Presets
Playback
Pump, pipe and town
Flow and pressure follow from head balance: the pump head at the given speed must equal the static lift plus the friction and minor losses plus the required outlet head. Friction uses the Darcy-Weisbach law with the Haaland formula for the friction factor. The speed slider compresses time (up to 600x).
Test actions
Model checks
The science
What is modelled
A centrifugal pump lifting water through a rising main to a hill reservoir that supplies a town. The operating point is found by iterating the friction factor and flow until the pump head equals the head needed, and the reservoir volume follows the mass balance.
Equations
- Head balance:
Hpump(Q) = z + Hout + (f L / D + K) v2 / 2g. - Friction:
f = 64/Refor laminar flow, Haaland1/sqrt(f) = -1.8 log10[(e/D/3.7)1.11 + 6.9/Re]for turbulent flow. - Reservoir:
dV/dt = Qpump - Qtown - Qleak; the town is cut off below 22% fill. - Pump power:
P = rho g Q H / eta.
Checks run in the page
- Outlet head after the losses against the required head.
- Numerical reservoir level against the exact piecewise-linear solution.
- Haaland friction factor against an iterative Colebrook-White solution (or 64/Re when laminar).
- Laminar limit f = 64/Re.
- Continuity: velocity times open area equals the flow.
Honest simplifications
A single pipe and a fixed pump curve, constant fluid properties at 20 C, no water hammer, no pipe-network loops, and a simple efficiency curve. Not a hydraulic design tool.
What to try
- Press Narrow old pipe and see the friction loss eat the pump head, so the flow falls and the reservoir drains.
- Tick Main burst and watch the exact line and the numerical line separate after the leak changes.
- Throttle the valve: the operating point moves up the pump curve.