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Pump, tank and town
Flows in m3/s. The pump follows Q = Qmax n (1 - H/H0) but cannot exceed what the spring supplies; the tank level obeys A dh/dt = Q_pump - Q_town - Q_leak and the leak follows Q = k sqrt(h). The pump trips if its power exceeds the grid limit for 3 s.
Test actions
Model checks
The science
What is modelled
A single pump station on a spring: the pump curve falls linearly with total head, the spring caps the supply, the tank is a vertical-walled storage volume, the leak is an orifice law and the electrical power is the hydraulic power divided by the pump efficiency.
Equations
- Pump:
Q = Qmax n (1 - H / H0), withH = z + h. - Tank:
A dh/dt = Qpump - Qtown - Qleak. - Leak:
Qleak = k sqrt(h). - Pressure:
p = rho g H; power:P = rho g Q H / eta.
Checks run in the page
- Pump power against rho g Q H / eta.
- One bar equals a 10.2 m water column.
- Tank stepper against the closed-form level for constant flows.
- Long-run level against the equilibrium solved from pump flow = demand + leak.
- Volume conservation over a run.
Honest simplifications
A linear pump curve, a single storage tank, no pipe friction in this view (the 3D page and the other pair add it), a fixed outlet capacity and a simple trip timer. Illustrative, not a design tool.
What to try
- Press Dry ridge and watch the spring limit hold the pump below its curve.
- Tick Loose joint and watch the equilibrium level fall.
- Raise the pump speed until the power crosses the grid limit and the station trips.