514 APPLIED MECHANICS 
the delivery pipe, which is connected to the pump casing at H. 
expanding chamber or volute F, which collects the water from the wheel, 
has a varying radial section proportioned to the quantity of water 
through it in a given time, so that the mean velocity of the water in the 
volute is uniform. 
The object of the volute is to gradually reduce the velocity of the 
water after it leaves the wheel, and so convert part of its kinetic energy : 
into pressure energy. 
A centrifugal pump will not act unless it is fully charged with water. 
A foot valve in the suction pipe will keep the pump charged once it has” 
been filled with water. A common method of charging large pumps is to — 
withdraw the air by means of a steam ejector; this requires that the 
delivery pipe be fitted with a valve, which is closed while the ejector is 
actin 
Coiaivatinls the ordinary centrifugal pump with a plunger or piston 
pump, the former is much more efficient at low lifts, say under 30 feet. 
The centrifugal pump also gives a uniform delivery, and having no 
valves, it is much better adapted for pumping dirty water. 4 
443. Design of Vanes of Centrifugal Pumps.—Referring to Fig. 824, ; 
7, and 7, are the inner and outer radii of the wheel respectively. In 
practice 7, generally lies 
between 27, and 37r,, and 
is frequently equal to 27). 
B,B, represents one vane. 
Water enters the wheel at 
B, in the direction B,V, 
with an absolute velocity 
v,, and moving over the 
vane, leaves the wheel at 
B, in the direction B,V, 
with an absolute velocity 
v,, The tangential velo- 
cities of the wheel at B, 
and B, are c, and ¢, re- 
spectively. The parallelo- 
grams of velocities at B, co PES pty” diner ey 3 
and B, are constructed 
as in the case of turbines. Sige 
B,U, =, is the relative velocity of the water and vane at B,, and ¢, is- 
the inclination of the vane at-B, to the tangent to the wheel at that ~ 
point. B,U,=w«, is the relative velocity of the water and vane at B,, 
and ¢, is “the inclination of the vane at B, to the tangent to the wheel — 
at that point. 
B,S, = 8, is the radial velocity of the water at B,,and B,S,=s, isthe — 
radial velocity of the water at B,. If A, and A, are the areas of the . 
circumferential sections of the wheel at radii 7 and r, respectively, then 
s,A,=s,A,. Generally s,=s,, then A,=A,. If 6, and 0, are the ~ 
breadths of the wheel at inlet and outlet respectively, A,= lard, , and 
A,=2mr,b,. Hence if A,=A,, b,r,=),r,. If the radial velocity of — 
the water throughout the wheel i is to be constant, then the breadth 6 at — 
any radius 7 is given by the equation br = 0,r;. 
