Water-Lifting Devices – Pumps - Practices of Irrigation and On-farm Water Management - page 447

where

Q = pump capacity (gpm)

H = pump head (ft)

N = rotational speed of the pump (rpm)

BHP = required brake horse power

That is:

Q 1
Q 2 =

N 1
N 2

N 1
N 2

2

H 1
H 2 =

N 1
N 2

3

BHP 1
BHP 2 =

The above equations assume that the diameter of the pump impeller is constant.
In some cases the size of the impeller can be changed. Often a pump is very pre-
cisely matched to a specific application by trimming the impeller. It is not feasible
to increase impeller diameter.
Basically, the above relationships mean that an increase in pump speed will pro-
duce more water at a higher head but will require considerably more power to
drive the pump. These calculated values are very close to actual test results, pro-
vided pump efficiency does not change significantly. However, when conditions are
changed by speed adjustment, usually there is no appreciable change in efficiency
within the range of normal pump operation speeds.
For increase in pump speed, the NPSHr increases but it cannot be determined
from the affinity laws. Also the laws do not say anything about how the efficiency
of the pump will change with speed, but generally this is not a significant change.
NPSHr and efficiency changes must be obtained from the pump manufacturer's data
(pump characteristic curves).

Effect of Change of Diameter

There is a second set of affinity laws (Eq. 12.6 ) , which describes the relationships
between the same variables when the impeller size is changed under constant speed
conditions. These laws relate the impact of impeller diameter changes to changes in
pump performance. Since change of impeller diameter changes other design rela-
tionships in a pump, therefore, this second set of affinity laws does not yield the
accurate results of the first three laws discussed above and must be applied with
caution.