Water Hammer Calculator (Joukowsky Pressure Surge)
Pressure rise when a flow is stopped suddenly in a pipe, from the change in speed, the pressure-wave speed and the density, with the critical closing time.
Results
The dashed line marks the value you entered.
What this tool does
Stopping moving water abruptly sends a pressure wave along the pipe: Joukowsky's equation gives its size, Δp = ρ·c·Δv, and in a steel water pipe, where c is around 1000 m/s, every 1 m/s of speed stopped adds roughly 10 bar. The wave speed is lower in plastic pipes, a few hundred m/s, and in pipes with a lot of air. The wave takes 2L ÷ c to go to the end of the pipe and back; a valve that closes in less than that produces the full surge, while a slower closure gives less, so closing slowly is the cheapest protection. The figure here is the ceiling for a straight pipe.
Formula
Δp = ρ × c × Δv (Joukowsky) · Δh = c × Δv ÷ g · critical closing time = 2L ÷ c
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dv | Sudden change in flow speed | m/s |
c | Speed of the pressure wave in the pipe | m/s |
ro | Density | kg/m³ |
l | Pipe length from the valve to the first reflection | m |
tc | Valve closing time | s |
DP | Pressure surge (Joukowsky) | bar |
DH | Surge as a height of water | m |
TC | Critical closing time 2L ÷ c | s |
CL | Does the full surge apply? | — |
Worked example
- Sudden change in flow speed2 m/s
- Speed of the pressure wave in the pipe1000 m/s
- Density1000 kg/m³
- Pipe length from the valve to the first reflection500 m
- Valve closing time0.5 s
- Pressure surge (Joukowsky)20.00 bar
- Surge as a height of water203.9 m
- Critical closing time 2L ÷ c1.000 s
- Does the full surge apply?Yes — the valve closes within the critical time, so the full surge builds up
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.