Gate discharge (Torricelli / orifice model)
Q = C_d A sign(Δh) √(2 g |Δh|)
Chamber continuity
dh/dt = (Qin + Qout + Qpump + Qrain − Qleak) / Alock
Rainfall input
Qrain = (r × 0.001 / 3600) Alock
Floating boat (Archimedes)
draft = mboat / (ρwater Awaterplane)
freeboard = hull depth − draft
Constants: g = 9.81 m/s²; ρwater = 1000 kg/m³; discharge coefficient C_d = 0.62; chamber area = 80 m²; hull depth = 0.92 m.
Assumptions & simplifications: incompressible water, constant density and chamber area, quasi-steady orifice flow, box-like hull with constant waterplane area. Gate motion, boat acceleration and wind sway are simplified. The pump-only curve is an analytic constant-rate reference, not a prediction of the full gate-flow system.
Credits: original procedural scene and equations; no external 3D assets.