Flow Measurement · Free Calculator
Pump Affinity Laws Calculator
Predict how a centrifugal pump flow, head and power change with speed (for example with a VFD) or with a trimmed impeller, using the affinity laws.
Affinity lawsVFD speedImpeller trimEnergy saving
rpm or mm
rpm or mm
m³/h
m
kW
Affinity laws move the pump along similar operating points. On a system with static head, the real flow at reduced speed is lower than Q × r; check against the system curve.
New flow96 m³/h
New head28.8 m
New power11.26 kW
Ratio0.8000
Power saving48.8 %
How this result was calculated
- r = new ÷ original = 0.8000
- Q₂ = Q₁ × r, H₂ = H₁ × r², P₂ = P₁ × r³
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Affinity Laws
Q₂ ÷ Q₁ = n₂ ÷ n₁
H₂ ÷ H₁ = (n₂ ÷ n₁)²
P₂ ÷ P₁ = (n₂ ÷ n₁)³
(same ratios approximately for impeller diameter D)
H₂ ÷ H₁ = (n₂ ÷ n₁)²
P₂ ÷ P₁ = (n₂ ÷ n₁)³
(same ratios approximately for impeller diameter D)
n is the pump speed, D the impeller diameter, Q flow, H head and P shaft power. The laws relate similar operating points; efficiency is assumed unchanged. Where the system has significant static head, combine the scaled pump curve with the system curve to find the real duty.
Worked example
Slowing a pump from 2950 to 2360 rpm (80 %) changes 120 m³/h, 45 m and 22 kW to 96 m³/h, 28.8 m and 11.3 kW: about half the power.
Key insight: because power falls with the cube of speed, flow control by a VFD saves far more energy than throttling with a control valve, especially on friction dominated systems.
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Frequently Asked Questions
What are the pump affinity laws?
Rules that scale a centrifugal pump flow with speed, head with speed squared and power with speed cubed.
Do they apply to positive displacement pumps?
Only the flow law, roughly: flow is proportional to speed. Head is set by the system.
Why is real flow lower than predicted at low speed?
Static head does not scale with speed, so the pump meets the system curve at a lower flow than the simple law suggests.
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