Pump power and efficiency
water horsepowerbrake horsepowerBHPpump efficiencyNPSH3960 formula
Water horsepower, brake horsepower, pump efficiency, NPSH available and specific speed — sizing the motor and keeping the impeller wet.
Pump Water Horsepower
Useful power delivered to the liquid; the 3960 divisor assumes US gallons per minute, feet of head and horsepower output.
Pump Brake Horsepower
Shaft power the motor must actually supply; the 3960 constant assumes gpm, feet of head and horsepower, with efficiency as a fraction.
Pump Efficiency from Hydraulic and Shaft Power
Pump efficiency is the ratio of hydraulic power delivered to the liquid over the mechanical power absorbed at the shaft.
Hydraulic Power (P = ρgQh)
Power needed to lift a flow Q through a head h, with g = 9.80665 m/s².
Total Dynamic Head
The head a pump must develop: static lift plus friction losses plus velocity head, all expressed in feet or metres of the pumped liquid.
Net Positive Suction Head Available (NPSHa)
Absolute head available at the pump suction above the liquid's vapour pressure — the margin that keeps a pump from cavitating.
Pump Specific Speed (Ns)
The dimensional index that classifies impeller type, evaluated in US units with N in rpm, Q in gpm and H in feet at the best efficiency point.
How they fit together
Water horsepower is the useful work leaving the pump: flow times head times fluid weight. Brake horsepower is what the shaft has to supply, and the difference between them is the pump's efficiency. The trade form BHP = (GPM × ft) ÷ (3960 × η) carries a constant that is not arbitrary — 33,000 ft·lb/min per horsepower divided by 8.33 lb/gal gives 3961, and it is valid only for water at about 60 °F. For any other fluid, multiply by specific gravity, which is why a brine pump can trip a motor sized off the water numbers.
Work in this order: total dynamic head first, then water horsepower, then divide by efficiency at that operating point — not the peak efficiency on the curve, which you are almost never sitting at. Then check NPSH available against the manufacturer's NPSH required with a real margin, typically 3 to 5 ft. NPSH is where jobs actually fail: a pump that runs fine in April cavitates in August because the required NPSH is a property of the impeller while the available NPSH falls with fluid temperature, altitude and a dirty suction strainer. Specific speed is the sanity check on selection — it tells you whether you are asking a radial impeller to do an axial job — and a pump far off its best-efficiency point wears bearings and seals regardless of what the power calculation says.