Water Hammer Surge Pressure Calculator

How it works

Wave speed a = √[(K/ρ) ÷ (1 + K·D ÷ (E·t))]; Joukowsky Δp = ρ × a × Δv (valid when closure time ≤ 2L/a); slower closure: Δp ≈ Joukowsky × (2L/a) ÷ t_close; peak = static + Δp

When a valve slams shut, the moving column of water cannot stop instantly; its momentum converts into a pressure wave that races back up the pipe at the speed of sound in the water-pipe system and reflects, giving the bang and shudder called water hammer. Joukowsky’s equation shows the rise depends only on the fluid density, the wave speed and the velocity killed — about 50–60 psi for every 1 ft/s in rigid metal pipe — not on the static pressure, which is why even low-pressure systems can burst fittings. The wave speed falls in elastic pipe, so PEX and PVC see much smaller surges than copper or steel. A closure slower than the round-trip time of the wave (2L/a) lets the reflected wave relieve pressure before the valve is fully shut, cutting the surge in proportion; that, plus keeping velocities under about 5–8 ft/s and fitting arrestors near solenoid valves, is the whole toolkit.

Worked example

Water at 6 ft/s in 1″ copper (0.05″ wall) has a wave speed of about 4,150 ft/s; an instant closure would raise pressure 335 psi. Eighty feet of pipe gives a 39 ms critical time, so a 50 ms solenoid still produces about 260 psi — a peak near 320 psi on a 60 psi line, double the 160 psi fitting rating; a valve closing in ≥ 0.2 s or an arrestor is needed.

Frequently asked questions