Pump Brake Horsepower (BHP)
Hydraulic horsepower, brake horsepower, and motor input power for a centrifugal pump. Standard formulas for water and other fluids by specific gravity, with pump and motor efficiencies.
Defaults: 500 gpm at 100 ft TDH, water, 75% pump efficiency, 92% motor. Real pumps run at varying duty points — use the BEP (best efficiency point) of your selected pump curve, not nameplate.
The 3960 constant
The denominator 3960 in WHP = QHS/3960 comes from: 1 hp = 33,000 ft·lb/min, 1 gpm × 1 ft × ρ_water (8.34 lb/gal) = 8.34 ft·lb/min. So 33,000 / 8.34 = 3957 ≈ 3960. Specific gravity SG simply scales the fluid density.
Pump efficiency in the real world
Centrifugal pumps have a single best efficiency point (BEP) on the H-Q curve. Operating left of BEP (lower flow): efficiency drops, recirculation cavitation, vibration. Operating right of BEP (higher flow): efficiency drops, suction cavitation, motor overload. ANSI/HI 9.6.3 recommends operating between 70–120% of BEP flow.
- Small (under 50 gpm) close-coupled centrifugals: η = 50–65%
- End-suction centrifugal, 100–500 gpm: η = 65–80%
- Split-case double-suction, 500+ gpm: η = 80–90% at BEP
- Submersible sewage: η = 50–70%
- Vertical turbine well pump: η = 70–85%
NPSH — not in this calc but check it
A pump that has enough hydraulic capacity can still fail to deliver if NPSHavailable < NPSHrequired. For sea-level installations: NPSHa = 33.9 ft (atm) − vapor pressure − suction lift − suction friction loss. NPSHr is from pump curve at duty Q. Allow at least 3 ft margin (NPSHa ≥ NPSHr + 3 ft). Insufficient NPSH means cavitation, noise, performance drop, impeller damage.
Total dynamic head — what's in H
TDH includes: static lift (elevation difference) + pressure head difference (if discharging to pressurized vessel) + friction loss in suction and discharge piping + minor losses (valves, fittings, entrance/exit). System curve plots TDH vs Q (parabolic if fully turbulent friction). Pump duty point is where pump curve crosses system curve.
Service factor and motor selection
Selected motor hp ≥ BHP at end-of-curve (max Q point) ÷ service factor (typically 1.15 for premium efficiency). Don't size to "BHP at design Q" because system curve drift over time can shift duty point, and pump curve may end higher than the design point. Bigger motor = small cost increase, prevents overload.
Reference: Hydraulic Institute (2021). HI Pump Standards. Karassik, I.J., et al. (2008). Pump Handbook, 4th ed., McGraw-Hill. Avallone, E.A., Baumeister III, T. (2007). Marks' Standard Handbook for Mechanical Engineers, 11th ed.