Water & Wastewater
Pump Horsepower and Total Dynamic Head
Hydraulic horsepower, brake horsepower, and motor input power from flow, head, specific gravity, and efficiency.
Calculated reference results
- Total dynamic head
- 63.0ft
- Hydraulic horsepower
- 7.95hp
- Brake horsepower
- 11.36hp
- Next catalog motor size
- 15 hp
- Motor input power
- 9.12kW
- Energy at continuous duty
- 218.8kWh per day
- Wire-to-water efficiency
- 65.1%
27.3 psi
At 70% pump efficiency
Confirm the motor is non-overloading across the full operating range, not just at this point.
At 93.0% motor efficiency
Pump and motor combined. Drive and transmission losses are additional.
The arithmetic
- TDH = 45.0 static + 18.0 friction + 0.0 pressure = 63.0 ft
- WHP = (500 gpm x 63.0 ft x 1.00) / 3960 = 7.95 hp
- BHP = 7.95 / 0.70 = 11.36 hp
- Motor input = 11.36 hp x 0.746 / 0.93 = 9.12 kW
What this does not account for
- A pump operates where its curve crosses the system curve, which is often not the point you calculated. Check the duty point on the manufacturer curve rather than assuming.
- Pump efficiency varies across the curve. The value at the best efficiency point does not apply at the ends, and a pump run far from that point wastes energy and wears quickly.
- Size the motor to be non-overloading across the whole operating range. A pump running out on its curve at low head can draw more power than at the design point.
- Friction losses change as pipe ages and as the system fouls. A force main sized on new-pipe friction will see higher head years later.
How this is calculated
Hydraulic horsepower is flow in gallons per minute multiplied by total dynamic head in feet, multiplied by specific gravity, divided by 3960. Brake horsepower is that figure divided by the pump efficiency, and motor input power is brake horsepower divided by the motor efficiency.
Formulas
WHP = (Q x H x SG) / 3960
- Q — flow in gallons per minute
- H — total dynamic head in feet
- SG — specific gravity
BHP = WHP / pump efficiency
Motor input kW = BHP x 0.746 / motor efficiency
Assumptions and limitations built into this calculator
- Centrifugal pump at a single duty point.
- Head values are supplied by you. This does not calculate friction from pipe data.
- Ignores drive losses, mechanical seal losses, and any transmission.
Frequently asked questions
- Where does 3960 come from?
- It is the unit conversion that turns gallons per minute and feet of head into horsepower: 33,000 foot-pounds per minute per horsepower divided by 8.34 pounds per gallon.
- Should I use specific gravity for wastewater?
- Raw wastewater is close enough to 1.0 for most purposes. Thickened sludge is meaningfully heavier and the specific gravity matters there.
Direct contact
Have a controls question?
Reach Eric Sullivan directly about anything on this site, a controls or automation topic, or one of his personal projects.