Duty and pipe
- Design flow rate
- Static lift between water levels
- Pipe length, suction to discharge
- Pipe internal diameter (DN50 PE)
- Pipe roughness (PE, example)
- Water density (20 °C)
- Kinematic viscosity (20 °C)
- Sum of fitting K-values
- Gravity
Hydraulics · worked example · 4 pages
Pumping water between two tanks
The motor power needed to pump water up to a header tank: velocity from the flow, friction from the Darcy–Weisbach equation with an explicit Swamee–Jain friction factor (no iteration needed), fitting losses from K-values, then hydraulic and shaft power. Two pipe bores are compared. Valid for turbulent flow (Re > 4000), which the sheet checks.
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What this calculation covers
Velocity and flow regime, as functions of bore
- Mean velocity in a bore d
- Reynolds number in a bore d
- Velocity in the DN50 pipe
- Velocity within the usual 3 m/s guide
- Reynolds number, DN50
- Turbulent, so the friction model applies
Friction and total head
- Swamee–Jain explicit friction factor
- Pipe friction head for a bore d
- Fitting losses for a bore d
- Total pumping head for a bore d
- Friction factor, DN50
- Total head, DN50
Power
- Pump efficiency at duty (example)
- Motor sizing margin
- Hydraulic (water) power
- Shaft power into the pump
- Motor power to specify
A smaller bore for comparison
- Velocity in DN40
- Total head with DN40 pipe
- Shaft power with DN40 pipe
Results summary
- Through DN50 pipe the duty is 3 L/s against 14.5 m of head (12 m static + 2.5 m of losses): 427 W of water power, 712 W at the shaft, so a 0.75–1.1 kW motor with the 15% margin. Dropping to DN40 raises the losses to 7.1 m and the shaft power by almost a third — pipe bore is usually cheaper than pump power.
Try changing…
- Double the flow to 6 L/s — friction losses quadruple (v²) and the DN50 velocity check fails.
- Use rough steel (ε = 0.045 mm) — the friction factor climbs about a tenth on this duty.
- Set Δz to 0 — head is pure friction; compare how the two bores then differ fourfold.