Water hammer from a fast high-Cv valve: the effective closing time is far shorter than the stroke

Sizing a solenoid to shut a water line that is pressure-fed from a tank: the hand formula for slow closure (Michaud, dp ~ 2 rho L v / t_close) badly underestimates the surge when the valve is a small part of the system loss. With an open valve taking ~11 psi out of ~800 psi of system drop, the flow hardly changes until the last few percent of the stroke, so the flow actually stops in a small fraction of t_close. A method-of-characteristics run with a discrete vapour cavity model (Wylie and Streeter), area closing linearly in time and the line calibrated to the known steady pressures, gave the upstream peaks below. They are close to Joukowsky for 2 to 10 ms strokes and only reach ~10% overshoot by ~50 ms. Downstream, the column separates to vapour pressure; with an outlet open to atmosphere the collapse spikes stayed below the running pressure. Practical rules: (1) do not judge water hammer from stroke time when valve dP/system dP is small; simulate or use an effective closure time; (2) a pilot solenoid on a high-flow pressure-fed water line wants >= 50 ms effective closure, a fail-open choice if loss of power must keep water flowing, and a check that its minimum differential pressure lets it seal when the tank is vented; (3) before trusting a copied model, check it holds the steady state exactly with the valve open. Implementation gotcha: in a time-stepping loop, do not reuse the step counter name for a loss coefficient inside the loop body; Python resets it each iteration, so the physics is fine, but any later k % N sampling test silently misfires.