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

WHP=QHSG3960WHP = \frac{Q \, H \, SG}{3960}

Useful power delivered to the liquid; the 3960 divisor assumes US gallons per minute, feet of head and horsepower output.

Pump Brake Horsepower

BHP=QHSG3960ηBHP = \frac{Q \, H \, SG}{3960 \, \eta}

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

η=PhydPshaft\eta = \frac{P_{hyd}}{P_{shaft}}

Pump efficiency is the ratio of hydraulic power delivered to the liquid over the mechanical power absorbed at the shaft.

Hydraulic Power (P = ρgQh)

P=ρgQhP = \rho g Q h

Power needed to lift a flow Q through a head h, with g = 9.80665 m/s².

Total Dynamic Head

TDH=hs+hf+hvTDH = h_s + h_f + h_v

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)

NPSHa=hatm+hshfhvpNPSH_a = h_{atm} + h_s - h_f - h_{vp}

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)

Ns=NQH0.75N_s = \frac{N \sqrt{Q}}{H^{0.75}}

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.