fluid_mechanics

12.4 The Centrifugal Pump 659
and this quantity, expressed in terms of horsepower is traditionally called the water horsepower.
Thus,
h a
Pump overall efficiency
is the ratio
of power actually
gained by the fluid
to the shaft power
supplied.
Falling
head
curve
Rising
head
curve
Q
(12.22)
with g expressed in lbft 3 , Q in ft 3 s, and h a in ft. Note that if the pumped fluid is not water, the g
appearing in Eq. 12.22 must be the specific weight of the fluid moving through the pump.
In addition to the head or power added to the fluid, the overall efficiency, h, is of interest,
where
h
p f water horsepower gQh a
550
power gained by the fluid
shaft power driving the pump
The denominator of this relationship represents the total power applied to the shaft of the pump
and is often referred to as brake horsepower 1bhp2. Thus,
h gQh a550
bhp
(12.23)
The overall pump efficiency is affected by the hydraulic losses in the pump, as previously discussed,
and in addition, by the mechanical losses in the bearings and seals. There may also be
some power loss due to leakage of the fluid between the back surface of the impeller hub plate
and the casing, or through other pump components. This leakage contribution to the overall efficiency
is called the volumetric loss. Thus, the overall efficiency arises from three sources, the hydraulic
efficiency, h h , the mechanical efficiency, h m , and the volumetric efficiency, h v , so that
h h h h m h v .
Performance characteristics for a given pump geometry and operating speed are usually given
in the form of plots of h a , h, and bhp versus Q 1commonly referred to as capacity2 as illustrated in
Fig. 12.11. Actually, only two curves are needed since h a , h, and bhp are related through Eq. 12.23.
For convenience, all three curves are usually provided. Note that for the pump characterized by
the data of Fig. 12.11, the head curve continuously rises as the flowrate decreases, and in this case
the pump is said to have a rising head curve. As shown by the figure in the margin, pumps may
also have h a Q curves that initially rise as Q is decreased from the design value and then fall
with a continued decrease in Q. These pumps have a falling head curve. The head developed by
the pump at zero discharge is called the shutoff head, and it represents the rise in pressure head
across the pump with the discharge valve closed. Since there is no flow with the valve closed, the
related efficiency is zero, and the power supplied by the pump 1bhp at Q 02 is simply dissipated
as heat. Although centrifugal pumps can be operated for short periods of time with the discharge
valve closed, damage will occur due to overheating and large mechanical stress with any extended
operation with the valve closed.
As can be seen from Fig. 12.11, as the discharge is increased from zero the brake horsepower increases,
with a subsequent fall as the maximum discharge is approached. As previously noted, with h a
and bhp known, the efficiency can be calculated. As shown in Fig. 12.11, the efficiency is a function
p f
W # shaft
Shutoff head
Head
Head, ha
Brake horsepower, bhp
η
Efficiency,
Efficiency
Brake horsepower
Normal or
design flowrate
0
0 Flowrate, Q
F I G U R E 12.11 Typical performance
characteristics for a centrifugal pump of a
given size operating at a constant impeller speed.