Affinity Laws and Fan Laws
The affinity laws (also called the fan laws when applied to fans and blowers) describe how a rotodynamic machine’s flow, head, and power change with impeller speed or diameter. Flow scales with speed, head with the square of speed, and power with the cube.
Definition
For a change in rotational speed (N) or impeller diameter (D), the performance scales as:
Q₂/Q₁ = (N₂/N₁) × (D₂/D₁)
H₂/H₁ = (N₂/N₁)² × (D₂/D₁)²
P₂/P₁ = (N₂/N₁)³ × (D₂/D₁)³
where Q is volumetric flow, H is generated head, and P is shaft power. The same relationships apply to pumps, fans, and blowers, which is why they are known as the affinity laws for pumps and the fan laws for fans.
Engineering context
The cube relationship between speed and power is the basis of variable-speed energy savings: a modest reduction in speed produces a large reduction in power, provided the duty point moves along the system curve. The laws hold for geometrically similar conditions and are most accurate for moderate changes in speed or impeller trim. FluidFlow automatically applies the affinity laws when modeling changes in pump speed or impeller diameter, so the shifted curve and the new duty point come straight from the network solution.
Related definitions
Pump curve · System curve · Best Efficiency Point (BEP)
See it in FluidFlow
Model a speed or impeller change and watch the pump or fan curve shift. FluidFlow applies the affinity laws and re-solves the network, so the new duty point, head, and power are reported directly.
Go deeper
Related content
Reviewed by the FluidFlow Engineering Team · Last reviewed: June 2026 · Applies to FluidFlow v3.54 (steady-state analysis)
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