Surge / Water Hammer Calculator

Formula overview

SI: ρ in kg/m³, K and E in Pa, D and e in m, L in m, V in m/s, c in m/s, ΔP in Pa.

Korteweg wave speed:
  c = √( 1 / ( ρ · (1/K + D/(e·E)) ) )

Rapid closure — Joukowsky, when t_close ≤ 2L/c:
  ΔP = c · ρ · V

Slow closure — Michaud–Allievi, when t_close > 2L/c:
  ΔP = 2·L·ρ·V / t_close

2L/c is the time for the wave to travel to the far end and back — the
boundary between the two regimes.

Worked example

Water in a 6" Sch 40 steel line at 2 m/s, L = 500 m:
ρ = 998 kg/m³, K = 2.15 GPa, D = 0.154 m, e = 0.00711 m,
E = 210 GPa

1/K       = 4.65×10⁻¹⁰      D/(eE) = 1.03×10⁻¹⁰
c         = √(1 / (998 × 5.68×10⁻¹⁰)) = 1 328 m/s
2L/c      = 1 000 / 1 328 = 0.75 s   critical closure time

Closing in under 0.75 s gives the full Joukowsky rise:
ΔP = 1 328 × 998 × 2 = 2 650 000 Pa = 26.5 bar

On a line operating at 10 bar that is a peak near 36 bar — far above
the design pressure, from a valve closing in under a second.

Common mistakes

• Assuming a valve closes slowly because its actuator is slow. What matters is the last part of the travel, where most of the flow is cut off. A valve that takes 30 seconds to move can still produce a rapid stop in its final few percent, and a slamming check valve is faster still.
• Ignoring the pipe material. Wave speed depends on the pipe's elasticity as well as the fluid's — the same water in HDPE propagates at a few hundred metres per second instead of well over a thousand, so a plastic line sees a far smaller surge than steel.
• Overlooking column separation. If the downsurge drops local pressure to the vapour pressure, the column parts and rejoins, and the rejoining impact can exceed the original Joukowsky rise. That case needs a transient model, not a closed-form estimate.

FAQ