Pump affinity laws: speed and impeller trim
Flow rate, head and power of a centrifugal pump at another speed — including an ESP or a pump on a variable speed drive — and with a trimmed impeller.
Q_2 = Q_1 · (n_2 / n_1) · (D_2 / D_1)H_2 = H_1 · (n_2 / n_1)² · (D_2 / D_1)²P_2 = P_1 · (n_2 / n_1)³ · (D_2 / D_1)³The affinity laws move a point of the pump curve along the parabola H ∝ Q² at constant efficiency. It is not yet the operating point of the system: with a large static head (lift, manifold pressure) a lower speed cuts the flow by more than n_2 / n_1. The speed laws are accurate over the usual control range; the trim laws are approximate and suit small diameter reductions. At a higher speed the power grows as the cube — check the motor load.
Source: Affinity laws of centrifugal pumps: Karassik I. J. et al., Pump Handbook; Hydraulic Institute
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
For an ESP or a pump on a variable speed drive the speed is proportional to the supply frequency: you may enter frequencies in hertz as n_1 and n_2 — only their ratio matters.
As a percentage of the original; 100 % if the impeller is not trimmed.
Unit converter for this formulaLiquid rate · Length · Power · Rotational speed · Fraction and percent
- m³/d1
- m³/h0.0416667
- L/s0.0115741
- L/min0.694444
- m³/min0.000694444
- bbl/d6.28981
- Mbbl/d0.00628981
- ft³/d35.3147
- US gpm0.183453
- bbl/min0.00436792
A day is 24 hours.
- H_2 — New head–
- P_2 — New shaft power–
More in Pumps
Hydraulic power from the flow rate and head, shaft power from the pump efficiency, power drawn from the supply, and the smallest motor rating with a margin.
The actual total head of a running pump from the suction and discharge pressures, the gauge height difference and the pipe velocities — to compare with the rated curve.
Net positive suction head available (NPSHa) for a pump taking liquid from a tank, separator or vessel, and its margin over the NPSH required (NPSHr) from the pump curve.
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.