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🔄 Pump Affinity Laws Calculator

Calculate changes in pump performance (flow, head, and power) when the rotational speed or impeller diameter changes.

Inputs

Initial State (1)

RPM

gpm

ft

hp

Target State (2)

RPM

Results (State 2)

New Flow (Q₂)
∝ N
0.0
gpm
New Head (H₂)
∝ N²
0.0
ft
New Power (P₂)
∝ N³
0.0
hp

Performance Change Comparison

0
Q
0
H
0
P
State 1
State 2

Calculator Description

The pump affinity laws relate how the flow rate (Q), head (H) and power (P) of a centrifugal pump change when its rotational speed (N) or impeller diameter (D) is altered. They let engineers predict the performance curve of geometrically similar pumps and are essential whenever a duty point is shifted via variable-speed control (VFD) or impeller trimming.

What this calculator finds

By entering the reference operating point (1) and the ratio of the new speed (or impeller diameter) to the old one, the calculator returns the new flow, head and power (point 2). In short, it quantifies “how much does pump performance change if we spin it faster or slower”.

Why it matters

  • Sizing motor capacity by predicting power/head changes when adding a VFD
  • Estimating performance when trimming an oversized impeller to match the duty point
  • Comparing energy savings between throttling and speed control

Formula

Pump Affinity Laws

The three relations below are written for the ratio x = N₂/N₁ (or D₂/D₁). Flow scales with the first power, head with the square, and power with the cube of the ratio.

Q2=Q1(N2N1)Q_2 = Q_1\left(\dfrac{N_2}{N_1}\right)
H2=H1(N2N1)2H_2 = H_1\left(\dfrac{N_2}{N_1}\right)^{2}
P2=P1(N2N1)3P_2 = P_1\left(\dfrac{N_2}{N_1}\right)^{3}
  • N — Pump speed [RPM] or impeller diameter [m or ft]
  • Q — Volumetric flow rate [m³/h or gpm]
  • H — Pump head [m or ft]
  • P — Power consumption [kW or hp]

How the formula works

  • Doubling the speed doubles the flow, quadruples the head, and octuples the power. Conversely, slowing down sharply cuts power, giving large energy savings.
  • Because head depends on the square and power on the cube, even a small speed increase demands much more power.
  • The same laws approximately apply to impeller diameter changes, but diameter changes affect efficiency and geometry more strongly.

Assumptions & scope

These laws hold exactly for geometrically similar pumps under the assumption that efficiency stays constant. In practice efficiency shifts when speed moves far from the design point, and impeller trimming alters geometry ratios, introducing error.

Worked example

Suppose a pump runs at N₁ = 1750 RPM with Q₁ = 100 m³/h, H₁ = 50 m and P₁ = 15 kW. Reducing speed to N₂ = 1400 RPM gives x = 0.8, so Q₂ = 80 m³/h, H₂ = 32 m and P₂ ≈ 7.68 kW — the power is cut to roughly half.

Useful Tips

Practical tips

  • When reducing flow, VFD speed control saves far more power than valve throttling, because power drops with the square/cube of speed.
  • Running slower also lowers the required NPSH roughly with the square of speed, reducing cavitation risk.
  • If operating far from the design speed, allow margin on power because real efficiency drops.

Limitations & cautions

  • The laws assume constant efficiency, so real power may differ from the prediction.
  • Impeller trimming changes geometry ratios, so larger trims reduce reliability of the estimate.
  • Do not apply these laws to compare pumps that are not geometrically similar.