TABLE VIII.-WORK LOST IN PUMPING AGAINST THE The work wasted is equal to of the effective work at full load and to 1 of the effective work at the lightest load. At full load a well-designed non-condensing engine does not use much more steam per effective i.h.p. than a condensing engine. The greater back pressure in the former is partly balanced by the greater cylinder condensation in the latter, due to the greater temperature range. But with light loads it is very different. Hence condensing engines should be used, if possible, whenever the load is a very varying one. It is stated that at the electric station at Gothenburg the fuel consumption was reduced by sixty per cent. when condensers were added to the engines. This economy was obtained in spite of the fact that at full load the engines worked nearly as economically when non-condensing as when condensing. If the power of an engine is varied by varying its speed, instead of by varying the work per stroke, the speed being constant, then the conditions are different. If the power is varied by varying the speed, then the work against back pressure bears the same ratio to the effective work at all loads. Influence of the Type of Engine, the Speed, and the Mode of Regulation on the Thermal Efficiency.-It has already been pointed out that there are very large thermal losses in heat engines which are not shown on the indicator diagram, and which have a very important effect on economy of working. Those thermal losses are greater also at light loads than at full load, and they vary very much with the type of engine and some other conditions of working. Unfortunately, there is not a great deal of information available as to the steam consumption of different engines, except in the case of full load trials. There are the experiments of the late Mr. P. W. Willans, to which reference will be made presently. But, except these, there are very few which afford much guidance as to the relative economy of engines working with varying loads. 1 It is possible to get a good idea of the influence of conditions of working on the thermal efficiency in this way. Professor Cotterill has found a means of calculating the cylinder condensation in an unjacketed simple engine. The rest of the steam used can be ascertained in other ways. By examining the steam consumption in a variety of conditions for such an engine, a good deal of insight may be gained applicable to all cases. With the aid of Professor Cotterill's formula the steam consumption has been calculated for a number of cases and the results plotted in curves. Some check on the general bearing of these results can then be obtained by plotting in a similar way such experimental results as are available. An engine has been assumed working at full load in given conditions. Then the effect on the steam consumption of varying the speed, the initial steam pressure, and the ratio of expansion has been calculated. The results have been plotted in curves which give the steam consumption in pounds per i.h.p. hour at any fraction of full load. is the condensation per pound of steam admitted to the cylinder. Let p1 be the initial (absolute) steam pressure and p, the back pressure in pounds per square inch; v, the volume in cubic feet of a pound of steam at p1. Then the indicated work done on the piston per pound of steam not condensed is, In consequence of condensation the work per pound of steam The Steam Engine, 1890, chap. xi. actually used is reduced in the ratio 1 to 1 + in an engine in which condensation occurs, the effective work per pound of steam is But a h.p. hour is 1,980,000 ft. lbs. of work.. Consequently the number of pounds of steam required per i.h.p. hour will be c log, r) W = 1,980,000 (1 + dN 144 p,v, {1 + log, r — r Pb Pi For the following calculations the engine has been assumed to have a cylinder four feet in diameter, and the constant c has been taken equal to six. In considering the effect of speed, a slow engine working at 12 revolutions per minute, an ordinary engine working at 25 revolutions per minute, and a fast engine running at 50 revolutions per minute, have been assumed. The back pressure is taken at 3 lbs. per square inch for condensing, and at 16 lbs. per square inch for non-condensing engines. Methods of Regulation when the Load varies.-There are three ways in which the conditions of working may be varied when the power demand varies. The speed may be varied, as is often done in the case of pumping engines. The initial steam pressure may be varied, which alters the weight of steam used per stroke by altering the density of the steam. This may be done by varying the boiler pressure or by throttling the steam. Lastly, the expansion may be varied. A case of an engine has been taken and the effect on the steam consumption of these different ways of varying the power has been calculated. Figs. 8 and 9 show by curves the results both for condensing and noncondensing engines. The results are theoretical, but they have been compared with data from various engines, and they agree with them quite closely enough for the purpose of comparison. Strictly, however, these results are applicable only to unjacketed engines. CONDENSING ENGINES = CASE I.-Power Varied by Varying the Speed.-p1 = 110 lbs. per sq. in.; v, 3.99 c. ft.; normal ratio of expansion 4. The steam consumption for these conditions per i.h.p. hour is given in fig. 9. As the speed changes from 50 revolutions at full load to 64 revolutions at 12 per cent. of full load, the steam consumption rises from 18 lbs. to 25 lbs. per i.h.p. hour. CASE II.-The Initial Pressure Varied.-Normal ratio of expansion 4; p1 at full load 110. The results for a fast, ordinary, and slow engine are shown in fig. 9. CASE III.-Ratio of Expansion Varied.-p1=110. The steam consumption is calculated for a fast, an ordinary, and a slow engine. The ratio of expansion at full load is taken at 2 only. The results are given in fig. 9. It is due partly to the small expansion assumed for full load that the steam consumption per i.h.p. diminishes as the load diminishes. It would increase with small loads if different assumptions were made. NON-CONDENSING ENGINES The same cases with the same data are calculated and the results given in fig. 8. Only, for the case of varying expansion, the ratio of expansion at full load is taken at 4. The results are plotted in the curves shown in figs. 8 and 9. These curves cannot be taken as absolute guides, partly because a constant value for c has been taken, partly because the formula is only trustworthy within limits. Still, they are very instructive as indicating the way in which variation of load causes a variation in the steam consumption. Curves for Actual Engines Similar to the Theoretical Curves.In order to test how far the curves just given agree with tests of actual engines, curves drawn in the same way for some engine trials in which the engine was tested at different loads are given in figs. 10, 11, 12. It will be seen that although these curves embrace a remarkable variety of engines, the size, the speed, the type of engine, and the initial pressure all varying considerably, yet the curves for corresponding cases are very similar to the theoretical curves previously given. |