Harbour Opening and Tidal Basin

What is modelled

A sharp-edged opening in a harbour wall joins the sea to a basin. The sea level is a sine tide. Water flows through the opening in proportion to the square root of the level difference, and the basin fills or empties in proportion to the flow divided by its area, so the basin level lags behind the sea and its range shrinks when the opening is small.

Equations

• Torricelli speed v = √(2 g h) and discharge Q = Cd A √(2 g h) with A = width × height.
• Hydraulic power scale P = ρ g Q h, an idealised rate and not turbine output.
• Basin continuity Ab dhb/dt = Q(ηsea(t) − hb) with ηsea = a sin(2 π t / T).
• Drain-down of a basin at constant sea level t = (2 Ab / (Cd A √(2 g))) (√h0 − √h).

Checks run in the page

• Torricelli speed, flow and power against the closed forms.
• Stepped drain-down time against the square-root solution.
• Trapezoid integral of the flow against the basin volume change over 1.3 tidal cycles.
• Wide-open limit: the basin range equals the tide range.

Honest simplifications

The sea is a pure sine with no waves, wind setup or surge, the basin has vertical walls, the head is the level difference with no velocity head downstream and no backwater, and the opening has a fixed discharge coefficient in both directions. It is an educational estimate, not a tidal forecast or a navigation aid.

• Press Tiny opening, strong lag and watch the basin range shrink and trail the sea.
• Press Wide opening and see the loop in the last graph close to a straight line.
• Press Big spring tide and read the peak flow and the hydraulic power.