Pipe Pressure Drop and Pump Power Calculator (Water)
The velocity, friction factor, head loss and pump power for a liquid flowing in a pipe, using the Darcy-Weisbach equation.
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How this calculator works
The pressure lost to friction in a pipe is given by the Darcy-Weisbach equation, h = f (L / D) v² / (2g). The friction factor f depends on the Reynolds number and the roughness of the pipe wall, and the calculator finds it for you. Fittings add loss in proportion to their loss coefficient K.
The pump must supply the static lift plus the friction and fitting losses. The power the pump draws from the motor is the hydraulic power divided by the pump efficiency.
Formulas used
- Re = \frac{\rho v D}{\mu}
- h_f = f\,\frac{L}{D}\,\frac{v^2}{2g}
- P = \frac{\rho g Q H}{\eta}
Worked example
With the default numbers in the calculator above:
- Velocity: 2.39 m/s
- Reynolds number: 190604
- Friction factor: 0.0193
- Friction head loss: 10.5 m
- Fitting head loss: 0 m
- Pressure drop in the pipe: 103 kPa
- Pump head: 16.5 m
- Hydraulic power: 1.94 kW
- Shaft power: 2.99 kW
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What roughness should I use?
About 0.045 mm for new commercial steel, 0.0015 mm for plastic, and 0.5 mm or more for old rusty steel.
How do I include valves and bends?
Add up their loss coefficients (K values) and enter the sum. A 90 degree elbow is roughly 0.3 to 0.9.
What flow velocity is typical in water pipes?
About 1 to 3 m/s. Higher velocities mean more friction loss and noise.
Related calculators
Further reading: White, Fluid Mechanics; Munson, Young and Okiishi, Fundamentals of Fluid Mechanics; Crane Technical Paper 410.
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