Pump Power

How big a pump do you need to lift water to a tank or push it through a long pipe? From the flow and the total head to the power at the shaft and from the socket — and what it costs to run it for a year.

FluidsPumpsEnergy

Inputs

Input examples

The head is the height the pump effectively lifts the fluid, including what it loses to friction. With lift + pipe friction the friction is calculated as on the Pressure loss tab (steady flow, both ends open to the air). Efficiencies are typical guesses unless you know your pump; hours and price are optional.

Flow rate Q

Density ρ

Total head H

Static lift Δz — height difference of the two water levels

Pipe inner diameter

Pipe length

Roughness ε

Viscosity μ

Minor losses ΣK — bends, valves, entry and exit

Pump efficiency — %

Motor efficiency — %

Running hours per year — optional

Electricity price — optional, per kWh

What a Pump Has to Deliver

A pump gives the fluid energy. Per second that is the hydraulic power: weight of fluid moved per second (ρ·g·Q) times the height it is effectively raised, the head. That head is the real height difference plus the friction losses in the pipes, which grow roughly with the square of the flow.

No pump is perfect: only part of the shaft power ends up in the fluid (check the efficiency on the pump’s data sheet), and the motor loses some more. The system curve on the right shows how much head the pipe system asks for at each flow; the pump must deliver at least that at the flow you want.

1 L/s up 10 m≈ 98 W of water power

friction head∝ Q²

pump ηfrom the data sheet

10 m head≈ 1 bar

System Curve

head

Result

Enter the values above

Where the Power Goes

your inputs

Stage	Power	Lost here

Worked Techniques

Hydraulic Power

The power that actually goes into the fluid.

Example: 10 L/s of water, 25 m: 998 × 9.81 × 0.01 × 25 = 2.45 kW.

Total Head of a System

The lift between the two water levels plus the friction in the pipe and its fittings.

Example: 20 m lift, 200 m of 80 mm steel pipe at 10 L/s, ΣK = 5: about 31 m in total.

Running Cost

Over the life of a pump the electricity usually costs far more than the pump itself, which is why efficiency and wide pipes pay off.

Example: 3.9 kW for 2 000 hours at 0.30: 2 331 a year.

Sources & Verification

References

Y. A. Çengel & J. M. Cimbala, Fluid Mechanics: Fundamentals and Applications, 4th ed., McGraw-Hill, 2018 — Ch. 8 (Internal Flow).