Pump shaft and input power

Estimate hydraulic, shaft and motor electrical input power for a specified pump head and liquid flow.

How this calculation works

This calculation separates useful hydraulic power from the mechanical and electrical power needed to provide it. Supply the liquid volume flow, total developed pump head and liquid density at the operating point. Hydraulic power is density times gravitational acceleration, volume flow and head. Dividing by pump efficiency gives required shaft power; dividing again by motor efficiency gives motor electrical input. Efficiencies entered as percentages are converted to fractions, and each should correspond to the stated operating condition. The distinction matters when comparing a fluid energy requirement with measured electrical consumption. This tool assumes steady incompressible flow and excludes separate drive losses. It does not find the intersection of a pump curve and system curve, select a motor rating or account for starting current and additional sizing margins.

Inputs and units

Liquid flow (L/s)
Total developed head (m)
Liquid density (kg/m³)
Pump efficiency (%)
Motor efficiency (%)

Method and formula

Phydraulic = ρgQH; Pshaft = Phydraulic/ηpump; Pelectric = Pshaft/ηmotor. Q is m³/s, g = 9.80665 m/s², efficiencies are fractions; divide W by 1000 for kW.

Worked example

Example inputs

Liquid flow: 5 L/s
Total developed head: 20 m
Liquid density: 1000 kg/m³
Pump efficiency: 70 %
Motor efficiency: 90 %

Calculation steps

Flow = 5 / 1000 = 0.005 m³/s. Hydraulic power = 1000 × 9.80665 × 0.005 × 20 / 1000 = 0.980665 kW.
Shaft power = 0.980665 / 0.70 = 1.40095 kW.
Motor electrical input = 1.40095 / 0.90 ≈ 1.556611 kW.

Example results

Hydraulic power: 0.980665 kW
Required shaft power: 1.40095 kW
Motor electrical input: 1.556611111 kW

Assumptions

Steady incompressible flow; efficiencies supplied for this operating point.

Limitations

No motor-size margin, drive losses, start-up current or pump-curve/system intersection.
Preliminary educational check; verify inputs and equipment data before design or operation.

Sources

DOE Fundamentals: Fluid Flow: Continuity and Bernoulli energy balance; centrifugal pumps, equations 3-19 through 3-25; series and parallel piping