and abscissæ the horizontal distances the plunger has moved, the area da'k' represents the work done by the retarded water in forcing the plunger forward, and the area d''f represents the work done in delivering the extra water during the suction stroke; and the work done under normal conditions is pro

portional to the area efnm; hence the discharge of the pump

under these conditions is greater in the ratio 1 +

area a'b'f

area efnm

to I. This ratio is known as the "discharge coefficient" of the pump. This quantity can be readily calculated for the case of a long connecting-rod thus

Let R = the radius of the crank in feet;

L= the length of connecting-rod in feet;

L

n = R

N = revolutions of the pump per minute;

w= the weight of a unit column of water 1 foot high and I sq. inch section = 0'434 lb.;

=

W weight of the reciprocating parts per square inch of plunger in pounds; in this case the weight of a column of water of 1 sq. inch sectional area and whose length is equal to that of the suction pipe, i.e. 0'434LwL;

P = the "inertia pressure" at the end of the stroke, i.e. the pressure required to accelerate and retard the column of water at the beginning and end of the stroke.

Then, if the suction pipe be of the same diameter as the pump plunger, we have P 0'00034WRN2, but if the area of the suction pipe be A,, and that of the plunger A,, we have, substituting the value of W given above

This value will not differ greatly from that found for a pump having a short connecting-rod when running at the same speed.

The discharge coefficients found by experiment agree quite closely with the calculated values, provided the pump is running under normal conditions, i.e. with the plunger always in contact with the water in the barrel.

Cavitation in Reciprocating Pumps.-During the suction stroke of a pump the water follows the plunger only so long as the absolute external pressure acting on the water is greater than that in the pump barrel; the velocity with which the water enters the barrel is due to the excess of external pressure over the internal, hence the velocity of flow into the barrel can never exceed that due to a perfect vacuum in the pump barrel plus the head of water in the suction sump above the barrel, or minus if it be below the barrel. In the event of the velocity of the plunger being greater than the velocity of

the surface speed of the water, the plunger leaves the water, and thereby forms a cavity between itself and the water. Later in the stroke the water catches up the plunger, and when the two meet a violent bang is produced, and the water-ram pressure then set up in the suction pipe and barrel of the pump is far higher than theory can at present account for. The "discharge coefficient," when cavitation is taking place, is also very much greater than the foregoing theory indicates.

The speed of the pump at which cavitation takes place is readily arrived at, thus

Adhering to the notation given above, and further—
Let h

= the suction head below the pump, i.e. the height
of the surface of the water in the sump below
the bottom of the pump barrel; if it be above,
this quantity must be given the negative sign;
= the loss of head due to friction in the passages
and pipes. Then the pressure required to
accelerate the moving water at the beginning of
the suction stroke, in this case when the plunger
is at the bottom of the stroke, is as before-

The height of the water-barometer may be taken as 34 feet, then the effective pressure driving the water into the pump barrel is (34-, - h)w. Separation occurs when this quantity is less than P; equating these two quantities, we get the maximum speed N, at which the pump can run without separation taking place, and reducing we get

That the theory and experiment agree fairly well will be seen from the following results :

The manner in which the "discharge coefficient" varies with the speed is clearly shown by Fig. 594d, which is one of the series of curves obtained by the author, and published in the Proceedings of the Institution of Mechanical Engineers, 1903.

The dimensions of the pump were

The manner in which the water ram in the suction pipe is dependent upon the delivery pressure is shown in Fig. 595. Direct-acting Steam-pumps. The term "directacting" is applied to those steam-pumps which have no crank or flywheel, and in which the water-piston or plunger is on the same rod as the steam-piston; or, in other words, the steam and water ends are in one straight line. They are usually made double acting, with two steam and two water cylinders. The relative advantages and disadvantages are perhaps best shown thus:

We have seen that, when a pump is driven by a uniformly revolving crank, the velocity of the piston, and consequently the flow, varies between very wide limits, and, provided there is a heavy flywheel on the crank-shaft, the velocity of the piston (within fairly narrow limits) is not affected by the resistance it has to overcome; hence the serious ramming effects in the pipes and pump chambers. In a direct-acting pump, however, the pistons are free, hence their velocity depends entirely on the water-resistance to be overcome, provided the steampressure is constant throughout the stroke; therefore the water is very gradually put into motion, and kept flowing much more steadily than is possible with a piston which moves practically irrespectively of the resistance it has to overcome. A diagram

Water ram pressure in suction pipe, Lbs. per sq. inch.

70

Revolutions per minute.

FIG. 595.