178

HYDRAULIC MACHINES—REMARKS ON PUMPS.

[Class V.

water through the pump. This fact cannot he too dis-tinctly stated. There are hydraulic machines whichyield, in the water raised, from 75 to 80 per cent, of thework done to raise it, and 00 per cent, is a common pro-portion ; but so imperfect an instrument is the lift andforce-pump, that the best yields only 45 per cent., theaverage not yielding more than 36 per cent. So that ifthat pump could be so improved as to be no more waste-ful of power than a well-made water-wheel, or a turbine,or Mr. Appold’s centrifugal pump; then the same powerapplied to it would raise from a given depth nearly twicethe amount of water that it now does. The causes ofthis loss of power are to be sought—

1st. In the small size and the peculiar construction ofthe valves.

2nd. In the proportion of the section of the barrel tothat of the suction and force pipes.

3rd. In the form of the suction-pipe at the extremitywhere the water enters it, and of the force-pipe at theextremity where the water is discharged.

4th. In the forms of these pipes where they unite withthe barrel.

5th. In the proportion of the length of the barrel tothe depth from which the water is raised.

It is impossible to say to what extent the loss of powerdue to these causes may be removed, without experimentsdirected expressly to that end; this much is, however,certain, that it would be sensibly diminished by increasingthe size of the valves, or by any other expedient whichshould diminish that sudden variation in the section ofthe stream which the valves create. That variation,attended as it is by a corresponding sudden variation ofthe velocity of the stream, involves a loss of power vary-ing as the square of the difference of the two velocities,*and dependent, therefore, on the ratios of the sections ofthe suction-pipe and force-pipe to the section of thebarrel. From inattention to this arises the second sourceof loss of power we have enumerated. It is well knownthat the form of the nozzle by which water is dischargedfrom a force-pump influences largely the amount of thedischarge, but it is not equally well known that the formof the extremity of the suction-pipe by which the waterenters has an equal effect in facilitating its ingress.f

A similar remark applies to that extremity of each pipeby which it communicates with the barrel, and the neglectof it accounts for a fourth source of the loss of power inpumps. A fifth cause to which attention appears nothitherto to have been directed, is the loss of power due tothe communication of an unnecessary velocity to thewater raised. Any one who gives a succession of quickstrokes to the piston of a common suction-pipe, allowingsufficient time between them for all the water which canfind its way into the barrel to enter it, will find the dis-charge per stroke to be considerably greater than whenthe piston is raised slowly. The reason of this is obvious;a certain amount of power, and no more, is required to bedone on the piston in order to raise enough water fromthe well to fill the barrel. If more than this is done, thesurplus manifests itself under the form of vis viva com-municated to the water, by which vis viva, if space beafforded for it to take effect (as in the common suetion-

* It is measured by half the vis viva due to the differenceof the velocities. This application of a theorem of Carnot,having reference to the impact of inelastic bodies, is due toM. Poncelet. It has been fully confirmed by experiment.

f It appears from the experiments of M. Eytelwein, thatby expanding that extremity of a pipe by which the waterenters, into a cone, the diameter of whose wider end is T2times that of the other, the contraction of the vein may benearly destroyed, the coefficient of the ingress beingincreased from *62 to *967. An analogous result may beproduced by expanding the extremity by which the water isdischarged. By uniting these expedients, a discharge maybe obtained which is greater than that due to the section of thepipe ; practically converting the contraction into an expan-sion of the fluid vein. If the length of the intervening pipebe nearly equal to its diameter, the coefficient of this expan-sion will be 1*35; if it be the length of sixty times thediameter, it will be 1 ‘ 17.—A/ori/i, Legons de Jllecaniquepratique , vol. ii., pp. 49, 50.

pump by efflux from the spout, or by the raising of thevalve in the bucket), more water is brought into the barrelthan is due to the volume generated by the piston. Halfthe vis viva of the water under the piston at the end ofthe stroke measures this surplus work. If a sufficientpause be allowed, and if the head of water above thepiston be not considerable, as in the common suction-pump, the upward rush of the water beneath it at the endof the stroke will lift its valve, and a portion of thesurplus work (represented by half the vis viva) will takeeffect in the elevation of more water into the barrel thanwould fill the space generated by the piston: and thus isexplained the fact of the greater discharge from suchpumps when worked by quick strokes with interveningpauses, than when worked slowly. If the head of waterabove the piston be, however, considerable, as in theforce-pump, any vis viva which may remain in the waterat the end of the stroke will produce a shock, and a cor-responding loss of power. This shock, commonly expe-rienced in the action of force-pumps, is accompanied by aviolent and prejudicial action of the valves, especiallywhen they are of metal. When the down-stroke of thepiston follows so rapidly on the up-stroke as to meetthe ascending stream produced by the preceding stroke,the resistance to its descent is increased, as well as the lossof power due to the commotion of the particles of the fluidit traverses.

It is obvious, therefore, that the proportions of a pump,to be worked by a given motive power, should be such,that the power to he expended at every stroke may justbring the water raised to rest, at the end of each stroke.*

It is immaterial in what proportions this work is dis-tributed over the stroke, or under what varying degreesof pressure it is generated, provided that the pressurenever exceeds that of the atmosphere on the surface ofthe piston.t If this pressure he exceeded, the piston mayseparate itself from the water beneath it in the barrel, thepump drawing air; and this is more likely to occur at thecommencement than at any other period of the stroke,the motion of the water at that point being necessarilyslow.

To communicate a finite velocity to the water at thecommencement of the stroke, or while the space describedby the piston is still exceedingly small, requires a muchgreater pressure than afterwards; and, the greater, as thesection of the suction-pipe is less, as compared with thatof the barrel, and as the lift is greater. Tims at thecommencement of the stroke a finite velocity of the pistoncan only be obtained by an extraordinary effort of themotive power associated with the chance of drawing airand of a shock, if the pressure be suddenly applied. Aremedy for some of these evils in the working of a pumplias been sought in the application to it of a second airvessel, communicating with the suction-pipe immediatelybelow the barrel, or with the top of the suction-pipe andthe bottom of the barrel. The commencement of eachstroke is eased by a supply of water from this air-chamberto the space beneath it. The influx of the water into that

* These proportions are determined without difficulty.If a represent the vertical height of the bottom of the bar-rel above the surface of the water to be raised, b the lengthof the stroke, K the section of the piston, and the weightof a cubic unit of water: then nK. b represents the weightof the water raised from the well into the barrel perstroke, and a + \ b is the height of its centre of gravityabove the surface from which it has been raised ; thereforeK t ib(a + ^b') represents the work done in raising it.Taking then U to be the work yielded by the motive powerper stroke, we have, in order that the whole of this workmay be expended in raising the water, and that there maybe no vis viva in it when all has been raised,

/ *> U

K/i b (g + l b) = U; whence b = a / a- + ^ — a.

V /ik

t If we conceive the stroke to be completed under aconstant pressure, which, with the assistance of the valve-reservoir, is possible, the extreme height to which the waterin the barrel will ascend is greater than that at which thispressure would hold it suspended without the closing of thesuction-valve.