LOW LIFT PUMPING MACHINERY. LXXI. 
resultant shews the direction of the vanes at the circumference, 
the intermediate portion being filled in with any flat curve. These 
angles are not always adhered to for practical reasons, but it will 
be seen from the diagram that any variation in the speed of 
rotation or velocity of flow through the wheel, requires a different 
angle of vane to enable the pump to work without shock. 
The fan has to rotate at a peripheral velocity not less than V2gh 
= 8h per second, i being the height to which the water has to 
be lifted, this speed does not cover any losses in the pump, and the 
revolutions have to be increased, so as to give a peripheral speed 
in excess of that given by the formula s = ¥2gh, where s = 
velocity in feet per second of the outer circumference of the pump. 
This speed c Y¥2gh varies with the velocity v at which the water 
passes through the fan, and also depends upon the angle «, which 
the outer ends of the vanes make with the circumference. Figure 
7, shews the result obtained by the author on a large pump 
when delivering varying quantities of water, the different values 
of ¢ being plotted as absciss and the cubic feet of water delivered 
per second as ordinates. 
In a valuable paper by Professor Unwin on the “ Centrifugal 
Pump,” are given the formule connecting the speed of rotation, 
rate of delivery of water and efficiency for different angles of vanes 
for a pump with spiral casing, and also with whirlpool chamber, 
and in it he shews that the smaller the angle made by the vanes 
with the outer circumference up to 30°, the greater the theoretical 
efficiency will be, but that the speed at which the pump has to be 
driven also increases; the angle made by the vane with the inner 
circumference does not enter into the question of speed, but effects 
the efficiency, for with radial vanes that is 8 = 90°, the water 
entering the wheel has its direction suddenly changed, whereas if 
f is as drawn in Figure 6, there is no change in direction. 
Many attempts have been made to use the centrifugal pump for 
high lifts, but it has either meant a large fan, or an excessive 
1 Proceedings Inst. C.E., Vol. bx11. 
