516 APPLIED MECHANICS 
pressure energy by gradually reducing the velocity in an expé nding 
chamber or volute. If no part of the velocity head is utilised, then the 
theoretical lift is reduced from 202 ty Woke _ a > 
g g 2% 
446. Centrifugal Head Imparted to Water by Wheel of Centrifug; 
Pump.—Suppose the pump to be fully charged with water, and that 
wheel is rotating with angular velocity », but that 
no water is being delivered. The water within the 
wheel will have rotary motion only, and the centri- 
fugal force of this water will cause the pressure at 
the outer circumference to be greater than that at 
the inner circumference. 
To determine the difference of pressure at the outer 
and inner circumferences of the wheel due to the cen- 
trifugal force of the water in the wheel, consider (Fig. 
826) a wedge of this water of breadth > and angle 0, . 
as shown. ‘Take an element FH of this wedge at radius r ‘aaa thickneaall a 
dr. If w is the density of the water, then the weight of the element « 
2 
FH is whr6dr, and its centrifugal force is en To prevent. FH : 
from moving outwards in a radial direction the intensity of the pressure ’ 
on its outer face must exceed the intensity of the pressure on its inner ~ 
whrOdr - wr > dpa ’rdr ah ‘4 
difference of the intensities of the pressures on the outer and inner ends. | 
" ww'rdr wor 73 a and ; 
ve Soa 2 
if h, is the head equivalent to this difference of pressure, i. 
Ie w(rs —7i) _¢3 —er << 
er 29 A 
In order that the pump may discharge water through the delivery 
pipe the actual head must be less than the centrifugal head. 
447. Turbine Pumps.—A greater amount of the kinetic energy of — 
the water as it leaves the wheel of a centrifugal pump may be converted _ 
into pressure energy by providing suitably designed guide passages in — 
the chamber surrounding the wheel. The centrifugal pump then becomes — 
a turbine pump. A single wheel turbine pump will raise water to a much? i 
greater height than an ordinary centrifugal pump. 
448. Multi-stage Turbine Pumps.— Water may be pumped to alma 4 
any height by mounting a series of turbine pump wheels side by side on — 
the same shaft, each wheel being provided with a suitable casing. The 
water enters the eye of the first wheel, and is delivered through its’ = 
casing to the eye of the second wheel, and so on to the delivery pipe, | 
which leads the water from the casing of the last wheel. 
Fig. 827 shows a multi-stage turbine pump, as made by Messrs. — 
W. H. Allen, Son, & Co., of Bedford. This pump is provided with a — 
balancing arrangement, designed with a view to reducing the leakage of — 
water through the clearance between the balancing piston A and the 
bush B. The cylinder C is attached to the pump casing, and is provide ‘ 
face by an amount dp, and dp - bré = 
of the wedge of water within the wheel is 
