Water hammer surge pressure
Surge pressure from fast valve closure or a pump trip — wave speed for steel, ductile iron, PVC or HDPE pipe, critical closing time and the column-separation check.
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How this calculator works
When a valve closes or a pump stops, the moving liquid column is brought to rest and the pressure rises by ΔP = ρ·a·Δv (Joukowsky), where a is the speed of the pressure wave. The wave runs to the far end of the line and back in the critical time 2L/a; a valve that closes faster than that sees the full Joukowsky surge. The wave speed depends on how compressible the liquid is (bulk modulus K) and how much the pipe wall stretches: a = √((K/ρ)/(1 + c·K·D/(E·e))), with the restraint factor c of Wylie and Streeter. For slower closure the calculator gives the Michaud estimate 2·ρ·L·Δv/tc. Water density and bulk modulus come from IAPWS-IF97.
Example: 100 m³/h of water at 20 °C (1.49 m/s) in 500 m of 6-inch Schedule 40 steel pipe anchored throughout, with a valve that shuts in 0.5 s. The wave speed is 1,350 m/s (1,484 m/s in a rigid pipe), the critical time 0.74 s, so the closure is fast and the surge is the full 20.1 bar (205 m of water). From 5 bar g that gives 25.1 bar g — above a PN 16 rating — and on the downstream side the pressure would fall to vapour pressure. Closing the same valve in 10 s cuts the surge to about 1.5 bar. Checked against an independent calculation with the IAPWS-95 water properties of CoolProp: wave speeds agree within 0.2 % (the IF97/IAPWS-95 difference).
Limits: a screening calculation for one line between a valve and a reservoir. It does not model friction, line packing, pump inertia, air valves or column separation and its collapse — pump trips, long pipelines, networks and any result near the pressure rating need a full transient (method of characteristics) study. Use the effective closing time of the valve, not its full stroke time. References: E. B. Wylie and V. L. Streeter, Fluid Transients in Systems (1993); A. R. D. Thorley, Fluid Transients in Pipeline Systems (2004); N. Joukowsky (1898).