Pump Power Calculator Formula

Understand the math behind the pump power calculator. Each variable explained with a worked example.

Formulas Used

Hydraulic Power

hydraulic_power = density * 9.81 * q_m3s * total_head / 1000

Required Shaft Power

shaft_power = density * 9.81 * q_m3s * total_head / (1000 * eta)

Variables

VariableDescriptionDefault
flow_rateFlow Rate (Q)(L/s)20
total_headTotal Dynamic Head (H)(m)30
densityFluid Density (rho)(kg/m^3)1000
efficiencyPump Efficiency(%)75
q_m3sDerived value= flow_rate / 1000calculated
etaDerived value= efficiency / 100calculated

How It Works

Pump Power Calculation

The power a pump must supply depends on the flow rate, the head it must overcome, and pump efficiency.

Formulas

Hydraulic power = rho g Q H (useful work on the fluid)

Shaft power = rho g Q H / eta (actual input from motor)

where rho is fluid density, g = 9.81 m/s^2, Q is volumetric flow rate, H is total dynamic head, and eta is pump efficiency.

Worked Example

A pump delivers 20 L/s of water against 30 m total head at 75% efficiency.

flow_rate = 20total_head = 30density = 1000efficiency = 75
  1. 01Q = 20 L/s = 0.020 m^3/s
  2. 02Hydraulic power = 1000 x 9.81 x 0.020 x 30 = 5886 W = 5.89 kW
  3. 03Shaft power = 5.89 / 0.75 = 7.85 kW
  4. 04Select a motor of at least 7.5 kW (next standard size up).

Ready to run the numbers?

Open Pump Power Calculator