Affinity Laws

Pumps can operate at variable speeds (adjustable in the Variable Speed tab in the Pump Properties window). Affinity laws (also called homologous laws) allow an estimation of the pump performance at speeds other than the design speed.

To a somewhat lesser degree, impeller diameter changes (Impeller Modifications) follow the same laws as speed changes. Substituting impeller changes for speed changes below can be used to see the effect of an impeller change or for a small impeller trim (larger trims deviate significantly from this estimation).

Before discussing the affinity laws, it should be noted that the affinity laws are an approximation. In many cases, pump manufacturers will have performance data for a number of speeds. Manufacturer-provided data should be used if available. Multiple Configurations can be entered to save pump curves at different speeds. When data is not available for varying speeds/impeller trims, the affinity laws can be used with an understanding that an approximation is being made.

Pump curves can generally be curve fit to a polynomial:

The speed ratio is defined in terms of the design impeller speed, N₁ and the desired operating speed N₂ as:

Affinity Laws

For the following ratios, subscript 1 represents the parameter from the defined curve (assumed to be at 100% speed). Subscript 2 represents the given parameter at the desired operating speed N₂.

Flow rate -

Pump head -

Note: By default NPSHr will follow the same relationship as pump head rise. The speed ratio exponent used for NPSHr can be changed on the Configuration Data tab in the Pump Configuration window.

Power consumption -

Efficiency -