THE SUCTION AND LIFTING PUMP.

363

259. In the common suction pump of domestic use the upper valve is placed in the bucket or piston, so that water passes through the bucket and is lifted by it, when the upper valve closes, to the desired level (fig. 80).

If the piston rod is thickened so that its cross section is about half that of the pump barrel, half the water will be ejected during the down stroke of the bucket, and a more equable flow is thereby secured,

The suction of a pump is the height reckoned from the surface of the water supply to the lower valve, but the height of the discharge above the lower valve is the height to which the water is forced or lifted.

When the lift of the pump is considerable, a relief valve, opening upwards, is placed in the discharge pipe, and the barrel is closed with a cover and stuffing box, through which the piston rod works; the lower fixed valve may now be dispensed with, and this arrangement is called a Lifting Pump; but if the bucket valve is suppressed, the water is raised in the down stroke, and this is called a Forcing Pump (fig. 8).

The suction is limited theoretically by the barometric head of water, about 33 ft or 10 m, but water can be lifted or forced to an indefinite height; the suction and forcing pumps of a mine or of the pumping engines of water works must therefore be placed at a low level, very nearly that of the water supply.

Instances are recorded in which the suction of a pump has reached even 40 ft; but in such cases the water must be highly aerated; so that we may consider the column in the suction pipe as composed of alternate strata of liquid and air, as in the Sprengel pump (§ 275), instead of continuous solid water.

364

LIMITATIONS OF WORKING

Denote by a and ẞ the cross section, in ft2, of the suction pipe AO and barrel OB of a vertical suction pump, by a the height of the suction pipe, and by b and c the greatest and least height, OB and OC, of the lower side of the bucket P above the lower fixed valve 0 (fig. 80).

Then in the nth stroke, while the pump is sucking, the water rises in the suction pipe AO from a height xn-1 to xn ft above the level A of the supply, and the air above the column changes in density from Pn-1 to

and the tension of the pump rod increases from

Dẞxn-1 to Dẞxn lb.

Also by Boyle's law,

so that

where

a(a−xn)Pn+ẞbpn= a(a — Xn-1) pn-1+ßcp ;

a{ (α − xn−1)(H − x n − 1)−(α − xn)(H − xn)} = ß{b(H−xn)−cH}, a quadratic equation for x, in terms of n-1, of which the positive root must be taken, the negative root corresponding to a different physical problem.

This equation may be written

B(b−c)—a(xn−în-1)= ß(b−c)(a−xn−1)+cxn ̧

H+a-Xn-Xn-1

and the second member being positive, it follows that a(xn-Xn-1), the volume which enters the suction pipe in the nth stroke, is less than B(b-c), the volume swept out by the bucket.

The water will reach the barrel in the first stroke if x1=α, x。 being zero; and therefore if

It will just reach the barrel in the second stroke, if x=a; and the condition is obtained by eliminating x1 between the equations

a(a− x1)(H−x1)= ß{b(H− a )—cH}, a{aH−(a−x1)(H − x1) = ß{b(H—x ̧)—cH};

and so on.

If the pump will not suck, then an is always less than a; and the greatest height x to which the water rises in the suction pipe is obtained by putting

Pn=Pn-1, Xn-Xn-1= x;

a(a−x)(H−x)+ßcH= a(a−x)(H−x)+ßb(H − x),

The first requisite for the pump to work is therefore

so that water can be drawn through the lower valve.

260. Now if xm-1 and xm denote the height above the level of the supply of the water in the barrel at the beginning and end of the mth stroke, the air which occupied a length a+c-xm-1 of the barrel under a head H at the beginning of the stroke will at the end occupy a length a+b-xm under a head H-xm; so that,

(a+b−xm)(H−xm) = (a+c− xm - 1)H,

a quadratic for determining xm in terms of xm-1.

Also the tension of the pump rod, due to the pressure of the air, increases from zero to Dẞam during the stroke; and if the lower valve O opens when the pressures above and below are equal, the bucket has then risen a distance z, given by сн

+xm―α= H−a, or

=

c+ z

с

Xxm
H-Xm

Similarly the position of the bucket in the down stroke when its valve opens can be determined.

The greatest height to which the water can be drawn in the barrel, provided it does not reach the bucket, is obtained by putting xm-1=xm=x; and therefore

x={(a+b)+√/{4(a+b)2−(b−c)H};

and therefore a requisite condition is

(b−c)H<{(a+b)2, or BC<AB2/H;

otherwise the water would sink during the successive strokes; and the least value of x is thus (a+b).

Finally for the pump to draw, C must be below this level; and now, in full working order with the passages full of water, if h denotes the height of the discharge above the lower valve, and y the height of the bucket at any part of the stroke, the tension of the pump rod is DB(H+h—y)—Dß(H—a—y)=Dß(a+h) lb;

so that the work done in one stroke is

DB(a+h)(b-c) ft lb;

the work required to lift the volume of water ß(b−c) ft3 through a+h ft.

261. Air Pumps.

In the ancient method of producing a vacuum, as invented by Otto von Guericke, 1650, the vessel to be exhausted (the Magdeburg hemispheres, for instance) was first filled with water, which was afterwards pumped out by a water pump.

The mechanical improvements of the pump made by Boyle, Hooke, and Hauksbee enabled them to dispense with the water, and to construct the true air pump, as we have it nowadays.

Two suction pumps, side by side, actuated in opposite directions by racks on the piston rods engaging in a

OF HAUKSBEE, SMEATON, AND TATE.

367

toothed wheel between them, worked in a reciprocating motion by a handle, constitute Hauksbee's air pump; and two pumps are used, so that the atmospheric pressure on the tops of the pistons should balance them in any position.

The pumps draw the air through a pipe which terminates in the centre of a horizontal brass plate, upon which the glass jar or receiver, which is to be exhausted, has been placed, the lower edge of the glass having been ground and greased so as to make an air-tight contact with the brass plate.

262. Smeaton's air pump is essentially the lifting pump; he formed it by closing the top of Hauksbee's air pump with a cover, provided with a stuffing box for the piston rod and a valve opening outwards; the piston is thereby relieved from the pressure of the air during the greater part of the stroke, so that two pumps, balancing each other, are not required.

The lower fixed valve may also be dispensed with; and the piston valve too, if the pipe communicating with the receiver enters the side of the barrel at a distance from the bottom a little over the thickness of the piston.

These principles are illustrated in Tate's air pump, consisting of a double acting pump and the receiver (fig. 81); the piston is made long and provided with cannelures, by which leakage of air past it is prevented, in spite of the absence of packing; which may however be supplied by cupped leathers, as in figs. 11, 12, p. 23.

A valve at each end, consisting of a small flap of oiled silk covering from the outside a narrow slit, permits the escape of the air when compressed to the atmospheric pressure; no valve is required in the middle, as the