Oct. 2, 1885. THE ENGINEER. 253 boiler and condenser pressures, with the same measure of WHY THE COMPOUND ENGINE IS NEW HYDRAULIC FORMULAE. expansion and the same reciprocating speed of piston, is due By W. Donaldson , C.E. ECONOMICAL. to the fact that the steam condensed in the small cylinder by Tiie ordinary formula for the uniform velocity of flow We publish this week a very remarkable paper by Mr. the interaction of its metal is used upon the piston of the in pipes and open channels is of the form Isherwood, which we copy from the last number of the Jour- large one during its whole stroke, and expansively too nal of the Franklin Institute. This paper bears strongly on the if a cut-off be applied there." The italics are ours. In v = A. sj r s much vexed question, What is the most economical ratio of other words, the compound engine is economical, not in which v is the velocity in feet per second, r the hydraulic expansion? and we direct the attention of our readers to because the condensation of steam is prevented, but mean radius in feet, and s the rate of inclination. This it as a document deserving their most careful considera­ because its re-evaporation is utilised in a way which is not formula is based on the assumption that the retarding tion. Mr. Isherwood gives in it what seems to us to be a quite so easily attained, if indeed it can be attained at all, force of friction is directly proportional to the square of perfectly rational, albeit novel, explanation of the reason in the single-cylinder engine. There can be no doubt that the velocity at any instant, and inversely proportional to why a compound engine ought to be more economical than a many persons have held views on thissubject nearly identical the hydraulic mean radius. When the velocity, therefore, simple engine; and this explanation, we may add, has with Mr. Isherwood ’s. We are ourselves among the has reached its maximum value due to the rate of incli­ nothing whatever to do with one repeatedly put forward, number, but we are not aware that any writer has ever nation and size and shape of the channel, the retarding notwithstanding that its fallacy has been over and over before put the proposition so clearly, concisely, and defi­ force of friction is constant, and on the above hypothesis again demonstrated—namely, the “heat trap” theory. nitely. It must not be forgotten that although Mr. is equal to c -v* ■ , c being a constant determined by expe- That is to say, the assumption that the low-pressure cylinder Isherwood is speaking of an engine with two cylinders r prevents a large change of temperature causing condensation only, the same reasoning will apply to the triple expan­ riment. Since the angle 6 between the horizontal and the in the high-pressure cylinder. Mr. Isherwood ’s paper is sion engine. We are thus brought face to face with what line of the direction of the pipes is always small, the something much more than a translation of the report is virtually a new theorem, namely, that the best way to accelerating force of gravity is equal to g sin. 0 — g tan. 0 = made by a committee of German engineers. In 18/8 the secure economy in steam engine practice lies not so much g s, and this, when the velocity is constant, must be equal Industrial Society of Mulhouse offered a medal of honour in avoiding cylinder condensation, as in taking care that to the force of retardation due to friction. Therefore for the first compound engine built in Alsace that would give the work done in re-evaporation shall be utilised. Steam c v* a French horse-power—32,544 foot-pounds per minute—for is condensed at one pressure, comparatively high, and it is not more than 9 kilogrammes, or about 19'84 lb., of steam revaporised at another pressure comparatively low, and whence v — A. r 8 used per hour—equivalent to about 17'44 lb. per English it may be argued that the work done by this low-pressure horse-power. The action of the Industrial Society is highly steam must be less than would have been done had no con­ the ordinary formula. Now it has been found by experi­ to be commended, and it is to be regretted that no similar densation taken place. This argument is sound, but it is not so ment that the value of A is not constant, but varies with stimulus to improvement is ever offered in this country. important as may appear at first sight. Let us suppose, for the varying values of the hydraulic mean radius. D’Arcy In 1879 the challenge was accepted by Messrs. Weyher example, that a pound of steam was received from a boiler and Bazin assume that A is a function of r of the form— 1 and Richemonde under circumstances which Mr. Isherwood and expanded in a non-condensing cylinder, so that no con­ fully sets forth. The result of the trial was that their densation other than that due to the performance of work engine won the prize. Three distinct experiments were took place. This being a constant quantity determined by made with steam expanded 6'25 times, the consumption of the amount of work done and by nothing else we may So that Alias an appreciably different value forevery section. feed-water being at the rate of 17 T lb. per English horse­ neglect it. Let the initial pressure be 100 lb. absolute, then In considering this question it struck me that the necessity power per hour. One experiment was made with steam one pound of such steam can do without expansion 58,273 of adopting this varying value of A arose from assuming expanded 9'64 times, the weight of feed-water used being foot-pounds. If we expand it 6’2 times it can do 150,630 that for all sizes of pipes the retardation caused by friction 16 93 lb. Thus no practical advantage whatever was foot-pounds, or nearly three times as much as it did without is inversely as the first power of the hydraulic mean radius, gained from the higher ratio of expansion. As the expansion. But it may be shown that the work done during and that a formula of the form— experiment was intended to settle the value of expansion expansion is very little affected by the pressure of the y = A r n f 8 per se without introducing complications in the way of steam. Between the extremes of 65 lb. to 165 lb. on might be obtained which would give the same values for v alterations of pressure, the initial pressure was as nearly as the square inch, Mr. Clark has shown that the as those ascertained experimentally for wide ranges of the possible the same in all four experiments, namely, about difference of efficiency is not more than about 2£ value of the hydraulic mean radius, the constant A and 92 lb. per square inch. For details we must refer our per cent, in favour of the higher pressure. If, then, index n being taken as the mean of a series of values. readers to the comprehensive table which will be found on one-tentli of all the steam admitted to the cylinder Before giving a description of the method I adopted for page 266. be condensed during the steam stroke, and re-evaporated determining these values, I propose to discuss briefly the This investigation supplies matter for consideration by and worked expansively during the exhaust stroke, the loss question, Does the retardation caused by friction vary as those who still maintain that the—to them—otherwise caused by the initial condensation may be very small. The the square of the uniform velocity or simply as the first unaccountable economy of the compound engine is due to initial pressure maybe 1001b., corresponding to a tem­ oower? I believe that some authorities maintain the last the protection afforded by the large cylinder to the small perature of 328 deg. ; but the total heat given up by one aw to be correct. It is a point which can be set at rest one, and the consequent prevention of condensation in the pound of this steam condensed cannot be more than 1181 deg. by experiments in any pumping station from which the latter. It is a curious aspect of this controversy that no and will be considerably less in proportion as the cylinder rising main is free from obstructions, sudden contractions one has ever yet given or attempted to give any direct is hotter than 32 deg. The total heat required to recon­ or enlargements, and ought not therefore to be a question proof that condensation is reduced ; while, on the other vert this condensed 1001b. steam into steam of, say, 30 lb. in dispute. I have never availed myself of many oppor­ hand, we cannot call to mind particulars of a single pressure will be 1158 deg., or 26 deg. less. That is to say, tunities of doing this, but a friend has given me the experiment in which the condensation in the high-pressure the heat surrendered during condensation by a pound of following particulars, which I think have enabled me to cylinder of a compound engine has not been enormous. steam of one pressure is amply sufficient to produce settle the question. 1 n the case under consideration it will be seen that when another pound of steam at a somewhat lower pressure—a The engines referred to are beam engines of the very the small ran ge of expansion—6'25 times—was employed, fact the truth of which is demonstrated, indeed, every day best construction, which, working at the rate of 14 strokes no less than aibout one-fourth of all the steam admitted to by the use of steam for evaporating purposes.