Centrifugal Pumps Design and Application 2nd ed - Val S. Lobanoff, Robert R. Ross (Butterworth-Heinemann, 1992)

Specific Speed and Modeling Laws 21
Factoring Law
In addition to the affinity law and model law, there are some other
principles of similarity that are very useful to the pump designer. The
"factoring law" can be used to design a new pump that has the same specific
speed and running speed as the existing model but which is larger or
smaller in size. Factoring the new pump can be determined by using capacity
or impeller diameter ratio. From BEP condition, a new pump head
and flow are calculated from:
where Qi = Capacity of new pump
HI = Head of new pump
DJ = Impeller diameter of new pump
Q m = Capacity of model pump
H m = Head of model pump
D m = Impeller diameter of model pump
Thus, the capacity will change with factor cubed (f 3 ). The head and all
areas will change with factor squared (f 2 ), and all linear dimensions will
change directly with factor (f).
The specific speed of the model pump should be the same as the new
pump or within ±10% of the new pump's specific speed. The model
pump should ideally be of the same type as the new pump.
Example
If we take the 3-in. x 9-in. pump shown in solid lines on Figure 2-1,
With a performance at the BEP of 500 GPM; 300 ft; 74% efficiency;
55 maximum HP; 3,550 RPM; and 9-in. impeller diameter, and increase
pump size to 700 GPM at BEP and running at 3,550 RPM, the
new performance would be: