The science
Unsteady 1D pipe flow: ∂H/∂t + (a²/gA) ∂Q/∂x = 0, ∂Q/∂t + gA ∂H/∂x + f Q|Q|/(2DA) = 0, solved on the characteristic lines C±: H ± B Q - R Q|Q| = const with B = a/(gA) and Courant number 1. A reservoir of constant head sits upstream; downstream a valve obeys an orifice law Q = C_v τ sqrt(H - H_tail) with opening τ(t).
Closing the valve faster than 2L/a gives the Joukowsky jump Δp = ρ a v; slower closure approaches the Michaud estimate ΔH = 2Lv/(g t_c).
Simplifications: constant wave speed (no pipe elasticity change with pressure), steady-friction factor, no column separation model (a vapour-pressure warning is shown instead), isothermal incompressible-ish water, level pipe. Values are illustrative orders of magnitude, not a design calculation for a real pipeline.
Made with ChatGPT · 2D companion of the 3D page; same solver and numbers.