Pump Brake Horsepower

Brake horsepower is water horsepower divided by the pump's efficiency: the power that actually shows up on the coupling, and therefore the number that sizes the motor. Take 500 gpm at 100 ft on water through a 70%-efficient pump: 500 × 100 × 1.0 / (3960 × 0.70) ≈ 18.0 hp, so a 20 hp motor. The 3960 is the same US-customary constant as in water horsepower, and this page evaluates the exact SI equivalent ρgQH/η so you may enter L/s, metres and kilowatts freely.

Efficiency is not a property of the pump; it is a property of the operating point. A pump rated 78% at best efficiency may run at 55% out on the far right of its curve, and the shaft power can then exceed the nameplate even though the flow looks reasonable. Read η off the curve at your actual duty, not off the datasheet headline, and add the motor's own efficiency (typically 90–94%) if you want electrical input rather than shaft power.