Calculate the power needed at a pump shaft to deliver 500 US gpm against 100 ft of total differential head at 75% pump efficiency.
1. Calculator Inputs
Select the units below before entering the numbers. These are fixed benchmark inputs for checking the calculator.
| Calculator field | Value | Unit / setting |
|---|---|---|
| Energy input | Differential head | |
| Flow rate | 500 | gpm |
| Liquid density | 62.4 | lbm/ft³ |
| Pump efficiency | 75 | % |
| Differential head | 100 | ft |
2. Step-by-step Math
Convert the flow and density
Q = 500 × 0.003785411784 / 60 = 0.0315450982 m³/s ρ = 62.4 × 0.45359237 / 0.3048³ = 999.5521145 kg/m³ H = 100 × 0.3048 = 30.48 m η = 75 / 100 = 0.75
The 100 ft represents total differential head at the duty point, not just straight-pipe friction.
Calculate hydraulic power
Pₕ = ρgQH Pₕ = 999.5521145 × 9.80665 × 0.0315450982 × 30.48 Pₕ = 9,424.817821 W ≈ 9.42 kW Pₕ = 9,424.817821 / 745.699871582 ≈ 12.6 hp
Hydraulic power is the rate of useful energy delivered to the liquid. Horsepower here means mechanical horsepower.
Account for pump efficiency
Pshaft = Pₕ / η Pshaft = 9.424817821 / 0.75 ≈ 12.6 kW Pshaft = 12.638888889 / 0.75 ≈ 16.9 hp
Divide by efficiency. Multiplying would incorrectly make shaft power lower than hydraulic power.
Cross-check using pressure rise
ΔP = ρgH = 298,772.816037 Pa ≈ 43.3 psi Pₕ = QΔP = 0.0315450982 × 298,772.816037 Pₕ ≈ 9,420 W
Switch Energy input to Pressure rise and enter 43.333333333 psi. Keep the same flow, density and efficiency; both power results should match.
3. Compare Your Answers
Keep full precision during the calculation. The calculator may display fewer digits; compare answers rounded to three significant figures; retain unrounded intermediate values.
| Result | Expected answer | Your answer |
|---|---|---|
| Hydraulic power | 9.42 kW / 12.6 hp | __________ |
| Required shaft power | 12.6 kW / 16.9 hp | __________ |
| Equivalent head | 30.48 m / 100 ft | __________ |
| Equivalent pressure rise | 299 kPa / 43.3 psi | __________ |
Second check
At 100% pump efficiency, shaft power would equal hydraulic power: 12.6 hp. A real motor also has losses; for an assumed 90% motor efficiency, electrical input would be 12.6 / 0.90 = 14 kW.
4. Assumptions and Method
This is a steady, incompressible-liquid duty-point calculation. It does not select a motor size or verify NPSH, pump curves, startup, operating range, or service factor. Pump efficiency and motor efficiency are separate.
Equation definitions and implementation: Pump Power Calculator. See also calculation methodology and other worked examples.