How to calculate water hammer surge pressure
Slam a valve shut and the kinetic energy of the moving column of water has nowhere to go, so it converts into pressure. The surge is given by the Joukowsky equation, ΔP = ρ × a × Δv, where ρ is the density of water, a is the speed of the pressure wave in that particular pipe and Δv is the velocity that was destroyed. This calculator works out the wave speed first, then reports the surge in psi and as an equivalent head in feet.
Wave speed comes from a = √[(K/ρ) ÷ (1 + K·D/(E·e))]. The bulk modulus of water K is about 318,000 psi, which gives roughly 4,860 ft/s in a perfectly rigid pipe. Real pipe stretches under the surge and slows the wave down: 4 in. steel typically lands near 4,300 ft/s, ductile iron a little lower, and PVC only 1,100 to 1,600 ft/s. That is exactly why a flexible pipe material sees a smaller pressure spike than steel at the same velocity.
If the valve shuts faster than the critical time 2L/a, the reflected wave has not returned yet and the full Joukowsky pressure develops. Close it more slowly and the surge falls off roughly in proportion to the closure time, which makes slow-closing valves the cheapest available fix. Surge arrestors, air chambers and slow-closing check valves are the next options, and the final piping design should be confirmed by a licensed mechanical engineer before construction.
Frequently asked questions
Aim for several times the critical time 2L/a. If the calculated critical time is 0.3 seconds, stretching closure over 2 to 3 seconds cuts the surge dramatically.
At the same velocity the lower wave speed does produce a smaller surge. But PVC also has a lower pressure rating, so judge it as a margin against the pipe class rather than on the surge value alone.