Scale pump flow, head, and power for a change in speed or impeller diameter using the affinity laws, with an overlaid original-vs-scaled curve chart.
US + metric
Formula shown
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Affinity Laws
These laws scale the pump, not the system
The affinity laws move the whole pump curve, but the new operating point is set by where that curve meets your system curve. Find it with the system curve & duty point finder.
ft
hp
rpm
rpm
dia
dia
Ratio r = 0.829
Flow Q₂ (∝ r)
414 gpm
Head H₂ (∝ r²)
68.7 ft
Power P₂ (∝ r³)
8.53 hp
Illustrative pump curve through the entered duty point, original vs scaled. The dots are the duty points before and after the change.
Formula & method
Q₂/Q₁ = r · H₂/H₁ = r² · P₂/P₁ = r³ (r = N₂/N₁ or D₂/D₁)
The speed form is accurate over a wide range; the diameter form is a modest-trim approximation (~10–20%). Both assume constant efficiency, which is only approximately true.
For preliminary sizing and educational use. Verify final design against manufacturer performance curves and applicable codes; final designs should be reviewed by a licensed professional engineer.
The affinity laws predict how a centrifugal pump’s flow, head, and power change when you change its speed or trim its impeller. Flow scales with the ratio, head with the ratio squared, and power with the ratio cubed: Q₂/Q₁ = r, H₂/H₁ = r², P₂/P₁ = r³, where r is N₂/N₁ for a speed change or D₂/D₁ for an impeller trim.
Worked example
A pump delivering 500 gpm at 100 ft and drawing 15 hp at 1,750 rpm is slowed to 1,450 rpm (r = 0.829):
Flow: 500 × 0.829 = 414 gpm
Head: 100 × 0.829² = 68.7 ft
Power: 15 × 0.829³ = 8.53 hp
Note the power result: a 17% speed reduction cut power by about 43%. That cubic relationship is exactly why variable-speed drives save so much energy — see the energy cost calculator.
The most important caveat: the laws scale the pump, not the system
This is the single most common misuse. The affinity laws move the entire pump curve, but they do not tell you the new operating point on their own. Where the pump actually runs is set by the intersection of the scaled pump curve with your system curve. If the system has static head, the duty point does not travel along a simple affinity parabola, and naively scaling the old duty point overstates the flow you will get. To find the real new operating point, use the system curve and duty point finder.
Other limits
The speed form is accurate across a wide range. The impeller-diameter form is an approximation valid only for modest trims — roughly within 10–20% of full diameter, and the exact limit is geometry-dependent — because trimming changes the impeller-to-casing geometry, not just its size. Both forms assume efficiency stays constant, which it does not: efficiency drifts with speed and drops with heavy trimming, so treat the scaled power as an estimate and confirm against a manufacturer curve for large changes.
Variables
Symbol
Meaning
US unit
SI unit
r
Ratio Nu2082/Nu2081 (speed) or Du2082/Du2081 (diameter)
