brake horsepower formula for centrifugal pump

The brake horsepower (BHP) of a centrifugal pump is the actual power required to drive the pump and move the fluid, accounting for efficiency losses. The formula for brake horsepower is:

Brake Horsepower (BHP) Formula:

$$\text{<span style="font-size: 18px;">BHP</span>}<span\; style="font-size:\; 18px;">=</span>\frac{\mathrm{<span\; style="font-size:\; 18px;">Q</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">H</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">\rho </span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">g</span>}}{\mathrm{<span\; style="font-size:\; 18px;">3960</span>}<span\; style="font-size:\; 18px;">\times </span>{\mathrm{<span\; style="font-size:\; 18px;">\eta </span>}}_{\mathrm{<span\; style="font-size:\; 18px;">p</span>}}}$$BHP=3960×ηpQ×H×ρ×g

Where:

• BHP = Brake horsepower (HP)

• Q = Flow rate (gallons per minute, GPM)

• H = Total head (feet, ft)

• ρ (rho) = Fluid density (pounds per gallon, lb/gal; water ≈ 8.34 lb/gal)

• g = Gravitational acceleration (implicit in the constant 3960)

• η_p (eta_p) = Pump efficiency (decimal, e.g., 0.85 for 85% efficiency)

Simplified Formula (for water at standard conditions):

Since ρ × g is constant for water (≈ 8.34 lb/gal), the formula reduces to:

$$\text{<span style="font-size: 18px;">BHP</span>}<span\; style="font-size:\; 18px;">=</span>\frac{\mathrm{<span\; style="font-size:\; 18px;">Q</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">H</span>}}{\mathrm{<span\; style="font-size:\; 18px;">3960</span>}<span\; style="font-size:\; 18px;">\times </span>{\mathrm{<span\; style="font-size:\; 18px;">\eta </span>}}_{\mathrm{<span\; style="font-size:\; 18px;">p</span>}}}$$BHP=3960×ηpQ×H

Alternative Formula (in SI Units: kW):

$$\text{<span style="font-size: 18px;">BHP (kW)</span>}<span\; style="font-size:\; 18px;">=</span>\frac{\mathrm{<span\; style="font-size:\; 18px;">Q</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">H</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">\rho </span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">g</span>}}{\mathrm{<span\; style="font-size:\; 18px;">1000</span>}<span\; style="font-size:\; 18px;">\times </span>{\mathrm{<span\; style="font-size:\; 18px;">\eta </span>}}_{\mathrm{<span\; style="font-size:\; 18px;">p</span>}}}$$BHP (kW)=1000×ηpQ×H×ρ×g

Where:

• Q = Flow rate (m³/s)

• H = Head (meters, m)

• ρ = Density (kg/m³; water ≈ 1000 kg/m³)

• g = 9.81 m/s²

• η_p = Pump efficiency

Key Notes:

1. 3960 Constant: Derived from converting (ft·lb/min) to horsepower (1 HP = 550 ft·lb/s = 33,000 ft·lb/min).

2. Efficiency (η_p): Typically ranges from 50% to 90% depending on pump design and operating conditions.

3. Density Adjustment: For fluids other than water, multiply by specific gravity (SG = ρ_fluid / ρ_water).

Example Calculation (US Units):

• Flow (Q) = 500 GPM

• Head (H) = 100 ft

• Efficiency (η_p) = 80% (0.8)

• Fluid = Water (ρ = 8.34 lb/gal)

$$\text{<span style="font-size: 18px;">BHP</span>}<span\; style="font-size:\; 18px;">=</span>\frac{\mathrm{<span\; style="font-size:\; 18px;">500</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">100</span>}}{\mathrm{<span\; style="font-size:\; 18px;">3960</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">0.8</span>}}<span\; style="font-size:\; 18px;">=</span>\frac{\mathrm{<span\; style="font-size:\; 18px;">50</span>}<span\; style="font-size:\; 18px;">,</span>\mathrm{<span\; style="font-size:\; 18px;">000</span>}}{\mathrm{<span\; style="font-size:\; 18px;">3168</span>}}<span\; style="font-size:\; 18px;">\approx </span>\mathrm{<span\; style="font-size:\; 18px;">15.8</span>}\text{<span style="font-size: 18px;"> HP</span>}$$BHP=3960×0.8500×100=316850,000≈15.8 HP

Conclusion:

Brake horsepower increases with higher flow, head, or fluid density, and decreases with better pump efficiency. Always verify pump curves for real-world performance.

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