Pumps - Affinity Laws

Affinity laws allows engineers to estimate changes in critical performance parameters like

• Flow rate (Q)
• Head (H)** / Pressure (P)
• Brake horsepower (BHP)

due to variation in

1. Shaft / motor speed (N)
2. Impeller diameter (D)

** Head refers to Total dynamic head (static head + losses OR differential head), since static head (process requirement) does not change with either shaft speed or impeller diameter or with flow rate.

Affinity laws are applicable on centrifugal pumps, fans or turbines (these are applicable only for centrifugal pumps, laws for fans are different) assuming the points on the system curve have approximately the same efficiency. The system curve changes with change in either shaft/motor speed or impeller diameter.

The following affinity laws are for a specific centrifugal pump.

Affinity law set 1	Affinity law set 2
Constant impeller diameter (d)	Constant motor speed (N)
Q α N	Q α D
H α N2	H α D2
BHP α N3	BHP α D3

Usually, there is no appreciable change in efficiency with range of normal operating speeds. Hence Affinity law set 1 can be considered accurate & reliable.

Whereas, on the other hand set 2 laws (same casing size, but different impeller diameter) are not as accurate as set 1 because large diameter reductions involve changes in the geometry of the blades (outlet width, blade angle, blade length) thus increasing the mismatch with the casing volute, which in turn causes change in the efficiency.

Note: The new impeller diameter should not be more than 10-20% of the original diameter.

The following affinity laws are for a geometrically similar pumps (meaning the pumps will run with same specific speed but with different impeller size.)

For set of geometrically similar pumps

Q α ND3

H α N2D2

BHP α N3D5