Hong Life CalculatorsUnderstanding the water hammer pressure surge calculator — concept and principle
Water hammer is the pressure surge that occurs when the flow in a pipe is stopped or changed suddenly, for example by a fast-closing valve or a pump trip. The calculator uses the Joukowsky equation to estimate the pressure rise from the velocity change, the pressure-wave speed and the liquid density, and gives the critical closure time 2L/c that separates "sudden" from "slow" closure.
How it is calculated
- Joukowsky surge: Δp = ρ · c · Δv, in Pa, divided by 10⁵ to give bar.
- Critical closure time: t_c = 2L ÷ c, the time for a pressure wave to travel to the far end of the pipe and back.
- Units: ρ in kg/m³, c and Δv in m/s, L in m.
The principle
When a valve shuts, the water next to it stops first. Its momentum ρΔv per unit volume must be removed, and the only way is a sharp rise in pressure that compresses the liquid and stretches the pipe slightly. This disturbance travels upstream at speed c, stopping the water as it passes. Momentum balance across the moving wave front gives Δp = ρcΔv, derived by Nikolai Joukowsky from experiments in Moscow around 1897–1898. The wave reflects at a reservoir and returns as a relief wave after 2L/c. If the valve closes faster than that, the full Joukowsky pressure develops; slower closure lets the returning wave cancel part of the rise.
Worked example
- Inputs: Δv = 2 m/s, c = 1200 m/s, ρ = 998 kg/m³, L = 500 m.
- Δp = 998 × 1200 × 2 = 2,395,200 Pa.
- In bar: 2,395,200 ÷ 100,000 = 23.952 bar, equal to about 245 m of water head.
- t_c = 2 × 500 ÷ 1200 = 0.833 s.
| Velocity change (m/s) | Pressure rise (bar) |
|---|---|
| 0.5 | 5.988 |
| 1 | 11.976 |
| 1.5 | 17.964 |
| 2 | 23.952 |
| 2.5 | 29.94 |
| 3 | 35.928 |
| 4 | 47.904 |
How to read the result
Closing faster than 0.83 s adds almost 24 bar to the operating pressure, beyond the rating of many pipes. For closures slower than 2L/c, Michaud's rough estimate Δp ≈ 2ρLΔv ÷ t gives an idea of the reduction: closing over 5 s gives about 4 bar here. Wave speed depends on the pipe: for water it is typically about 1,000–1,400 m/s in steel or ductile iron and only a few hundred m/s in plastic pipes, so plastic pipes see much smaller surges.
Common mistakes
- Using the speed of sound in open water (about 1,480 m/s) for every pipe, ignoring wall elasticity.
- Assuming a slow-looking valve is safe; most of the flow is often cut off in the last part of a valve's stroke.
Frequently asked questions
How is wave speed calculated?
For a thin-walled pipe, c = √((K/ρ) ÷ (1 + K·D ÷ (E·e))), where K is the liquid's bulk modulus, E the pipe material's modulus, D the diameter and e the wall thickness.
How can water hammer be reduced?
Close valves more slowly, use surge tanks, air vessels or relief valves, and limit pipeline velocity.
Why do house pipes bang when a tap shuts?
A fast valve stops the flow almost instantly and the surge shakes loosely fixed pipes.
Sources: N. Joukowsky, On the hydraulic hammer in water supply pipes (trans. O. Simin), Proceedings of the American Water Works Association, 1904 · E. B. Wylie and V. L. Streeter, Fluid Transients in Systems, Prentice Hall