fluid_mechanics

658 Chapter 12 ■ Turbomachines
Theoretical or ideal head, h i
Head
Other
losses
Friction losses
Actual head, h a
Flowrate
F I G U R E 12.9 Effect of losses
on the pump head–flowrate curve.
Ideal and actual
head rise levels differ
by the head loss.
Figure 12.9 shows the ideal head versus flowrate curve 1Eq. 12.182 for a centrifugal pump
with backward curved vanes 1b 2 6 90°2. Since there are simplifying assumptions 1i.e., zero losses2
associated with the equation for h i , we would expect that the actual rise in head of fluid, h a , would
be less than the ideal head rise, and this is indeed the case. As shown in Fig. 12.9, the h a versus
Q curve lies below the ideal head-rise curve and shows a nonlinear variation with Q. The differences
between the two curves 1as represented by the shaded areas between the curves2 arise from
several sources. These differences include losses due to fluid skin friction in the blade passages,
which vary as Q 2 , and other losses due to such factors as flow separation, impeller blade-casing
clearance flows, and other three-dimensional flow effects. Near the design flowrate, some of these
other losses are minimized.
Centrifugal pump design is a highly developed field, with much known about pump theory
and design procedures 1see, for example, Refs. 4–62. However, due to the general complexity of
flow through a centrifugal pump, the actual performance of the pump cannot be accurately predicted
on a completely theoretical basis as indicated by the data of Fig. 12.9. Actual pump performance
is determined experimentally through tests on the pump. From these tests, pump characteristics
are determined and presented as pump performance curves. It is this information that is most
helpful to the engineer responsible for incorporating pumps into a given flow system.
12.4.2 Pump Performance Characteristics
The actual head rise, h a , gained by fluid flowing through a pump can be determined with an experimental
arrangement of the type shown in Fig. 12.10, using the energy equation 1Eq. 5.84 with
h a h s h L where is the shaft work head and is identical to h i , and is the pump head loss2
h s
h a p 2 p 1
g
z 2 z 1 V 2 2 V 1
2
(12.19)
with sections 112 and 122 at the pump inlet and exit, respectively. Typically, the differences in elevations
and velocities are small so that
2g
h L
h a p 2 p 1
g
The power, p f , gained by the fluid is given by the equation
p f gQh a
(12.20)
(12.21)
(2)
z 2 – z 1
(1)
F I G U R E 12.10 Typical
experimental arrangement for determining
the head rise gained by a fluid flowing
through a pump.