Affinity laws for centrifugal pumps and fans

The affinity laws describe how the volumetric flow rate, head, and power consumption of a centrifugal pump or fan change with impeller speed and/or impeller diameter. They are approximations, valid over a limited range, and assume constant efficiency.

I’m not planning to regurgitate the many sources on this topic. More detail available here on Engineering Toolbox.

Limitations

• These laws assume constant efficiency between states 1 and 2. In practice, efficiency falls off at the extremes of a pump’s operating range, so results become less reliable far from the best efficiency point (BEP).
• Diameter-based laws are generally reliable only for small trims (a few percent).
• Always validate against manufacturer pump curves where precision matters. The affinity laws are a scaling tool, not a substitute for tested performance data.

Fixed diameter, variable speed

For the same impeller, changing rotational speed (rpm):

where is volumetric flow rate, is head, is power, and is rotational speed.

Fixed speed, variable diameter

For the same speed, with a change in impeller diameter (small trims only — large changes distort the velocity triangles and this approximation degrades):