A pump supplies hydraulic power to the fluid, but its shaft must supply more power because the pump is not perfectly efficient.
Difficulty
Intermediate
Read time
4 min
Prerequisites
Consistent SI units, algebra, and the physical assumptions listed below
Source
Teng-Jui Lin — Equation SheetsAdapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.
Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Expressed the power in watts, not horsepower, and specified the efficiency boundary.
A pump supplies hydraulic power to the fluid, but its shaft must supply more power because the pump is not perfectly efficient. The efficiency in this equation is pump shaft-to-hydraulic efficiency, so motor electrical losses are separate.
| Symbol | Meaning | Units |
|---|---|---|
| Mechanical power supplied at the shaft | ||
| Fluid density | ||
| Gravitational acceleration | ||
| Volume flow rate | ||
| Total head added by the pump | ||
| Pump efficiency as a fraction |
Estimate mechanical shaft power at an operating point.
Compare required power at the same flow and head.
A pump moves 0.01 m³/s of water through a total added head of 20 m. Use ρ = 1000 kg/m³, g = 9.81 m/s², and pump efficiency 0.70.
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.
Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Expressed the power in watts, not horsepower, and specified the efficiency boundary.
Assumptions
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