Polder Drainage Under a Storm

What is modelled

The polder is a storage basin with a fixed surface area. Rain fills it at a steady rate. When the sea outside is lower than the water in the polder, the sluice gate lets water out by gravity, with a flow that grows with the square root of the head. When the sea is higher, the gate closes and no water can flow in. A pump station switches on when the polder level reaches a start level and off at a lower stop level, so the level stays near its target while the pumps keep up and rises when they do not.

Equations

• Sea level η(t) = a cos[2π(t − t0) / T] with T = 12.42 h.
• Sluice flow Qs = Cd b Hd √(2 g (h − η)) when h > η, otherwise 0.
• Storage A dh/dt = qin − Qs − Qp.
• Sluice window per tide T [1 − arccos(L / a) / π] for a polder level L.

Checks run in the page

• Rain in equals sluice out plus pumps out plus storage change.
• RK4 emptying against the closed form (sqrt(d0) − κ t / 2)².
• A scan of the tide cycle against the window formula.
• Highest level for a 30 s and a 5 s step.

Honest simplifications

The polder has vertical sides and a single level, the gate opening, the discharge coefficient and the pump head and efficiency are round teaching values, wave set-up, wind surge, seepage, groundwater and the changing tide range between spring and neap tides are not modelled. It is a classroom model, not a design tool for a real polder.

• Press Storm, small pumps and watch the level pass the flood line.
• Press Storm, big pumps and compare the highest level.
• Press High tide range and see how the sluice window changes.