Scale pump flow, head, and power to a new speed or impeller diameter using the affinity laws.
Q ∝ N, H ∝ N², P ∝ N³ (and ∝ D, D², D³ for impeller trim)
How it works
The affinity laws scale a known operating point to a new speed or impeller diameter: flow scales linearly with the ratio, head with its square, and power with its cube.
Worked example
A pump doing 100 m³/h at 50 m, 20 kW, sped up from 1450 to 1750 RPM. Flow rises to ≈ 121 m³/h, head to ≈ 73 m, and power to ≈ 35 kW — note the steep power cost.
Inputs
Change
Original speed / diameter — RPM or mm — match the selected change.
New speed / diameter — RPM or mm.
Flow at original (m³/h)
Head at original (m)
Power at original (optional) (kW)
Frequently asked questions
Why does power rise so fast with speed?
Power scales with the cube of the speed ratio, so a 20% speed increase raises power by about 73%. This is why variable-speed drives save so much energy when you slow a pump down.
Are the diameter laws as accurate as the speed laws?
No. Speed scaling is accurate along the same system curve; impeller-trim scaling is approximate and degrades beyond roughly 10–20% diameter reduction. Verify large trims against the manufacturer's curve.
Assumptions
Speed scaling assumes operation along the same system resistance curve.
Diameter (trim) scaling is approximate; small trims only, efficiency drifts with larger cuts.
Fluid properties and efficiency are assumed constant between the two points.
References
Affinity laws: Q∝N, H∝N², P∝N³ (and ∝D, D², D³ for trim). Hydraulic Institute / API 610.
Related Fluid Mechanics tools
Pipe Pressure Drop — Frictional ΔP and head loss for single-phase flow in a circular pipe (Darcy–Weisbach, Swamee–Jain friction factor).
Fittings Pressure Drop (K-factors) — Minor losses through elbows, tees, and valves by the ΣK excess-head method — the companion to straight-pipe friction.
Pipe Velocity & Reynolds — Line velocity, Reynolds number, and flow regime from flow rate and pipe inside diameter.
Friction Factor (Moody) — Darcy (and Fanning) friction factor from Reynolds number and relative roughness — Colebrook–White solved exactly, with the Swamee–Jain explicit fit for comparison.