN'-fOO rt COO5 
 
 a" 8 b 
 
 3 05 3 
 
 111 
 
 M 
 
 1 8 
 
 OCOOOOO O Of O 
 
 IN CO CO 
 
 00 CM CM 00 CM 
 
 glC IN ^ 
 
 f f IO 
 
 ft! 
 
 a Is. 
 fl a N =s 
 
 I hi! 
 
 i i 
 
 5 S
 
 POSITION AND FIELD OF THE STEAM TURBINE. 121 
 
 5 ti 
 
 Z W 
 
 08 -a 
 
 la Ss &|a 5 
 
 l^llll 
 
 ii 
 
 Hj3 J 
 
 * > 
 
 Ol^t^OOCN) >O5 0000 
 
 j 
 
 t~ t~ 
 
 S 3 
 
 111 
 
 b <= 
 
 O CO O O O rH CO t-_ O 00 
 
 lOOMrHrH Tj<O rHt^- C^ 
 
 <NOrH(NTt< O^ P H t- 
 
 cococococo coco coco ^ 
 
 i 
 
 K 
 
 K) 
 
 rHOOtO>OrH t^ IN1O * 
 
 CO-*COrHr-J 10 f'lN ** 
 
 CO CO rH 
 
 IN 8&Sflo*Sfl8oSio 53 
 
 IN IN (NOINrHO (NrH Wrt O5O5 n 
 
 i.g's 
 a 8 
 > 11 
 
 II 
 
 s 
 
 
 
 
 I : I 
 
 > -a ; -s i'a I 
 
 IPPP1 
 
 I _;
 
 122 
 
 STEAM TURBINES. 
 
 Looking at the economy on a basis of steam per H. P. hour, 
 the following table gives the results obtained from some recipro- 
 cating engines of exceptionally high economy. 
 
 
 
 2 
 
 S" 
 
 
 
 fc 
 
 
 
 V 
 
 
 
 M 
 
 
 I ** 
 
 B ' S 
 
 
 Engine 
 
 1 
 
 , 
 
 1 
 S 
 
 S 
 
 j! 
 
 H 
 
 Authority 
 
 
 i 
 
 I o 
 
 1 
 
 Pk 
 
 ji 
 
 IB 
 
 
 
 W 
 
 
 
 tf 
 
 
 CO 
 
 
 Westinghouse Vertical 
 
 5400 
 
 185 
 
 27.3 
 
 76 
 
 
 11.93 
 
 Eng. Record 
 
 Brooklyn, N. Y. 
 
 
 
 
 
 
 
 May 28, 1904. 
 
 Rockwood-WTieelock 
 
 595 
 
 159 
 
 25.4 
 
 76.4 
 
 
 13. 
 
 F. W. Dean 
 
 Natick, R. I. 
 
 
 
 
 
 
 
 A. S. M. E., 1895. 
 
 Mclntosh and Seymour 
 
 1076 
 
 123 
 
 27.1 
 
 99.6 
 
 20 
 
 12.76 
 
 F. W. Dean 
 
 Webster, Mass. 
 
 
 
 
 
 
 
 A. S. M. E., 1898. 
 
 Rice and Sargent 
 
 627 
 
 151 
 
 28.6 
 
 121 
 
 
 12.1 
 
 D. W. Jacobus 
 
 Brooklyn, N. Y. 
 
 
 
 
 
 
 
 A. S. M. E., 1903. 
 
 Rice and Sargent 
 
 420 
 
 142 
 
 25.8 
 
 102 
 
 297 
 
 9.56 
 
 D. W. Jacobus 
 
 Phila., Pa. 
 
 
 
 
 
 
 
 A. S. M. E., 1904. 
 
 Horizontal Four- Valve 
 
 658 
 
 150.4 
 
 26.4 
 
 80 
 
 16.4 
 
 12.03 
 
 Barrus' Eng. Tests. 
 
 Leavitt Pumping Engine 
 
 575 
 
 175.7 
 
 27.25 50.6 
 
 
 11.2 
 
 E. F. Miller 
 
 Chestnut Hill, Mass. 
 
 
 
 1 
 
 
 
 Tech. Quart'ly, vol. ix. 
 
 The following is a table of tests of 23 engines in commercial 
 operation, and may be taken as indicating average results. 
 
 Indicated 
 Horse Power 
 
 Steam per 
 I. H. P. Hr. 
 
 Indicated 
 Horse Power 
 
 Steam per 
 I. H. P. Hr. 
 
 i 
 
 659. 
 
 11.89 
 
 725. 
 
 13.27 
 
 658. 
 
 12.03 
 
 1714. 
 
 13.27 
 
 670. 
 
 12.29 
 
 1030. 
 
 13.21 
 
 798. 
 
 13.28 
 
 843. 
 
 13.53 
 
 1017. 
 
 13.26 
 
 382. 
 
 14.05 
 
 689. 
 
 12.69 
 
 873. 
 
 14.18 
 
 708. 
 
 12.45 
 
 676. 
 
 14.6 
 
 636. 
 
 13.28 
 
 1540. 
 
 14.1 
 
 280. 
 
 13.37 
 
 300. 
 
 15.78 
 
 719. 
 
 13.09 
 
 606. 
 
 16.28 
 
 741. 
 
 13.23 
 
 716. 
 
 19.36 
 
 739. 
 
 13.01 
 
 
 
 In comparison with these results are the following. 1 In reducing 
 
 1 French. " Steam Turbines.'
 
 POSITION AND FIELD OF THE STEAM TURBINE. 123 
 
 the given steam rates to I. H. P. the combined efficiency factors 
 used are: 
 
 For units 300 . 
 For units 500. 
 For units 2000 . 
 
 . 400 K. W oo 7o 
 
 .1500 K. W 90% 
 
 .3000 K. W 92% 
 
 Where 93% is used the test was made on brake H. P. basis. 
 
 Engine efficiency alone without generator, for units from 400 
 to 500 H. P., or 300 to 400 K. W., taken at 93%. 
 
 Engine efficiency corresponding to the 300 H. P. De LaVal 
 turbine, taken at 92%. 
 
 Typical Steam Consumptions of Turbines. 
 
 Turbine 
 
 Nominal 
 Power 
 
 Steam Rate 
 
 Estimated Equiv. 
 Consumption 
 per I. H. P. 
 
 S** 
 g$| 
 
 ^5 W 
 %ti 
 
 W l 
 SS^ 
 
 o> 
 
 fc 
 
 I m 
 
 Per Elect. 
 H. P. 
 
 
 W 
 
 1 
 
 Saturated Steam 
 
 De Laval 
 
 300 H. P. 
 500 H. P. 
 500 H. P. 
 500 H. P. 
 400 H. P. 
 1250 H. P. 
 
 15.17 
 13.63 
 
 
 
 13.96 
 13.11 
 14.12 
 13.28 
 12.68 
 12.72 
 
 92. 
 88. 
 88. 
 90. 
 93. 
 90. 
 
 Rateau 
 
 14.9 
 16.05 
 14.76 
 
 21.5 
 19.78 
 
 Zoelly 
 Curtis, American 
 Westinghouse-Parsons . 
 Westinghouse-Parsons . 
 
 14.13 
 
 18.95 
 
 Moderate Superheat 
 Up to 150 
 
 De Laval 
 
 300 H. P. 
 500 H. P. 
 500 K. W. 
 500 K. W. 
 300 K. W. 
 1500 K. W. 
 3000 K. W. 
 400 K. W. 
 1250 K. W. 
 
 13.94 
 12.07 
 
 14.05 
 15.29 
 13.28 
 14.96 
 13.44 
 11.79 
 
 13.78 
 
 18.82 
 20.50 
 17.79 
 20.06 
 18. 
 15.8 
 
 18.48 
 
 12.82 
 12.36 
 13.76 
 11.95 
 13.16 
 12.10 
 10.85 
 11.23 
 12.40 
 
 92. 
 88. 
 90. 
 90. 
 88. 
 90. 
 92. 
 93. 
 93. 
 
 Zoellv 
 
 Curtis, English 
 Curtis, American 
 
 
 Parsons 
 Westinghouse-Parsons . 
 Westinghouse-Parsons .
 
 124 STEAM TURBINES. 
 
 Typical Steam Consumptions of Turbines. Continued. 
 
 High Superheat 
 180 to 290 
 
 Curtis, American 500 K. W. 
 
 
 11.26 
 
 15.1 
 
 10.14 
 
 90. 
 
 Curtis, American 2000 K. W. 
 
 
 11.27,15.12 
 
 10.36 
 
 92. 
 
 Parsons 3000 K. W. 
 
 
 11. 
 
 14.74 
 
 10.12 
 
 92. 
 
 Westinghouse-Parsons . 400 K. W. 
 
 11.17 
 
 
 
 10.39 
 
 93. 
 
 
 
 I 
 
 
 In comparison with the last test in the table, with the high 
 super heat, may be taken the tests of a Van der Kerchove engine, 
 made by Prof. Schroeter. 
 
 I. H. P. 
 
 Superheat in 
 Deg. Fahr. 
 
 1 
 
 Steam per 
 I. H. P. Hr. 
 Lbs. 
 
 Equivalent 
 Pounds of 
 Saturated 
 Stm. 
 
 Heat Units 
 per I. H. P. 
 Hr. 
 
 222. 
 
 0. 
 
 12.06 
 
 12.08 
 
 250. 
 
 226. 
 
 43.7 
 
 11.58 
 
 11.77 
 
 244. 
 
 227. 
 
 97.7 
 
 11. 
 
 11.44 237. 
 
 223. 
 
 151.7 
 
 10.67 
 
 11.33 
 
 234. 
 
 223. 
 
 221.2 
 
 9.81 
 
 10.69 221. 
 
 218. 
 
 310.9 
 
 1 
 
 8.86 
 
 10.01 
 
 207. 
 
 The Rice and Sargent engine, in table, p. 122, is perhaps a still 
 better comparison. 
 
 The following list of tests of engines and turbines may be 
 taken as representing the comparative economy obtained by 
 each type to January, 1911. The B. T. U. per K. W. minute 
 are obtained by multiplying the steam rate per K. W. minute 
 by the difference between the B. T. U. per pound of steam at the 
 initial conditions of pressure and superheat and the B. T. U. in 
 1 pound of water at the vacuum pressure, col. 4. The last column 
 gives the best basis for comparison.
 
 POSITION AND FIELD OF THE STEAM TURBINE. 125 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 
 
 
 1 
 
 
 
 Load 
 K. W. 
 
 Steam 
 Press. 
 
 Super- 
 heat or 
 Mois- 
 
 Vacu- 
 um 
 
 Lbs 
 Steam 
 perK. 
 
 B.T.U. 
 per 
 K. W. 
 
 
 
 Abs. 
 
 ture 
 
 
 . 
 Hour 
 
 Min. 
 
 Turbines 
 
 
 
 
 
 
 
 N. Y. Edison, Westinghouse 
 
 9870 
 
 192 
 
 97F 
 
 27.31 
 
 15 
 
 294 
 
 City Electric, Westinghouse 9173 
 
 182 
 
 59 
 
 27.90 
 
 14.57 
 
 282.4 
 
 Bklyn Rpd. Transit, Westing- 11466 
 
 192 
 
 106 
 
 28.15 
 
 14.45 
 
 287.5 
 
 house. 
 
 
 
 
 
 
 
 Chgo. Edison, Curtis 
 
 10186 
 
 191 
 
 147 
 
 29.47 
 
 12.9 
 
 270 
 
 Carville, Parsons 
 
 5059.4 
 
 209 
 
 95 
 
 29.27 
 
 13.35 
 
 271.7 
 
 Frankfort, Brown-Bovari 
 
 3521.6 
 
 157 
 
 130 
 
 28.90 
 
 13.70 
 
 278 
 
 Turin, Escher-Wyss 
 
 3540 
 
 187 
 
 90 
 
 28.35 
 
 15 
 
 297.4 
 
 Berlin Moabit., A. E. G 
 
 3169 
 
 185 
 
 215 
 
 29 
 
 12.7 
 
 268.4 
 
 Rummelsburg, A. E. G 
 
 4239 
 
 188 
 
 285 
 
 29 
 
 11.9 
 
 258.5 
 
 Engines 
 
 
 
 
 
 
 
 N. Y. Edison, Westinghouse 
 
 3872 
 
 200 
 
 dry 
 
 27 
 
 16.78 
 
 312 
 
 Interborough, 59th St., Allis 1 . . 
 
 5496 
 
 190 
 
 dry 
 
 25.02 
 
 17.82 
 
 225 
 
 Boston Edison, Mclntosh 
 
 1500 
 
 176.5 
 
 92 
 
 25.4 
 
 16.47 
 
 315 
 
 Berlin Moabit 
 
 1920 
 
 202.7 
 
 223 
 
 28 
 
 13.35 
 
 276 
 
 Berlin Luisenstrasse | 1950 
 
 202.7 
 
 264 
 
 27 
 
 14 
 
 295 
 
 1 
 
 
 
 
 
 
 1 Without L. P. Exhaust Turbines, see Art. 22. 
 
 The results brought out in the foregoing indicate 
 
 1. That with high vacuums the larger turbines show economies 
 somewhat better than reciprocating engines. 
 
 2. That with moderate vacuum, in the medium sizes, the 
 advantage in economy still lies with the refined types of recipro- 
 cating engine. 
 
 Problems. 
 
 1. Look up and report on methods of testing steam turbines. Paper 
 by Dickinson and Robinson, Am. Inst. of Elect. Eng'rs, December, 
 1910. 
 
 2. Report on "Test of a 9000 K. W. Turbo-generator Set." Paper 
 by F. H. Varney, Trans. A. S. M. E., vol. xxxii, December, 1910. 
 
 3. Report on chapters on testing of turbines in Moyer's "Steam 
 Turbines." 
 
 References. 
 
 STODOLA: "The Steam Turbine." 
 
 MOYER: "Steam Turbines." ' 
 
 JUDE: "Theory of the Steam Turbine." 
 
 FRENCH: "Steam Turbines."
 
 126 
 
 STEAM TURBINES. 
 
 NEILSON: "The Steam Turbine." 
 
 THOMAS: " Steam Turbines." 
 
 KERR: Paper, Trans. A. S. M. E., vol. xxv. 
 
 Art. 26. General Comparison of Engines and Turbines. 
 
 Other considerations, however, enter such as steadiness and 
 economy under widely fluctuating working loads, the room 
 required, the foundations, cost of installation and operation. 
 
 The governors of reciprocating engines regulate the effort 
 from stroke to stroke to meet varying load conditions, but fluctu- 
 ations due to the effect of the connecting rod and the weight of 
 the reciprocating parts can be cared for only by the flywheel. 
 The flywheel can at best only reduce these fluctuations to within 
 prescribed limits. In direct connected generating units, espe- 
 cially when running in parallel, the turbine has the advantage of 
 a total absence of reciprocating motion and a uniform turning 
 effort, the high speed of the rotor and heavy armature acting as a 
 powerful regulating force. In fact it has been found possible 
 with turbines to run railway, power, and lighting circuits from 
 the same machine, and where a turbine has been installed to run 
 in parallel with piston engines it has always been found to have a 
 steadying effect on the whole system. 
 
 But the turbine is a one-speed machine. In this respect it is 
 distinctly inferior to the reciprocating engine, for it cannot be 
 run at speeds lower than that for which it is designed without 
 serious effect on its economy. This is one of the limitations to 
 its use in marine work, and has proved one of the difficult prob- 
 lems in that connection. Even turbine advocates do not recom- 
 mend them for intermittent services and varying speeds. The 
 field available for the marine turbine seems to be deep sea service, 
 where the work consists of long runs at uniform speed. Tests 
 made on a Curtis turbine for variation in steam consumption in 
 relation to the speed resulted as follows: 
 
 R. P. M. 
 
 Steam per K. W. 
 
 hr. 
 
 1900 
 
 19.75 
 
 
 1600 
 
 20.74 
 
 
 1300 
 
 22.7 
 
 
 1000 
 
 27. 

 
 POSITION AND FIELD OF THE STEAM TURBINE. 127 
 
 In the torpedo-boat destroyers built by the British Navy for 
 comparing turbines and reciprocating engines, the turbine boats 
 were superior in economy to the engine-driven boats at normal 
 speeds, but invariably inferior when running at slow cruising 
 speeds. 
 
 In good practice reciprocating engines are not installed to run 
 under frequent overloads greater than 50% of the normal 
 capacity. Corliss engines can be made to carry overloads of 
 100%, but not with good economy. The tendency is to provide 
 an engine large enough to handle the maximum loads easily, 
 and let it operate at an average load considerably below its rated 
 capacity. Prof. Carpenter has reported tests of thirty-five street 
 railway power plants. In these this tendency is clearly marked. 
 The following table gives a summary of seven of these tests made 
 on compound condensing engines of the Corliss or similar types. 
 The remaining ones not given show the same tendency. 
 
 H. P. of 
 
 Mean 
 
 %of 
 
 Steam per 
 
 Engine 
 
 observed H. P. 
 
 Capacity 
 
 I. H. P. Hour. 
 
 825 
 
 482 
 
 58.2 
 
 22.7 
 
 1,000 
 
 277 
 
 27.7 
 
 21.9 
 
 1,000 
 
 314 
 
 31.4 
 
 20.0 
 
 350 
 
 182 
 
 52.2 
 
 16.64 
 
 500 
 
 290 
 
 58. 
 
 16.90 
 
 2,000 
 
 814 
 
 40.7 
 
 14.50 
 
 200 
 
 145 
 
 72. 
 
 17.30 
 
 Average 
 
 
 48 6 
 
 18 6 
 
 
 
 
 
 The average load on these engines was less than half their 
 rated capacity, and they were operated at an average steam rate 
 of over 18 pounds instead of 14 and 15 pounds, which the type 
 of engine is capable of. 
 
 As turbines have been rated they have been capable of operat- 
 ing under heavy overloads and at very fair steam rates. Guar- 
 antees were regularly made on the rates for overloads of 25%, 
 50%, and 100%. 
 
 As a result turbines have been installed more with reference
 
 128 STEAM TURBINES. 
 
 to the average load to be carried, and less with reference to the 
 maximum load than a steam engine, the turbine operating at 
 nearly its best economy most of the time, whereas an engine, 
 rated nearer the maximum load, would be operating at less than 
 its most efficient rating. 
 
 The following table shows the variations in consumption 
 reported for a Westinghouse turbine on loads varying from 1/2 
 load to 100% overload. 
 
 
 Steam Rate 
 
 Steam Rate 
 
 Load 
 
 Saturated 
 
 100 Superheat 
 
 1/2 load 
 3/4 load 
 Full load 
 
 15.86 
 15.05 
 13.89 
 
 14.34 
 13.45 
 
 12.48 
 
 1 1/4 load 
 1 1/2 load 
 
 13.85 
 
 12.41 
 12.79 
 
 100% overload 
 
 15.12 
 
 13.55 
 
 Here an overload of 100% was carried with an increase of only 
 10% in the steam rate. Such a load could not be carried indefi- 
 nitely with safety to the generator, but overloads of 50% are 
 often met. 
 
 It should be added however, that turbine manufacturers are 
 rating their machines higher now and this difference is becoming 
 less marked. 
 
 In respect to the room occupied, the advantage in favor of the 
 turbine alone is very marked. If the condensing apparatus be in- 
 cluded in the comparison the difference is not so great, but even then 
 it is usually in favor of the turbine. This is brought out clearly in 
 Fig. 77, which shows a 3,500 K. W. engine-driven unit, l and two tur- 
 bine-driven units, one 5000 K. W. and behind one of 7500 K. W. in 
 the Waterside Station of the N. Y. Edison Co. Four of the engine- 
 driven units similar to that shown in the picture are being re- 
 placed by three turbine units, each of 20,000 K. W. capacity. 
 
 A comparison of these turbine units with the reciprocating 
 engine shows the equally marked difference in the foundations. 
 
 The selling price of turbines to-day is governed largely by that 
 
 1 The engine of this unit is really capable of turning out 6000 H. P., although the genera- 
 tor is rated at 3500 K. W.
 
 POSITION AND FIELD OF THE STEAM TURBINE. 129
 
 130 
 
 STEAM TURBINES. 
 
 of the competing engines. The manufacturing cost is probably 
 less, but as there are few turbines in the market and compara- 
 tively little competition as yet between them, the competition 
 has' been rather with the old type engines. Any estimate of cost, 
 however, must include the land, buildings, and foundations. 
 These elements vary so with different conditions that no general 
 results can be given. The general adoption of the turbine 
 shows that for large units at least it is the cheaper, and it has 
 practically driven out its rival for large power station work. 
 
 Mr. Stott, Supt. of Motive Power of the Interborough R. T. Co., 
 New York City, in a paper before the A. I. E. E., makes the 
 following comparison of the operating cost of large engine-driven 
 and turbine-driven units. He says: "The turbine shows more 
 uniform steam rate for varying loads, practically as good 
 economy with saturated steam, and a thermal economy of 6.6% 
 better for superheated steam." The various items are derived 
 from actual costs. 
 
 Comparison of Charges per K. W. Hr. 
 
 Maintenance 
 
 Comp. 
 
 Cond. Turbine 
 Engine 5000 H. P. 
 7500 H. P. 
 
 Engine room, mechanical 
 
 2 57 
 
 51 
 
 Boiler room 
 Coal and ash handling apparatus 
 Electrical apparatus 
 
 4.61 
 .58 
 1.12 
 
 4.30 
 .54 
 1.12 
 
 Operation 
 
 
 
 Coal and ash handling labor 
 
 2 26 
 
 2 11 
 
 Removal of ashes 
 Dock rental 
 Boiler room, labor 
 Boiler room, oil, waste, etc 
 Coal 
 
 1.06 
 .74 
 7.15 
 .17 
 61 30 
 
 .94 
 .74 
 6.68 
 .17 
 57 30 
 
 Water 
 Engine room, mechanical labor 
 Lubrication. ... 
 
 7.14 
 
 6.71 
 1 77 
 
 .71 
 1.35 
 35 
 
 Waste, etc 
 Electrical labor 
 
 .30 
 2 52 
 
 .30 
 2 52 
 
 
 
 
 Relative cost of maintenance and operation 
 Relative investment in per cent 
 
 100. 
 100 
 
 79.64 
 82 52 
 
 

 
 POSITION AND FIELD OF THE STEAM TURBINE. 131 
 
 The general statement that the turbine requires much less oil 
 is borne out in this table, where the turbine requires but 20% of 
 that for the engine generator. In a turbine oil is used only in 
 the bearings, free from contact with the steam, so that the steam 
 is returnable to the boilers as soon as condensed, a property of 
 great value in places where feed water is expensive. 
 
 Problems. 
 
 i. Report on the power of plant of Public Service Corp'n. of N. J., 
 described in Power, November 23, 1909, p. 853. 
 
 References. 
 
 STEVENS AND HOBART: "Steam Turbine Engineering." 
 MOVER: " Steam Turbines." 
 FRENCH: " Steam Turbines." 
 MURRAY: " Electric Power Plants." 
 
 WALDRON: Paper, "The Steam Turbine from an Operating Stand- 
 point." Trans. A. S. M. E., vol. xxiv. 
 
 Art. 27. Relative Fields of Engines and Turbines. 
 
 The reciprocating engine is superior to the turbine in starting 
 power, in reversing, in operating at varying speeds on inter- 
 mittent and irregular service. It requires less condensing 
 apparatus and gives a higher economy for saturated steam at 
 average vacuums. It can run at moderate speeds and will 
 therefore have a monopoly of many services where the high 
 speeds of the turbine are prohibitive. These considerations 
 indicate that the steam engine will hold its place in locomotive 
 work, hoisting, rolling mills, lighter marine work, and belt and 
 rope driving. Turbines are being applied to centrifugal air 
 compressers and to pumps, with considerable success, but it will 
 be some time before they will be a serious rival in this field or in 
 blowing engines. If the steam engine encounters serious com- 
 petition in the smaller sizes for miscellaneous work it seems 
 much more likely that it will come from the gas engine than 
 from the turbine. 
 
 The turbine, on the other hand, has demonstrated that it, too, 
 has its field. For direct connected services such as for generators 
 and marine work, especially in the larger units, it has proven
 
 132 STEAM TURBINES. 
 
 superior to the reciprocating engine. In central power station 
 service it has practically superseded the old type of engine. 
 
 Up to February, 1911, the sales of the three foremost manu- 
 facturers of large turbines in the United States were as follows : 
 
 General Electric Co. 2,150,000 K. W. 
 
 Westinghouse Machine Co. 1,600,000 K. W. 
 
 Allis-Chalmers Co. 3 50 ! 000 K W - 
 
 Total 4,100,000 K. W. 
 
 When it is realized that scarcely a dozen of these machines 
 are 9 years old, and the vast majority not more than 5, one can 
 see the hold the turbine has obtained on this field. About 
 70 or 75% of the turbines built are for electric light, power, and 
 traction companies. 
 
 Here the turbine is at its best. It is practically immune from 
 danger from priming. Its uniform velocity and close regulation, 
 its high economy under widely varying loads, its compactness 
 and inexpensive foundations, and its exhaust free from oil, 
 together with the great saving in the generators due to the high 
 speeds, have made it distinctively the central station machine 
 for the generation of alternating current power. 
 
 In marine service the turbine has also been successful, although 
 its ascendancy here is not so marked as in power station work. 
 Mr. C. A. Parsons has lead the way into this field, and it is largely 
 to his indomitable will that the successful application of the 
 turbine to marine service is due. When he first began his 
 experiments, propeller shafts ran at from 80 to 120 R. P. M., 
 and the slowest turbines at 3,000 to 5,000 R. P. M. The 
 "Turbinia," the first experimental vessel, was equipped with 
 2,000 H. P. turbines designed for 3,000 R. P. M. It was 
 found that at the designed speed of rotation only 18 knots could 
 be obtained. Experimental investigation developed the exist- 
 ence of "cavitation," a cylindrical vacuum formed around the 
 propeller, causing great loss of power. 
 
 After clever and extensive experiments propellers were 
 developed on new lines, the power was divided up between 3 
 turbines driving 3 shafts, the revolutions reduced about 1/2, 
 and a combination of turbine and propeller obtained which gave 
 remarkable results. A speed of over 34 knots, never before 
 reached by any vessel, was obtained.
 
 POSITION AND FIELD OF .THE STEAM TURBINE. 133 
 
 From that time, 1894, the development has been steady. 
 From the Turbinia, with its 100 feet of length, 9 feet beam and 
 44 1/2 tons displacement, the turbine has been successfully 
 applied to destroyers, small passenger steamers on the Clyde, the 
 Channel, and Irish Sea services, to the Allan liners, the largest 
 Cunard liners and to the heaviest battleships. The Mauritania 
 and Lusitania have maintained average speeds of over 25 knots, 
 and developed over 70,000 H. P., 70% more power than has ever 
 before been concentrated in one set of engines. 
 
 The main advantages of the turbine in the marine service are: 
 
 1. Absence of engine vibration. 
 
 2. Lower center of gravity with consequent greater stability. 
 
 3. Less weight of machinery with consequent greater carrying 
 power. 
 
 4. Higher average economy. 
 
 5. Smaller propellers and therefore, from this and item three, 
 less draft. 
 
 6. Lower cost of operation i.e., attendance, supplies, etc. 
 
 Mr. Parsons, in a paper before the Institute of Marine Engi- 
 neers, speaking of the future of the marine turbine, says: 
 
 " I think we are safe in predicting that it will soon supersede 
 entirely the reciprocating engine in vessels of 16 knots sea-speed 
 and upward, and of over 5,000 I. H. P., and probably also in- 
 cluding vessels of speed down to 13 knots, of 20,000 tons and up- 
 ward, and possibly still slower vessels in course of time. At 
 present it may, I think, be said that the above most suitable field 
 comprises about 1/5 of the total steam tonnage of the world; but 
 it must be remembered that the speed of ships tends to increase, 
 and the turbine to improve, and so the class of ships suitable for 
 the turbine will increase. 
 
 Much interest and attention are being centered on the combina- 
 tion of reciprocating engines and turbines for marine work as in the 
 Olympic. The advantages to this combination have been con- 
 sidered in Art. 22, but it seems especially adapted for ships, giving 
 high economy and a greater flexibility than turbines alone. 1 
 
 1 "Combination System of Reciprocating Engines and Steaui Turbines," paper by C. 
 A. Parsons, Institution of Naval Architects., Lond., April 9, 1908. Reprinted in London 
 Engineering, April 17, 1908. 
 
 See also articles on the Engine of the White Star SS "Olympic," London Engineering, 
 Oct. 11, 1910.