Water Hammer Surge Pressure
Joukowsky surge from a sudden valve closure: elastic-pipe wave speed from bulk and pipe moduli, bore and wall; critical time 2L/c; slow-closure estimate.
Wave speed (rigid and elastic), the surge pressure and its head, the critical time for the pipe length, whether your closure is fast or slow, and the total with a static pressure — from your fluid and pipe data.
Example: Water (K 2.2 GPa) in a 100 × 5 steel pipe (E 200 GPa): wave speed 1,344 m/s, so stopping 2 m/s raises 2,683 kPa (274 m head); over 500 m the critical time is 0.74 s.
A pressure wave
at the speed of sound.
The Joukowsky equation, the wave speed in a real pipe, and what the critical time means.
Joukowsky
Stopping a moving liquid column suddenly turns its momentum into pressure: Δp = ρ·c·Δv, where c is the speed at which the pressure wave travels in the pipe. It is a peak that does not depend on the pipe length — only on how fast the liquid was moving and how fast the wave runs.
Wave speed
In a rigid pipe c = √(K/ρ) from the fluid’s bulk modulus. A real pipe stretches as the pressure wave passes, which slows the wave: c = √(K/ρ) ÷ √(1 + K·D/(E·e)) for a thin wall of modulus E and thickness e. The page shows both, so the rigid figure is visible as the upper bound. Fluid and pipe properties are yours from data sheets.
Critical time
The wave takes 2L/c to reach the far end and return. A valve closing within that time sees the full surge no matter how it closes; a slower closure lets relief arrive, and the rigid-column estimate Δp ≈ 2ρLΔv/t (Michaud) is shown, capped at the Joukowsky value. Branches, air, relief devices and column separation change the real transient and are not modelled. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Joukowsky Δp = ρ·c·Δv; thin-wall wave speed c = √(K/ρ) ÷ √(1 + K·D/(E·e)); critical time Tc = 2L/c; rigid-column estimate 2ρLΔv/t for closures slower than Tc — fluid and pipe properties are the user’s
Last reviewed 21 September 2026. How results are checked: How we verify.