Delivered scenarios: Torricelli drain of a tank (A_t dh/dt = −C_d A_o √(2gh)), with the hole area from its diameter A_o = πd²/4, and the constant-flow filling plan dh/dt = (Q_in − Q_out)/A.

A·dh/dt = Q_in − Q_out + C_d A_in·sgn(H_u − h)√(2g|H_u − h|) − C_d A_out·sgn(h − H_l)√(2g|h − H_l|) [m³/s].

Drain only: √(h − H_l) = √(h₀ − H_l) − C_d A_out√(2g)/(2A)·t ⇒ empty at T = 2A√(h₀ − H_l)/(C_d A_out√(2g)). Fill only: T = 2A√(H_u − h₀)/(C_d A_in√(2g)).

Both sluices open: A_in²(H_u − h*) = A_out²(h* − H_l) ⇒ h* = (A_in²H_u + A_out²H_l)/(A_in² + A_out²). Constant flows only: h = h₀ + (Q_in − Q_out)t/A.

Honest simplifications. Quasi-steady orifice flow with a constant discharge coefficient and negligible velocity head in the chamber and pounds; a vertical-walled chamber of constant plan area; no gate opening time, culvert friction, surge or ship displacement; the chamber spills above its depth. The head-driven inlet and the lower pound are extensions of the delivered scenarios. Preset values and captions are those of the original simulations (the 2D-physics ones among them that could be read).

Canal Lock Chamber Filling and Draining: Sluice Flow and Water-Level Case-Study Lab

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