1902 Encyclopedia > Steam Engine > The Testing of Steam Engines

Steam Engine
(Part 5)

The Testing of Steam Engines

97. Under this head we may include experiments made to determine—(a) the horse-power of an engine; (b) the thermodynamic efficiency, or some more or less nearly equivalent quantity, such as the relation of power to steam supply or to coal consumption (§ 95); (c) the distribution of steam, that is, the relation which the several events of steam-admission, expansion, exhaust, and compression bear to the stroke of the piston; (d) the amount of initial condensation, the wetness of the steam throughout the stroke; and the transfer of heat between it and the cylinder walls; (e) the efficiency of the mechanism, or the ratio which the work done by the steam in the cylinder.

Tests (a) and (c) are of common application; test (b), in the simple form of a comparison of horse-power with coal burnt per hour, is not unusual. The actual measurement of efficiency, whether thermodynamic (b) or mechanical (e), and the analysis involved in (d) have been carried out in comparatively few instances.

98. In all these operation the taking of indicator diagrams forms a principal part. The indicator, invented by Watt and improved by M’Naught and by Richards, consists of a small steam cylinder, fitted with a piston which slides easily within it and is pressed down by a spiral spring of steel wire. The cylinder of the indicator is completed by a pipe below this piston to one or other end of the cylinder of the engine so that the piston of the indicator rises and falls in response to the fluctuations of pressure which occur in the engine cylinder. The indicator piston actuates a pencil, which rises and falls with it and traces the diagram on a sheet of paper fixed to a drum that is caused to rotate back and forth through a certain arc, in unison with the motion of the engine piston. In M’Naught’s indicator the pencil is directly attached to the indicator piston, in Richard’s the pencil is moved by means of a system of links so that it copies the motion of the piston on a magnified scale. This has the advantage that an equally large diagram is drawn with much less movement of the piston, and errors which are caused by the piston’s inertia are consequently reduced. In high-speed engines especially it is important to minimize the inertia of the indicator piston and the parts connected with it. In Richard’s indicator the linkage employed to multiply the piston’s motion is an arrangement similar to the parallel motion introduced by Watt as a means of guiding the piston-rod in beam engines (see § 188). In several recent forms of indicator lighter linkages are adopted, and other changes have been made with the object of fitting the instrument better for high-speed work. One of these modified forms of Richard’s indicator (the Crosby) is shown in fig. 21. The pressure of steam in the engine cylinder raises the piston P, compressing the spring S and causing the pencil Q to rise in a nearly straight line through a distance proportional, on a magnified scale, to the compression of the spring and therefore to the pressure of the steam. At the same time the drum D, which carries the paper, receives motion through the cord C from the crosshead of the engine. Inside this drum there is a spiral spring which becomes wound up when the cord is pulled, and serves to turn the drum in the reverse direction during the back stroke. The cap of the indicator cylinder has hole in it which admit air freely to the top of the piston, and the piston has room to descend, extending the spring S, when the pressure of the steam is less than that of the atmosphere. The spring is easily taken out and replaced by a more or less stiff one when higher or lower pressures have to be dealt with.

99. To register correctly, an indicator must satisfy two conditions: (1) the motion of the piston must be proportional to the change of steam pressure in the engine cylinder; and (2) the motion of the drum must be proportional to that of the engine piston.

The first of these requires that the pipe which connects the indicator with the cylinder should be short and of sufficient bore, and that it should open in the cylinder at a place where the pressure in it will not be affected by the kinetic action of the inrushing steam. Frequently pipes are led from both ends of the cylinder to a central position where the indicator is set, so that diagrams may be taken from either end without shifting the instrument; much better results are obtained, especially when the cylinder is long, by using a pair of indicators, each fixed with the shortest possible connecting pipe, or by taking diagrams successively from two ends of the cylinder with a single instrument set first at one end and then at the other. The general effect of an insufficiently free connexion between the indicator and the engine cylinder is to make the diagram too small. The first condition is also invalidated to some extent by the friction of the indicator piston, of the joints in the linkage, and of the pencil on the paper. The piston must slide very freely; nothing of the nature of packing is permissible, and any steam that leaks past it must have a free exit through the cover. The pencil pressure must not exceed the minimum which is necessary for clear marking. Be careful use of a well-made instrument the error due to friction in the piston and connected parts need not be serious. Another source of disturbance is the inertia of these parts, which tends to set them into oscillation whenever the indicator piston suffers a comparatively sudden displacement. These oscillations, superposed upon the legitimate motions of the piston, give a wavy outline to parts of the diagram, especially when the speed is great and when the last-named source o error (the friction) is small. When they appear on the diagram a continuous curve should be drawn mid-way between the crests and hollows of the undulations. To keep them within reasonable compass in high-speed work a stiff spring must be used and an indicator with light parts should be selected. Finally, to secure accuracy in the pencil’s movement, the strain of the spring must be kept well within the limit of elasticity, so that the strain may be as nearly as possible proportional to the steam pressure. Care must be taken that the spring is graduated to suit the temperature (about 212&Mac251; F.) to which it is exposed when in use ; its stiffness at this temperature is about 3 per cent. less than when cold.

With regard to the motion of the drum, it is, in the first place, necessary to have a reducing mechanism which will give a sufficient accurate copy, on a small scale, of the engine pistons stoke. Many contrivances are used for this purpose; in some a rigorous geometrical solution of the problem is aimed at, in others a close approximately. Fig. 22 shows a good form of indicator gear. A pendulum rod AB is pinned at one end to the crosshead A (the end of the piston-rod) of the engine. Its upper end is carried by a pin which is free to turn and slide in the fixed slot B. A cord from an intermediate point C leads over pulleys to the indicator drum. The pendulum rod should be much longer than the piston-stroke, and the cord should lead off for a considerable distance in the direction sketched, at right angles to the mean position of the rods. The accuracy of the drum’s motion does not, however, depend merely on the geometrical condition of the gear. It depends also on the rigidity of the parts, and especially on the stretching of the cord. The elasticity of the cord will cause error if it is not maintained in a state of uniform tension throughout the double stroke, and this error will be greater the longer and the more extensible the cord is. Hence short cords are to be preferred; and fine wire, stretches much less, may often be substituted for cord with great advantage. The stretching of the cord is perhaps the most serious and least noticed source of error the indicator is subject to in ordinary practice. The tension of the cord varies for three reasons,—the inertia of the drum, the varying resistance of the drum spring, and the friction of the drum, which has the effect of increasing the tension during the forward stroke and of the reducing it during the back stroke. These last causes of variation can be minimized only by good construction and careful use of instrument; but the other two causes can be made to neutralize one another almost completely. Since the motion is nearly simple harmonic, the acceleration of the drum varies in a nearly uniform manner form end to end of the stroke. The resistance of the drum spring also varies uniformly; and it is therefore only necessary to adjust the stiffness of the drum spring so that the increase in its resistance as the motion of the drum proceeds may balance the decrease in the force that the cord has to exert in setting the drum into motion. This adjustment will secure an almost uniform tension in the cord throughout the whole stroke; it must, of course, be altered to suit different engine speeds. The indicator plays so important a part in the testing of heat-engines, whether for practical or scientific purposes, that no pains should be spared to avoid the numerous and serous sources of error to which it is liable through faulty construction or unintelligent use.1

100. To determine the indicated horse-power, the mean effective pressure is found by dividing the area of the diagram by the length of its base. This gives a mean height, which, interpreted on the horse-scale of pressures, is the mean effective pressure in pounds per square inch. This has to be multiplied by the effective area of the piston in square inches and by the length of the piston stroke in feet, to find the work done per stroke in foot-pounds on the side of the piston to which the diagram refers. Let A1, be the area of the piston on one side and A2 on the other; p1 and p2 the mean effective pressures on the two sides respectively; L the length of the stroke in feet; and r the number of complete double strokes or revolutions per minute. Then the indicated horse-power

I.H.P. = nLp1A1+p2A2) .


In finding the mean pressure the are of the diagram may be conveniently measure by a planimeter or calculated by the use of Simpson’s rule. A less accurate plan frequently followed, is to divide the diagram by lines drawn at the middle of strips of equal width, as in figs. 23 and 24, and to take the mean pressure as the average height of these lines.

101. Space admits of no more than a few illustrations of actual indicator diagrams. Fig. 23 is a diagram taken from an antiquated non-condensing engine working without expansion. The line AB has been drawn at a height which represents the boiler pressure, in order to show the pressure in admission. The line CD is drawn at atmospheric pressure by indicator itself. In this engine admission continues till the end of the forward stroke, and as a result the back pressure is great, especially during the first stage of the exhaust. The diagram shows a slight amount of oscillation produced by the sudden admission of steam. This feature, however, is better illustrated by fig. 24, which is another diagram taken from the same engine, at the same boiler pressure, but with the steam much throttled.

Fig. 25 shows a pair of diagrams taken from a condensing engine in which the distribution of steam is effected by a common slide valve (chap. VIII). The two diagrams refer to opposite ends of the cylinder and are taken on the same paper by the plan already alluded to (§ 99) of fixing the indicator about midway between the ends of the cylinder, with a pipe leading from it to each end. Steam is cut off at a and d, release occurs at b and b1, and compressions begins at c and c1. The actual closing of the slide valves throttles the steam considerably before the cut-off is complete. The line of no pressure EF is drawn 14&Mac250;7 _ per square inch below CD, which is the atmospheric line; and the line of no volume AE of BF is drawn (for each end of the cylinder) at a distance (from the end of the diagram) equal to the volume of the clearance.

Fig. 26 is diagram taken from a Corliss engine working with a large ratio of expansion. The Corliss valve-gear, which will be described in chap. IX, causes the admission valve to close suddenly, and consequently defines the point of cut-off pretty sharply in the diagram. Through this point a dotted curve has been drawn (by aid of the equation PVn = const., _ 67), which is the curve that would be followed if the expansion were adiabatic. In drawing this curve it has been assumed that at the end of admission the steam contains 25 per cent. The actual curve first falls below and then rises adiabatic curve, in consequence of the continued condensation which takes place during the early stages of the expansion and the re-evaporation of condensed water during later stages (§ 82). Fig. 27 is another diagram from a Corliss engine, running light, and with the condenser not in action. Diagrams of this kind are often taken when engines are first exerted, for the purpose of testing the setting of the valves. Other indicator diagrams, for compound engines, will be given in chap. VI.

In place of the ordinary indicator an apparatus is occasionally used which integrates the two coordinates which it is the business of the indicator diagram to represent, and exhibits the power developed form stroke to stroke by the progressive movement of an index round a dial.

102. in tests of thermodynamic efficiency we may measure either the heat supplied or the heat rejected, and compare it with the work done. The heat supplied is on the whole capable of more exact measurement, but in any case a determination of the heat rejected furnishes a valuable check on the accuracy of the result. The trial must be continued for a period of some hours at least, during which the engine and boiler are to be kept working as uniformly as possible in all respects. The power is determined by taking indicator diagrams at short intervals. The heat supplied is found by noting the amount of feed-water required to keep the water-level in the boiler constant during the trial, the temperature of the feed, and the pressure of the steam. The only uncertainty which attaches to the measurements of heat-supply is due to priming. Every pound of water that passes over unevaporated to the engine takes less heat by the amount L (§ 60) than if it went over in the state of steam. To measure the degree of wetness in steam is a matter of some difficulty; it may be done by passing the steam into a known quantity of cold water, so as to condense it, and observing the rise of temperature which has taken place when the whole quantity of water present has increased by a measured amount.

If L1, be the latent heat of steam at the boiler pressure, h0 the heat in the feed-water per _, h1 the heat in the boiler water per _, and q the dryness of the steam as it leaves the boiler, the heat taken in per _ of the substance supplied to the cylinder is

qL1 + h1 – h0 .

To this must be added, in the case of a jacketed engine, the heat supplied to the jacket, a quantity which depends on the amount of steam condensed there, and also on whether the water that gathers in the jacket is drained back into the boiler to escape into the hot-well.

The heat rejected by an engine fitted with an injection condenser is made up of the following parts :—(a) heat rejected in the condensed water, less the heat turned to the boiler in the feed (if the feed is directly drawn from the hot-well without giving the water time to cool sensibly, this quantity vanishes : in a jacketed engine this item must include the heat rejected in the jacket drains); (b) heat used in warming the condenser water from the temperature of injection to the temperature of the air-pump discharge ; (c) heat rejected in air and vapour form the air pump ; (d) heat lost by radiation, conduction to supports, and aerial convection,—or, more properly, the excess of this heat over the heat developed within the engine by the friction of piston, valves, &c. Of these quantities, (a) is found without difficulty form a knowledge of the amount of the feed-water, its temperature, the temperature of the air-pump discharge, and amount and temperature of water drained from the jacket ; (b) is measured by gauging the whole discharge from the pump, deducting from it the amount returned to the boiler as fee-water, and measuring its temperature and that of the injection water; (c) does not admit of direct measurement ; (d) may be approximately estimated for a jacketed engine by filling the jacket with steam while the engine is out action, and observing the amount of steam condensed in the jacket during a long-interval, through radiation, &c., from the external surface.

In calculating the supply of heat by the boiler it is convenient to take the temperature 32&Mac251; F. as a starting point from which to reckon what may be termed the goes supply, and then to deduct from this the heat which is restored to the boiler in the feed-water. The difference, which may be called the net supply, is the true consumption of heat, and is to be used in calculating the efficiency of the engine. A similar convention may be followed in dealing with the heat-rejected.

103. This subject is most easily made intelligible by help of a numerical example. For this purpose the following data of an actual engine-test have been taken from one of Mr. Mair’s papers1; the data have been independently reduced, with reduced, with results that differ only to a small and unimportant extent form those stated by Mr. Mair. The engine under trial was a compound beam engine, steam-jacketed, with an intermediate receiver between the cylinders. The cylinders were 21 inches and 36 inches in diameter, and the stroke 5_ feet. The total ratio of expansion was 13&Mac250;6.


Boiler pressure, absolute, 76 _ per sq. in.

Time of trial................................................6 hours.

Revolutions................................................8632, or 24&Mac250;0 per minute


Feed-water.................................................12,032 _, or 1&Mac250;394 _ per rev. (M.).

Water drained from jackets.........................1605 _, 0&Mac250;186 _ per rev. (Mj).

Percentage of priming ................................4.

Temperature of feed, t0...............................59&Mac251;

Temperature of injection, t2........................50&Mac251;.

Temperature of air-pump discharge, t3.......73&Mac251;&Mac250;4.


Dryness of boiler steam, q = 0&Mac250;96

Supply to cylinder, Mc, = M – Mj = 1&Mac250;028 _ per rev.

Injection water per rev. = 51&Mac250;1 - 1&Mac250;208 = 49&Mac250;9 _.

L1=898, h1=278, h2=18, h2=41&Mac250;4, h0=27.

Gross supply of heat form boiler to cylinder per revolution.

= Mc(qL1+h1)

=1&Mac250;208 (0&Mac250;96x896+278)=1377 T.U.

Gross supply to hat from boiler to jackets per revolution

=M (qL1+h1)

=0&Mac250;186 (0&Mac250;96x898+278) =212 T.U.

Total gross supply per revolution=1377+212=1589 T.U.

Heat restored to boiler per revolution,

By feed water Mh0=1&Mac250;394x27=38 T.U.

By jacket drains=0.

Net supply of heat per revolution=1589-38=1551 T.U.

Heat converted into work, per revolution

= I.H.P. x 42&Mac250;75 = 227 T.U.


Total heat rejected per revolution = 1551-227=1324 T.U.

The rejected heat is accounted for as follows:—

Net heat rejected in air-pump discharge=Gross heat rejected in air-pump discharge —heat in injection water — heat restored to the boiler by the feed

= 51&Mac250;1x 41&Mac250;4—49&Mac250;9 x 18—38=1179 T.U.

Heat rejected in jacket drains = Mjh1=0&Mac250;186x278=52 T.U.

These two items account for 1231 units of rejected heat and leave a balance of 93 units unaccounted for. The balance is made up of heat rejected in air and vapour by the air-pump, heat lost by radiation, &c., and errors of experiment. In the example considered the loss by radiation was estimated at 45 thermal units, which reduces the discrepancy between the two sides of the account to 48 units, or only about 3 per cent. of the whole heat supplied.

The efficiency of the engine is 227/1551 or 0&Mac250;146. The efficiency of a perfect engine working between the same limits of temperature, 308&Mac251; F., would be 0&Mac250;335.

104. When it is desire to deduce from the test of an engine not only the thermodynamic efficiency but also the amount of initial condensation and the subsequent changes of wetness which the working fluid undergoes during expansion, it is necessary to know, in addition to the above data, the volume of cylinder and clearance, the relation of pressure to volume during the several stages of the stroke, and the whole amount of working substance present in the cylinder. This last is a quantity whose precise value is not easily ascertained. Assuming that the point at which compression begins can be distinguished on the diagram, we have the pressure and the volume of the steam that is afterwards compressed into the clearance space. From its pressure and volume we can infer its amount, if only its degree of dryness be known. The assumption usually made is that at the beginning of compression the steam shut up in the cylinder is dry. This assumption is to a certain extend supported by the fact that re-evaporation has been going on during expansion and exhaust; in good engines it is probably not far from the truth, though there are cases where, owing to excessive initial condensation and to be the exhaust ports being badly situated for draining the cylinder, water may accumulate in considerable quantities. Except in extreme cases of this kind, however, the assumption that the steam is dry when compression begins does not introduce an error which can seriously affect the subsequent calculations. Having found the quantity shut up in the clearance, we add to it the quantity delivered from the boiler per single stroke, to find the whole quantity of working substance in the cylinder. The substance is, and continues, a mixture in varying proportion of steam and water. Its volume may practically be taken as the volume of the dry steam it contains, the volume of the water being comparatively small. Taking any point of the stroke, and measuring the pressure and the volume there, we can say how much steam (at that pressure) would be required to fill the volume which the mixture then occupies. This quantity will always be less than the actual amount of the mixture; and the difference between them is the amount of water that is present. This calculation is of special interest at two places in the stroke—the point of cut-off and the point of release.

105. To illustrate it we may continue the numerical example quoted above. In the high-pressure cylinder of the engine to which the test refers the volume at the beginning of compression (including clearance) was 1&Mac250;52 cubic. The pressure, just before compression began, is shown by the indicator diagram (of which fig. 28 is a copy) to have been the 14&Mac250;8 _ per square inch. At this pressure the density (or mass 1 cubic foot) of steam is 0&Mac250;038 _. Hence (on the above assumption that the steam was then dry) the quantity shut up in the clearance was 1 _ 52 x 0&Mac250;058 _.

The amount delivered to the cylinder per single stroke (or half revolution) was 0&Mac250;604 _. of working substance present from the end of the admission to the beginning of the exhaust was therefore 0&Mac250;662 _.

At the point of cut-off the pressure I shown by the diagram to have been 64 _ per square inch (absolute), and the volume including clearance, was 2&Mac250;92 cubic feet. The density of steam for this pressure is 0&Mac250;151 _ per cubic foot. Hence, out of the whole mixture, the amount of steam was 2&Mac250;92 x 0&Mac250;51 = 0&Mac250;440 _. The water present at the point of cut-off was therefore 0&Mac250;662 - 0&Mac250;440 or 0&Mac250;222 _. This is 33&Mac250;5 per cent. of the whole amount of the mixture, and shows (after allowing for the priming water) that about 32 per cent. of the steam admitted was condensed on admission.

Next, to find the amount of water present at the end of the expansion. The diagram shows that at this point the pressure was 15&Mac250;2 _ per square inch and the volume 13&Mac250;235 cubic feet. Steam of this pressure has a density of 0&Mac250;0392 _ per cubic foot. The quantity of steam at release was therefore 13&Mac250;235 x 0&Mac250;0392, or 0&Mac250;519 _, and the quantity of water 0&Mac250;662 - 0&Mac250;519 = 0&Mac250;143 _. It appears therefore that re-evaporation from the cylinder walls during expansion reduced the amount of water present by 0&Mac250;079 _, so that the percentage of water fell from 33&Mac250;5 at the point of cut-off to 21&Mac250;6 at the point of release. The same method of calculation can obviously be applied to any other point in the expansion curve, and can be extended to the low-pressure cylinder of an engine which (like the one in this example) is compound. The amount of dry steam present at the point of release is sometimes spoken of as the "steam accounted for by the indicator diagram."

106. Having completed this analysis of the working-substance, we may proceed to find the quantity of heat which it gives to or takes from the walls of the cylinder during any stage of its action, by considering the changes of internal energy which the working substance undergoes, along with the external work done, from stage to stage. If we write m for the amount of steam and m’ for the amount of water present in the cylinder at any one stage, the internal energy of the mixture is (§ 62)

(m + m’)h + mp.

Let the value of this quantity be denoted by IA at any one stage in the expansion or compression of the mixture, such as the point of cut-off A, by IB at a later stage, such as the point of release B, the corresponding volumes of the whole mixture being VA and VB respectively. Then in passing form the first condition to the second the substance losses IA – IB of internal energy. It also does an


amount of external work WAB measured by &Mac186; PdV, or the area of the figure ABab.


If WAB is equal to IA – IB the process is adiabatic; otherwise the amount of heat taken up (from the cylinder walls) during the progress is

QAB = WAB – (IA – IB) .

Let A is the point of cut-off and B that of release, the quantity so calculated is the heat taken up from the cylinder walls during the whole process of expansion. The calculation applies equally, however, in determining the heat taken up during any stage of the process. When this has a negative value heat has been given up by the substance to the cylinder walls. In the numerical example which has been cited above the internal energy of the mixture at the beginning of expansion was 540 thermal units. At the end of expansion the internal energy was 584 thermal units. Between this point the indicator diagram (fig. 28) shows that the work done was equivalent to 55 thermal units. 44 + 55 = 99 units of heat were therefore taken from the cylinder walls during the process of expansion. A similar calculation, applied to the compression curve, shows that in that part of the operation heat was given up to the cylinder walls. During compression W is of course negative, since work is then spent upon the steam.

107. During the admission and also during exhaust another item enters into the account,—the amount of working substance is then undergoing change. To find the heat given up by the steam during admission we have first to calculate (by the method already described) the internal energy of the mixed steam and water that is shut into the clearance space at the end of the previous stroke; this may be called ID. The steam which then enters brings with it an additional amount of internal energy which may calculate from knowledge of the quantity of steam, its pressure at admission, and its dryness. Let IO denote this additional supply of internal energy. At the end of admission the state of the mixture is known form the indicator diagram; hence its internal energy IA may be found. The work done during admission, WDA, is also determined from the diagram. Then we have, for the heat given up by the steam during admission,

QDA = ID + IO – WDA.

In attempting to apply the same method of calculation to determine the heat taken up from the cylinder walls during exhaust (QBC), we are met by the difficulty that we do not know the state, as regards, dryness, of the mixture during its expulsion from the cylinder. We may, however, estimate the value of QBC as follows. Let QCD and QDA be, as before, the heat given up by the steam to the cylinder walls during compression and admission respectively, let QAB be the heat taken form the cylinder walls during exhaust; also let QR be the heat which the cylinder losses (per single stroke) by radiation (less the heat produced by piston and valve friction), and QJ the heat which it gains by condensation of steam in the jacket, if there is one. Then, as the cylinder neither gains nor loses heat on the whole, after a uniform regime has been arrived at, we have


The quantity QBC may also be calculated directly from knowledge of the gross heat rejected to the condenser, since the gross heat rejected is


IB being the internal energy of the mixture at release and WBC being the work done upon the steam in expelling it from the cylinder.

108. This heat QBC, which is taken up by the steam from the cylinder walls during exhaust, is a part of the heat deposited there during admission. It has passed through the cylinder without contributing in the smallest degree to the work of the engine. Probably for this reason it is treated by some writers as a quantity which measures the wasteful influence of the cylinder walls. This, however, is not strictly the case. The magnitude of QBC is certainly in some sense an index of the extent to which the alternate heating and cooling of the metal causes inefficiency; it is so much heat absolutely lost, and lost by the action of the walls. [In the high-pressure cylinder of a compound engine this loss is of course absolute only as regard that cylinder; the heat represented by QBC assists in the work of the low-pressure.] But besides this loss there is another which the walls cause by taking heat from the steam on admission and restoring it during the later stages of expansion. That part of the heat abstracted during admission which is restored before the point of release does not appear in QBC ; nevertheless it is a source of inefficiency. With steam that is dry at the end of the expansion the value of QBC is almost negligible; still the cylinder walls may cause a very sensible loss by abstracting heat from the hot steam as it enters and restoring it as the mixture expands. The quantity which has been denoted here by QBC—that heat, namely, which the steam takes up from the cylinder walls after release and during exhaust—appears in the writings of Hirn and his followers under the symbol Rc. He terms it "le refroidessement au condeuseur," and refers to it, somewhat inexactly, as "I’effet réel des parois."1 Prof. Cotterill applies the name "exhaust waste" to the sum of the tow quantities QBC and QR.2

109. It is obvious that the above analysis depends fundamentally on the strict accuracy with which the indicator diagram not only gives a measure of the work done by the engine under test, but shows the relation of pressure to volume at each stage in the process. Engine tests of a complete kind have now been made and discussed by a number of independent observes, working with widely different data. The results are in good general agreement. They demonstrate the influence of the sides beyond question, showing that 30 per cent. is no unusual amount of water to be present in the mixture at the point of cut-off, even in compound engines of the best types; that half of this water, or even more, is frequently found at the end of expansion; and that the heat denoted above by QBC ranges from about 10 to 20 per cent. of the whole heat supplied.3

110. An engine employed to drive other machinery delivers to it an amount of power less than the indicated power by an amount which is wasted in overcoming the friction of piston and piston-rod, slides, valves, journals, &c. The efficiency of the mechanism is the ratio of the "effective" or "brake" horse-power to the indicated horse-power. It may tested by measuring the power delivered by the engine when at work, either by using a transmission dynamometer or by substituting an absorption dynamometer for the mechanism usually driven. In the case of a pumping engine the efficiency of the engine and pumps together may be determined by observing the actual the actual work done in raising water or in delivering a measured volume against a known pressure. Attempts are sometimes made to find the amount of power wasted in engine friction by testing the indicated power needed to drive the engine against no other resistance than its own friction. This, however, fails to show the power which will be spent in overcoming friction when the engine runs under ordinary conditions, since the pressure at the slides, the journals, and elsewhere are then widely different from what they are when the engine is running without load. Experiments with large engines show that the efficiency of the mechanism may, in favourable cases, be 0&Mac250;85 or even 0&Mac250;9; in small engines, or in large engines running under light loads, it is generally much less than this.

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