Affinity laws

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The affinity laws are used in hydraulics and HVAC to express the relationship between several variables involved in pump or fan performance (such as head, volumetric flow rate, shaft speed, and power). They apply to pumps, fans, and hydraulic turbines. In these various rotary implements, the Affinity Laws apply both to centrifugal and axial flows.

The affinity laws state that:

1) Flow is proportional to shaft speed: {\dot V_1 \over \dot V_2} = { \left ( {N_1 \over N_2} \right )}

2) Pressure or Head is proportional to the square of shaft speed: {H_1 \over H_2} = { \left ( {N_1 \over N_2} \right )^2 }

3) Power is proportional to the cube of shaft speed: {P_1 \over P_2} = { \left ( {N_1 \over N_2} \right )^3 }

where

  • \dot V is the volumetric flow rate (e.g. CFM or GPM),
  • N is the shaft rotational speed (e.g. rpm),
  • H is the pressure or head developed by the fan/pump, and
  • P is the shaft power.

These laws assume that the pump/fan efficiency remains constant. In other words, η1 = η2 .

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