PUMPS 515 
8,V, =, cos 0, =, is the velocity of whirl of the water as it enters 
the wheel, and § V. 9 =, 008 9, = wy is the velocity of whirl of the water 
as it leaves the w eel, 
It is generally cabal that the velocity of 
whirl at entrance is zero, that is, the direction 
_ of motion of the water at entrance is radial, as 
_ shown in Fig. 825. In this case tan ¢ =s,/¢,. 
The radial velocity of flow through ‘de wheel 
may be from 2. to 10 feet per second, and is com- 
monly about 5 feet per second. 
444. Work Imparted to the Water by the 
Wheel.—The increase in the angular momentum of 
1 Ib. of water in parsing through the wheel of a 
centrifugal pump is : L (wre —W,7,), and this is equal 
Fig. 825. 
to T, the turning moment on the wheel. Hence if 
is the angular velocity of the wheel in radians per second, the work 
done per second per pound of water passing through the wheel is 
To = ; (warQo — wr) = - (WoC —W,e,). (See also Art. 419, p. 482.) 
If w, is zero, then To=-t3. 
_ If H is the maximum theoretical head or the height to which the 
fc oo will raise the water, neglecting all losses, then obviously 
H= = (040 - w,¢,), and when w,=0, H= are 
445. Efficiencies of Centrifugal Pumps, —lIf v denotes the velocity 
of the water as it leaves the delivery pipe, then the energy or head loss 
on account of this velocity is 2 per lb. of water delivered. The loss of 
energy or head in friction in the suction and delivery pipes may be 
computed as in Article 404, p. 462. Let the loss due to friction in the 
pipes be denoted by hi, and let A be the actual height through which the 
water is raised by the pump, then H,=Ah+/, + is called the gross 
head or gross lift of the pump. 
The ratio of the gross head H, to the maximum theoretical lift H 
(see preceding Article) is called the hydraulic efficiency of the pump. 
Except in small lifts the term 5 is unimportant, and for small lifts 
the term h, is unimportant. The velocity v may be reduced by making 
the delivery end of the pipe bell-mouthed. 
The actual or commercial efficiency of a centrifugal pump is the ratio 
of the work represented by the product of the weight of water raised, 
and the height to which it is raised to the work done in driving the shaft 
of the pump. 
2 
The kinetic energy or velocity head (3:) of the water as it leaves the 
wheel can only be utilised for lifting the water by first converting it into 
