How it’s calculated
The power delivered to the fluid is its weight flow rate times the head added. Dividing by pump efficiency gives the shaft (brake) power, and dividing again by motor efficiency gives electrical input. Assumes steady flow of an incompressible liquid.
Example: 100 gpm of water against 100 ft of head. Hydraulic power = 100 × 100 × 1.0 ÷ 3,960 = 2.53 hp (1.89 kW). At 70% pump efficiency the shaft needs 3.61 hp, and with a 90% efficient motor the electrical input is about 2.99 kW.
The U.S. DOE pumping sourcebook uses the 3,960 constant, which assumes water at room temperature; this calculator uses ρ = 1000 kg/m³ × SG and g = 9.80665 m/s², which agrees within about 0.2%.
Frequently asked questions
What is brake horsepower?
The mechanical power the pump shaft must receive: hydraulic power divided by pump efficiency. For a direct-coupled pump it is the motor’s output.
What head should I use?
Total dynamic head: the elevation difference plus all friction and fitting losses plus any difference in pressure between suction and discharge, all converted to height of the pumped fluid.
Where do I find pump efficiency?
On the manufacturer’s pump curve at your duty point. Operating near the best efficiency point (BEP) saves energy.
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Sources
- Improving Pumping System Performance: A Sourcebook for Industry (2nd ed.) — U.S. Department of Energy & Hydraulic Institute
- Pump Systems — U.S. Department of Energy
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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