Pump Formulas: Hydraulic, Shaft and Motor Power
Pump power formulas: hydraulic power from flow and head, shaft power from pump efficiency, motor input power, with a worked example and a table by flow.
The formulas
| To find | Formula |
|---|---|
| Hydraulic power | Ph (kW) = ρ × g × Q × H / 1000 |
| Shaft power | Pshaft = Ph / ηpump |
| Motor input power | Pin = Pshaft / ηmotor |
| Flow in m³/s | Q (m³/s) = Q (m³/h) / 3600 |
| Pressure from head | Δp (Pa) = ρ × g × H |
ρ is the liquid density in kg/m³ (1,000 for clean water), g = 9.80665 m/s², Q the flow in m³/s and H the total head in metres, which includes the static lift and the friction losses. The efficiencies are fractions. Take the pump efficiency from the pump curve at the duty point.
Worked example: 50 m³/h at 30 m head
Water, pump efficiency 70% and motor efficiency 90%.
- Q = 50 / 3600 = 0.01389 m³/s
- Ph = 1000 × 9.80665 × 0.01389 × 30 / 1000 = 4.086 kW
- Pshaft = 4.086 / 0.7 = 5.837 kW
- Pin = 5.837 / 0.9 = 6.486 kW electrical input
Power by flow at 30 m head
| Flow | Hydraulic power | Motor input (70% × 90%) |
|---|---|---|
| 10 m³/h | 0.8172 kW | 1.297 kW |
| 25 m³/h | 2.043 kW | 3.243 kW |
| 50 m³/h | 4.086 kW | 6.486 kW |
| 100 m³/h | 8.172 kW | 12.97 kW |
Frequently asked questions
What is total head?
It is the height the liquid is lifted plus the pressure and the friction losses in the pipe and fittings, all expressed as metres of liquid.
Does a heavier liquid need more power?
Yes. Power is proportional to the density, so a liquid of density 1,200 kg/m³ needs 20% more power than water for the same flow and head.
What size motor should I choose?
Choose a standard motor rating above the shaft power with a margin. The pump curve may show a higher power at the end of the curve, so check it.
Where do I find the pump efficiency?
It is on the manufacturer’s curve at the flow and head of your duty point. It is lower away from the best efficiency point.
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