Pump power calculator

Find the power a pump duty needs: the useful hydraulic power added to the fluid, the shaft power the pump draws once its efficiency is accounted for, and the electrical power the motor takes. Useful for early sizing and for sanity-checking a pump selection against its duty point.

Method

The hydraulic (useful) power added to the fluid is

P_hyd = rho g Q H

where rho is density (kg/m^3), g is 9.81 m/s^2, Q is volumetric flow (m^3/s) and H is the pump head (m of the fluid pumped). Dividing by efficiencies steps out to the shaft and then the electrical input:

P_shaft = P_hyd / eta_pump
P_elec  = P_shaft / eta_motor

Head is expressed in metres of the pumped fluid. If you have a pressure rise instead, convert with H = dp / (rho g). Citation: standard pump fundamentals (for example the Grundfos or KSB pump handbooks; White, Fluid Mechanics).

Limits. This is a duty-point power calculation. It does not select a pump, find the operating point against a system curve, or account for viscosity corrections on the pump curve. The Studio plots pump duty, the best efficiency point and the system curve for that.

Inputs

• Fluid preset (density) or manual density (kg/m^3).
• Flow Q (L/s).
• Head H (m).
• Pump efficiency eta_pump (per cent).
• Optional motor efficiency eta_motor (per cent).

Outputs

• Hydraulic power (kW).
• Shaft power (kW).
• Electrical power (kW), if a motor efficiency is given.

Worked example

Water (density 998.2 kg/m^3) at 20 L/s against 30 m of head, with a pump efficiency of 70 per cent and a motor efficiency of 90 per cent:

P_hyd  = 998.2 x 9.81 x 0.020 x 30 = 5.88 kW
P_shaft = 5.88 / 0.70 = 8.39 kW
P_elec  = 8.39 / 0.90 = 9.33 kW

Frequently asked questions

Is the head in metres or pressure?

Metres of the pumped fluid. Convert a pressure rise with H = dp / (rho g); for water, 10 m of head is about 98 kPa.

Where do I get the efficiency?

From the pump curve at the duty point (near the best efficiency point if the selection is good). The Studio shows pump duty and the best efficiency point.

Related

• Pipe flow and pressure drop calculator
• Sizing a pump against a real system? Open the Studio to solve the pump against the network and see its duty point.