Pump power: hydraulic, shaft and input
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.
P_h = ρ · g · Q · HP_sh = P_h / η_pP_in = P_sh / η_mP_m ≥ P_sh · (1 + k_m)Shaft power is proportional to the density: a pump selected on water loads its motor more when it pumps brine. For viscous oil, the head, flow and efficiency of the water curve are corrected for viscosity (ANSI/HI 9.6.7). Choose the next standard motor size not below P_m; with several duty points, size it on the largest shaft power.
Source: ISO 9906 (pump power output P_u = ρ · g · Q · H); API 610 — power margin of the driver
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
The duty point on the pump curve or the measured flow rate.
Fresh water 1 000, crude oil 800–900, formation water 1 050–1 180 kg/m³.
From the curve at the duty point: centrifugal pumps 60–85 %, ESPs 35–65 %.
IE3 induction motors of 15–200 kW: 92–96 %; with a variable speed drive, multiply by its efficiency (≈ 0.97).
API 610: at least 25 % for motors up to 22 kW, 15 % for 22–55 kW, 10 % above 55 kW.
Unit converter for this formulaLiquid rate · Length · Density and °API · Power · Pressure · 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.
- P_h — Hydraulic power–
- P_in — Power drawn from the supply–
- P_m — Smallest motor rating–
- ΔP — Pressure rise across the pump–
More in Pumps
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.
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.
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.