Pump 11 stroke must be such that the rectangle MNAH may Por be greater than any rectangle that can be made of the parts of AN, that is, greater than the square of half AN. Or, if the length of the stroke be already fixed by other circumstances, which is a common case, we delivery si must make AN so short that the square of its half, mea- water. sured in feet, shall be less than 33 times the stroke of the piston. clasticity with the external. The space MA am, therefore, contains air of the common density and elasticity. These may be measured by h, or the weight of a column of water whose height is . Now, let the piston h. be drawn up to N n. The air which occupied the space MA am now occupies the space NAan, and its density MAam is now Its elasticity is now diminished, beNAan ing proportionable to its density (see PNEUMATICS), and no longer balances the pressure of the atmosphere. The valve G will therefore be forced up by the water, which will rise to some height SA. Now let the piston again descend to Mm It cannot do this with its valve shut; for when it comes down so far as to reduce the air again to its common density, it is not yet at M, because the space below it has been diminished by the water which got into the pipe, and is retained there by the valve G. The piston valve, therefore, opens by the air which we thus attempt to compress, and the superfluous air escapes. When the piston has got to M, the air is again of the common density, and occupies the space MS s m. Now draw the piston up to N. The air will expand into the space NSsn, and its density will be reMS s m duced to and its elasticity will no longer baNSsn' lance the pressure of the atmosphere, and more water will enter, and it will rise higher. This will go on continually. But it may happen that the water will never rise so high as to reach the piston, even though not 33 feet above the water in the cistern: For the successive diminutions of density and elasticity are a series of quantities that decrease geometrically, and therefore will have a limit. Let us see what determines this limit. At whatever height the water stands in the lower part of the pipe, the weight of the column of water SA as, together with the remaining elasticity of the air above it, exactly balances the pressure of the atmosphere (see PNEUMATICS, N° 108.). Now the elasticity of the air in the space NS sn is equal to h× fore, in the case where the limit obtains, rises no farther, we must have h=AS+h There and h=h-AS, HS, and NS: NS MS s m NS s n and the water MS sm NS s n , or, because the column is of the same diameter throughout, MS MS h=AS+NS' MS-HA: HS, and NS-MS: NS HA-HS: HA, or NM: NS=AS: AH, and NM× AH=NS XAS. Therefore, if AN, the distance of the piston in its highest position from the water in the cistern, and NM the length of its stroke, be given, there is a certain determined height AS to which the water can be raised by the pressure of the air: For AH is a constant quantity; and therefore when MN is given, the rectangle ASXSN is given. If this height AS be less than that of the piston in its lowest position, the pump will raise no water, although AN may be less than AH. Yet the same pump will raise water very effectually, if it be first of all filled with water; and we have seen professional engineers much puzzled by this capricious failure of their pumps. A little knowledge of the principles would have prevented their disappointment. To insure the delivery of water by the pump, the Suppose that the fixed valve, instead of being at the surface of the water in the cistern, is at S, or anywhere between S and A, the performance of the pump will be the same as before: But if it be placed anywhere above S, it will be very different. Let it be at T. It is plain that when the piston is pushed down from N to M, the valve at T prevents any air from getting down; and therefore, when the piston is drawn up again, the air contained in the space MT tm will expand into the MT This is less space NT t n, and its density will be ΝΤ which expresses the density of the air which Mode suring the MS than NS' was left in the space TS st by the former operations.The air, therefore, in TS s t will also expand, will open the valve, and now the water will rise above S. The proportion of SN to NT may be evidently such that the water will even get above the valve T. This diminishes the space NTn; and therefore, when the piston has been pushed down to M, and again drawn up to N, the air will be still more rarefied, and the water will rise still higher. The foregoing reasoning, however, is sufficient to show that there may still be a height which the water will not pass, and that this height depends on the proportion between the stroke of the piston and its distance from the water in the cistern, We need not give the determination, because it will come in afterwards in combination with other circumstances. It is enough that the reader sees the physical causes of this limitation: And, lastly, we see plainly that the utmost security will be given for the performance of the pump, when the fixed valve is so placed that the piston, when in its lowest position, shall come into contact with it. In this Valves t case, the rarefaction of the air will be the completest casily kept | possible; and, if there were no space left between the piston and valve, and all were perfectly air-tight, the rarefaction would be complete, and the valve might be any thing less than 33 feet from the surface of the water in the cistern. But this perfect contact and tightness is unattainable; and though the pump may be full of water, its continual downward pressure causes it to filtrate slowly through every crevice, and the air enters through every pore, and even disengages itself from the water, with which a considerable portion had been chemically com bined. The pump by this means loses water, and it requires several strokes of brisk working to fill it again: and if the leathers have become dry, so much admission may be given to the air, that the pump will not fill itself with water by any working. It is then necessary to po vater into it, which shuts up these passages, and 990 sets all to rights again. For these reasons it is always prudent ic place the fixed valve as low as other circumstances wil permit, and to make the piston rod of such a length, that when it is at the bottom of its stroke it shall be almost in contact with the valve. When 12 air-tight we Pump. 13 Descrip sucking pumpFig. 5. we are not limited by other circumstances, it is evident that the best possible form is to have both the piston and the fixed valve under the surface of the water of the cistern. In this situation they are always wet and airtight. The chief objection is, that by this disposition they are not easily come at when needing repair. This is a material objection in deep mines. In such situations, therefore, we must make the best compensation of differ. ent circumstances that we can. It is usual to place the fixed valve at a moderate distance from the surface of the water, and to have a hole in the side of the pipe, by which it may be got out. This is carefully shut up by a plate firmly screwed on, with leather or cement between the parts. This is called the clack door. It would, in every case, be very proper to have a fixed valve in the lower end of the pipe. This would combine all advantages. Being always tight, the pipe would retain the water, and it would leave to the valve above it its full effect of increasing the rarefaction. A similar hole is made in the working barrel, a little above the highest position of the piston. When this needs repair, it can be got at through this hole, without the immense trouble of drawing up the whole rods. Thus we have conducted the reader step by step, from the simplest form of the pump to that which long experience has at last selected as the most generally convenient. This we shall now describe in some detail. The SUCKING PUMP consists of two pipes DCCD, tion of the BAAB (fig. 5.); of which the former is called the Barrel, or the Working Barrel, and the other is called the Suction pipe, and is commonly of a smaller diameter.These are joined by means of flanches F, F, pierced with holes to receive screwed bolts. A ring of leather, or of lead, covered with a proper cement, is put between them; which, being strongly compressed by the screw-bolts, renders the joint perfectly air-tight. The lower end A of the suction-pipe is commonly spread out a little to facilitate the entry of the water, and frequently has a grating across at AA to keep out filth or gravel. This is immerged in the standing water YZ. The working barrel is cylindrical, as evenly and smoothly bored as possible, that the piston may fill it exactly through its whole length, and move along it with as little friction as may be consistent with air-tightness. 7. The piston is a sort of truncated cone OPKL, generally made of wood not made to slip, such as elm or beech. The small end of it is cut off at the sides, so as to form a sort of arch OQP, by which it is fasten ed to the iron rod or spear. It is exhibited in different Fig. 6. and positions in figures 6, 7. which will give a more distinct notion of it than any description. The two ends of the conical part may be hooped with brass. This cone has its larger end surrounded with a ring or band of strong leather fastened with nails, or by a copper hoop, which is driven on at the smaller end. This band should reach to some distance beyond the base of the cone; the farther the better: and the whole must be of uniform thickness all round, so as to suffer equal compression between the cone and the working barrel. Necessity of The seam or joint of the two ends of this band must air-tight be made very close, but not sewed or stitched together. ness not This would occasion bumps or inequalities, which would properly attended o. spoil its tightness; and no harm can result from the want of it, because the two edges will be squeezed close together by the compression in the barrel. It is hy no 14 means necessary that this compression be great. This Pump. is a very detrimental error of the pump-makers. Itoccasions enormous friction, and destroys the very purpose which they have in view, viz. rendering the piston air-tight; for it causes the leather to wear through very soon at the edge of the cone, and it also wears the working barrel. This very soon becomes wide in that part which is continually passed over by the piston, while the mouth remains of its original diameter, and it becomes impossible to thrust in a piston which shall completely fill the worn part. Now, a very moderate pres-An easy sure is sufficient for rendering the pump perfectly tight, mode of and a piece of glove leather would be sufficient for this rendering purpose, if loose or detached from the solid cone; for pumps suppose such a loose and flexible, but impervious, band tight. of leather put round the piston, and put into the barrel; and let it even be supposed that the cone does not compress it in the smallest degree to its internal surface.Pour a little water carefully into the inside of this sort of cup or dish; it will cause it to swell out a little, and apply itself close to the barrel all round, and even adjust itself to all its inequalities. Let us suppose it to touch the barrel in a ring of an inch broad all round. We can easily compute the force with which it is pressed. It is half the weight of a ring of water an inch deep and an inch broad. This is a trifle, and the friction occasioned by it not worth regarding; yet this trifling pressure is sufficient to make the passage perfectly impervious, even by the most enormous pressure of a high column of incumbent water: for let this pressure be ever so great, the pressure by which the leather adheres to the barrel always exceeds it, because the incumbent fluid has no preponderating power by which it can force its way between them, and it must insinuate itself precisely so far, that its pressure on the inside of the leather shall still exceed, and only exceed, the pressure by which it endeavours to insinuate itself; and thus the piston becomes perfectly tight with the smallest possible friction. This reasoning is perhaps too refined for the uninstructed artist, and probably will not persuade him. To such we would recommend an examination of the pistons and valves contrived and executed by that cable from artist, whose skill far surpasses our highest conceptions, the human. the all-wise Creator of this world. The valves which frame. shut up the passage of the veins, and this in places where an extravasation would be followed by instant death, are cups of thin membrane which adhere to the sides of the channel about half way round, and are detached in the rest of their circumference. When .16 Proved to be practi Best form the blood comes in the opposite direction, it pushes the membrane aside, and has a passage perfectly free. But a stagnation of motion allows the tone of the muscular (perhaps) membrane, to restore it to its natural shape, and the least motion in the opposite direction causes it instant-ly to clap close to the sides of the vein, and then no 17 pressure whatever can force a passage. We shall recur of a pisto this again, when describing the various contrivances to recom of valves, &c. What we have said is enough for sup-mended. porting our directions for constructing a tight piston. But we recommended thick and strong leather, while our present reasoning seems to render thin leather preferable. If the leather be thin, and the solid piston in any part does not press it gently to the barrel, there will be in this part an unbalanced pressure of the incumbent, column of water, which would instantly burst.even s Pump. a strong leather bag; but when the solid piston, cover- Further de- At the joining of the working barrel with the suc- Fig. 8. Fig. 9. Fig. 10. 19 Its mode of operation. with it, or it is made in a separate plate. This last is if the pipe be only so wide, that the barrels shall fill Pump It is plain that there will be limitations to the rise of the water in the suction-pipe, similar to what we found when the whole pump was an uniform cylinder. Let a be the height of the fixed valve above the water in the cistern: let B and b be the spaces in cubic measure between this valve and the piston in its highest and lowest positions, and therefore express the bulks of the air which may occupy these spaces: let y be the distance between the fixed valve and the water in the suction-pipe, when it has attained its greatest height by the rarefaction of the air above it: let h be the height of a column of water in equilibrio, with the whole pressure of the atmosphere, and therefore having its weight in equilibrio with the elasticity of common air; and let a be the height of the column whose weight balances the elasticity of the air in the suction-pipe, when rarefied as much as it can be by the action of the piston, the water standing at the height a-y. Then, because this elasticity, together with the column a-y in the suction-pipe, must balance the whole pressure of the atmosphere, (see PNEUMATICS, N° 108.), we must have ha+a—y, and y=a+ x-h. When the piston was in its lowest position, the bulk of the air between it and the fixed valve was b. Suppose the valve kept shut, and the piston raised to its highest position, the bulk will be B, and its density b b weight will balance it, will be h. If the air in the Β ́ suction-pipe be denser than this, and consequently more The reader will now understand, without any repeti-, and its elasticity, or the height of the column whose tion, the process of the whole operation of a suckingpump. The piston rarefies the air in the working bar rel, and that in the suction-pipe expands through the valve into the barrel; and, being no longer a balance for the atmospheric pressure, the water rises into the suction-pipe; another stroke of the piston produces a similar effect, and the water rises farther, but by a smaller step than by the preceding stroke: by repeating the strokes of the piston, the water gets into the barrel; and when the piston is now pushed down through it, it gets above the piston, and must now be lifted up to any height. The suction-pipe is commonly of smaller size than the working barrel, for the sake of economy. is not necessary that it be so wide; but it may be, and often is, made too small. It should be of such a size, that the pressure of the atmosphere may be able to fill the barrel with water as fast as the piston rises. If a void is left below the piston, it is evident that the piston must be carrying the whole weight of the atmosphere, besides the water which is lying above it. Nay, fixed valve, y becoming negative. It We had ya+x-h. Therefore y=a+ —h,= a + B - B-b b B B-b a is less than h, the water will get above the But Pump. 20 The same pump is used in an inverted position; Fig. 11. 21 and is cal But it does not follow that the water will reach the piston, that is, will rise so high that the piston will pass through it in its descent. Things now come into the condition of a pump of uniform dimensions from top to bottom; and this point will be determined by what was said when treating of such a pump. There is another form of the sucking-pump which is much used in great water works, and is of equal efficacy with the one now described. It is indeed the same pump in an inverted position. It is represented in fig. 11. where ABCD is the working barrel, immersed, with its mouth downwards, in the water of the cistern. It is joined by means of flanches to the rising pipe or MAIN. This usually consists of two parts. The first, BEFC, is bent to one side, that it may give room for the iron frame TXYV, which carries the rod NO of the piston M, attached to the traverses RS, TOV of this frame. The other part, EGHF, is usually of a less diameter, and is continued to the place of delivery. The piston frame XTVY hangs by the rod Z, at the arm of a lever or working beam, not brought into the figure. The piston is perforated like the former, and is surrounded like it with a band of leather in form of a taper-dish. It has a valve K on its broad or upper base, opening when pressed from below. The upper end of the working barrel is pierced with a hole, covered with a valve I, also opening upwards. Now suppose this apparatus immersed into the cistern till the water is above it, as marked by the line 2, 3, and the piston drawn up till it touch the end of the barrel. When the piston is allowed to descend by its own weight, the water rises up through its valve K, and fills the barrel. If the piston be now drawn up by the moving power of the machinery with which it is connected, the valve K shuts, and the piston pushes the water before it through the valve I into the main pipe EFGH. When the the piston is again let down, the valve I shuts by its own weight and the pressure of the water incumbent on it, and the barrel is again filled by the water of the cistern. Drawing up the piston pushes this water into the main pipe, &c. and then the water is at length delivered at the place required. This pump is usually called the lifting pump; perhaps led a lift the simplest of all in its principle and operation. It needs no farther explanation: and we proceed to describe ing pump. 22 Forcing scribed. Fig. 12. The FORCING PUMP, represented in fig. 12. It pump de- consists of a working barrel ABCD, a suction-pipe CDEF, and a main or rising pipe. This last is usually in three joints. The first GHKI may be considered as making part of the working barrel, and is commonly cast in one piece with it. The second IKLM is joined to it by flanches, and forms the elbow which this pipe must generally have. The third LNOM is properly the beginning of the main, and is continued to the place of delivery. At the joint IK there is a hanging valve or clack S; and there is a valve R on the top of the suction-pipe. The piston PQTV is solid, and is fastened to a stout iron rod which goes through it, and is fixed by a key drawn through its end. The body of the piston is a sort of double cone, widening from the middle to each end, and is covered with two bands of very strong leather, fitted to it in the manner already described. 23 Its mode of operation, The operation of this pump is abundantly simple. Pump. When the piston is thrust into the pump, it pushes the air before it through the valve S, for the valve R remains shut by its own weight. When it has reached near the bottom, and is drawn up again, the air which filled the small space between the piston and the valve S now expands into the barrel; for as soon as the air begins to expand, it ceases to balance the pressure of the atmosphere, which therefore shuts the valve S. By the expansion of the air in the barrel the equilibrium at the valve R is destroyed, and the air in the suction-pipe lifts the valve, and expands into the barrel; consequently it ceases to be a balance for the pressure of the atmosphere, and the water is forced into the suction-pipe. Pushing the piston down again forces the air in the barrel through the valve S, the valve R in the mean time shutting. When the piston is again drawn up, S shuts, R opens, the air in the suction-pipe dilates anew, and the water rises higher in it. Repeating these operations, the water gets at last into the working barrel, and is forced into the main by pushing down the piston, and is pushed along to the place of delivery. 24 The operation of this pump is therefore two-fold, Is two fold. sucking and forcing. In the first operation, the same force must be employed as in the sucking-pump, namely, a force equal to the weight of a column of water having the section of the piston for its base, and the height of the piston above the water in the cistern for its height. It is for the sake of this part of the operation that the upper cone is added to the piston. The air and water would pass by the sides of the lower cone while the piston is drawn up; but the leather of the upper cone applies to the surface of the barrel, and prevents this. The space contained between the barrel and the valve S is a great obstruction to this part of the operation, because this air cannot be rarefied to a very great degree. For this reason, the suction pipe of a forcing-pump must not be made long. It is not indeed necessary; for by placing the pump a few feet lower, the water will rise into it without difficulty, and the labour of suction is as much diminished as that of impulsion is increased. However, an intelligent artist will always endeavour to make this space between the valve S and the lowest place of the piston as small as possible. The power employed in forcing must evidently surmount the pressure of the whole water in the rising pipe, and (independent of what is necessary for giving the water the required velocity, so that the proper quantity per hour may be delivered), the piston has to withstand a force equal to the weight of a column of water having the section of the piston for its base, and the perpendicular altitude of the place of delivery above the lower surface of the piston for its height. It is quite indifferent in this respect what is the diameter of the rising pipe; because the pressure on the piston depends on the altitude of the water only, independent of its quantity. We shall even see that a small rising pipe will require a greater force to convey the water along it to any given height or distance. When we would employ a pump to raise water in a crooked pipe, or in any pipe of moderate dimensions, this form of pump, or something equivalent, must be used. In bringing up great quantities of water from mines, the common sucking-pump is generally employ. ed, ! Pamp. 25 delivered by any .pump. ed, as really the best of them all; but it is the most expensive, because it requires the pipe to be perpendicular, straight, and of great dimensions, that it may contain the piston rods. But this is impracticable when the pipe is crooked. If the forcing pump, constructed in the manner now described, be employed, we cannot use forcers with long rods. These would bend when pushed down by their further extremity. In this case, it is usual to employ only a short and stiff rod, and to hang it by a chain, and load it with a weight superior to the weight of water to be raised by it. The machinery therefore is enployed, not in forcing the water along the rising-pipe, but in raising the weight which is to produce this effect by its subsequent descent. In this case, it would be much better to employ the lifting-pump of fig. 11. For as the load on the forcers must be greater than the resistances which it must surmount, the force exerted by the machine must in like manner be greater than this load. This double excess would be avoided by using the lifting-pump. Measure of It will readily occur to the reader that the quantity the quanti- of water delivered by any pump will be in the joint proty of water portion of the surface or base of the piston and its velocity for this measures the capacity of the part of the working barrel which the piston passes over. The velocity of the water in the conduit pipe, and in its passage through every valve, will be greater or less than the velocity of the piston, in the same proportion that the area of the piston or working barrel is greater or less than the area of the conduit or valve. For whatever quantity of water passes through any section of the working barrel in a second, the same quantity must go through any one of these passages. This enables us to modify the velocity of the water as we please: we can increase it to any degree at the place of delivery by diminishing the aperture through which it passes, provided we apply sufficient force to the piston. 26 The operation of pumps not 27 and the mode of making them so. It is evident that the operation of a pump is by starts, and that the water in the main remains at rest, pressing on the valve during the time that the piston is withdrawn equable; from the bottom of the working barrel. It is in most cases desirable to have this motion equable, and in some cases it is absolutely necessary. Thus, in the engine for extinguishing fires, the spout of water going by jerks could never be directed with a certain aim, and half of the water would be lost by the way; because a body at rest cannot in an instant be put in rapid motion, and the first portion of every jerk of water would have but a small velocity. A very ingenious contrivance has been fallen upon for obviating this inconvenience, and procuring a stream nearly equable. We have not been able to discover the author. At any convenient part of the rising-pipe beyond the valve S there is annexed a capacious vessel VZ (fig. 13. N° 1. and 2.) close a-top, and of great strength. When the water is forced along this pipe, part of it gets into this vessel, keeping the air confined above it, and it fills it to such a beight V, that the elasticity of the confined air balances a column reaching to T, we shall suppose, in the rising-pipe. The next stroke of the piston sends forward more water, which would fill the rising-pipe to some height above T. But the pressure of this additional column causes some more of it to go into the air vessel, and compress its air so much more that its elasticity now balances a longer co5 Fig. 13. lumu. Every succeeding stroke of the piston produces a like effect. The water rises higher in the main pipe, but →→ some more of it goes into the air vessel. At last the water appears at the place of delivery; and the air in the air vessel is now so much compressed that its elasticity balances the pressure of the whole column. The next stroke of the piston sends forward some more water. If the diameter of the orifice of the main be sufficient to let the water flow out with a velocity equal to that of the piston, it will so flow out, rising no higher, and producing no sensible addition to the compression in the air vessel. But if the orifice of the main be contracted to half its dimensions, the water sent forward by the piston cannot flow out in the time of the stroke without a greater velocity, and therefore a greater force. Part of it, therefore, goes into the air vessel, and increases the compression. When the piston has ended its stroke, and no more water comes forward, the compression of the air in the air vessel being great. er than what was sufficient to balance the pressure of the water in the main pipe, now forces out some of the water which is lying below it. This cannot return towards the pump, because the valve S is now shut, It therefore goes forward along the main, and produces an efflux during the time of the piston's rising in order to make another stroke. In order that this efflux may be very equable, the air vessel must be very large. If it be small, the quantity of water that is discharged by it during the return of the piston makes so great a portion of its capacity, that the elasticity of the confined air is too much diminished by this enlargement of its bulk, and the rate of efflux must diminish accordingly. The capacity of the air vessel should be so great that the change of bulk of the compressed air during the inaction of the piston may be inconsiderable. It must therefore be very strong. It is pretty indifferent in what way this air vessel is connected with the rising-pipe. It may join it laterally, as in fig. 13. N° 1. and the main pipe go on with out interruption; or it may be made to surround av interruption of the main pipe, as in fig. 13. N° 2. It may also be in any part of the main pipe. If the sole effect intended by it is to produce an equable jet, as in ornamental water-works, it may be near the end of the main. This will require much less strength, because there remains but a short column of water to compress the air in it. But it is, on the whole, more advanta geous to place it as near the pump as possible, that it may produce an equable motion in the whole main pipe. This is of considerable advantage: when a column of water several hundred feet long is at rest in the main pipe, and the piston at one end of it put at once into motion, even with a moderate velocity, the strain on the pipe would be very great. Indeed if it were possible to put the piston instantaneously into motion with a finite velocity, the strain on the pipe, tending to burst it, would be next to infinite. But this seems impossible in The des nature; all changes of motion which we observe are gra-tery m dual, because all impelling bodies have some elasticity tion of or softness by which they yield to compression. And, in the way in which pistons are commonly moved, viz. by cranks or something analogous to them, the motion is very sensibly gradual. But still the air vessel tends to make the motion along the main pipe less desultory, and therefore diminishes those strains which would really take place the po |