Summary

The pump affinity laws allow the prediction of centrifugal pump performance given changes to the speed of the pump or the diameter of impeller. This article presents the pump affinity laws for reference.

Definitions


$Q$	:	Volumetric flow rate
$N$	:	Pump shaft rotational speed
$h$	:	Pump head
$P$	:	Pump power
$D$	:	Impeller diameter

Introduction

The pump affinity laws can be used to predict the performance of a centrifugal pump as two variables change, the pump shaft rotational speed and the pump impeller diameter. They are useful particularly for the modification of existing pumps to meet a new service. These relationships are approximate and rely on the assumption that the pump efficiency is equal at both speeds/diameters. The prediction of performance based on impeller diameter changes also relies on the assumption that the impellers are geometrically similar.

Affinity Laws

These relationships do not apply to positive displacement pumps.

Changing Pump Rotational Speed

The effect on pump performance for a given change in pump shaft rotational speed can be estimated from the relationships below:

Property	Relationship
Flow Rate	$\displaystyle \frac{Q_{2}}{Q_{1}} = \left( \frac{N_{2}}{N_{1}} \right)$
Head	$\displaystyle \frac{h_{2}}{h_{1}} = \left( \frac{N_{2}}{N_{1}} \right)^{2}$
Power	$\displaystyle \frac{P_{2}}{P_{1}} = \left( \frac{N_{2}}{N_{1}} \right)^{3}$

Changing Pump Impeller Diameter

The effect on pump performance for a given change in pump impeller diameter can be estimated from the relationships below:

Property	Relationship
Flow Rate	$\displaystyle \frac{Q_{2}}{Q_{1}} = \left( \frac{D_{2}}{D_{1}} \right)$
Head	$\displaystyle \frac{h_{2}}{h_{1}} = \left( \frac{D_{2}}{D_{1}} \right)^{2}$
Power	$\displaystyle \frac{P_{2}}{P_{1}} = \left( \frac{D_{2}}{D_{1}} \right)^{3}$

Changing Both Pump Rotational Speed and Pump Impeller Diameter

The effect on pump performance for a given change in pump speed and pump impeller diameter can be estimated from the relationships below:

Property	Relationship
Flow Rate	$\displaystyle \frac{Q_{2}}{Q_{1}} = \left( \frac{N_{2}}{N_{1}} \right) \left( \frac{D_{2}}{D_{1}} \right)$
Head	$\displaystyle \frac{h_{2}}{h_{1}} = \left( \frac{N_{2}}{N_{1}} \right)^{2} \left( \frac{D_{2}}{D_{1}} \right)^{2}$
Power	$\displaystyle \frac{P_{2}}{P_{1}} = \left( \frac{N_{2}}{N_{1}} \right)^{3} \left( \frac{D_{2}}{D_{1}} \right)^{3}$

Pump Affinity Laws