Side view: culvert valve, chamber level, vessel and the filling curve.
The science
A lock raises or lowers a vessel by letting water flow through filling culverts between the chamber and a pool until the two water surfaces match. The flow through the culvert valves is an orifice flow: Q = Cd A_v sqrt(2 g h), where h is the head (level difference), A_v the open culvert area and Cd the discharge coefficient (0.68 as in the 3D page).
Filling dynamics. The chamber surface area is A = L W (32 m by 12 m), so A dh/dt = -Q. Separating variables gives the closed form sqrt(h(t)) = sqrt(h0) - Cd A_v sqrt(2 g) t / (2 A) and the fill time T = 2 A sqrt(h0) / (Cd A_v sqrt(2 g)). The head decays to zero in finite time, quickly at first and slowly at the end, which is why real locks open the valves in stages to limit surge. The page integrates the equation with RK4 and compares with the closed form.
Power. The hydraulic power dissipated in the culverts is P = rho g Q h. Gates. Mitre gates are pushed shut by the higher pool and can only open once the heads are equal, so the page opens them when h falls below 2 cm.
Honest simplifications: the pool outside the chamber is infinite (constant level); constant valve opening; no culvert friction losses beyond Cd, no surge or vessel-induced flow, no emptying delay; illustrative composite, not a design of any specific lock.