Water hammer

A flowing column of liquid has momentum. When a valve closes quickly, the liquid immediately upstream is stopped while the column behind it is still pushing on. Kinetic energy turns into pressure. The pressure rise travels as a wave at the speed of sound against the direction of flow, is reflected at the next vessel and oscillates until friction has consumed it.

Downstream of the valve the opposite happens: the liquid keeps moving and the pressure falls. The event is audible as a bang – hence the name.

The magnitude of the pressure rise for a sudden change in velocity is given by the Joukowsky equation:

Δp = ρ · a · Δv

Here ρ is the density of the liquid, a the propagation speed of the pressure wave and Δv the change in flow velocity. For water in steel pipe, a is of the order of 1000 m/s and above; it decreases with the flexibility of the pipe wall and is considerably lower in plastic pipe.

An example: water, a = 1200 m/s, flow stopped from 2 m/s to zero. The pressure rise is 1000 · 1200 · 2 = 2.4 · 10⁶ Pa, that is 24 bar – in addition to the operating pressure and regardless of how high that is.

The full Joukowsky surge occurs when the valve closes faster than the pressure wave needs to travel to the point of reflection and back. This reflection time is 2 · L / a. For a line 600 m long and a = 1200 m/s it is one second: any valve closing faster than that acts like one closed instantaneously.

If it closes more slowly, the returning relief wave arrives before closure is complete and the pressure rise is smaller. The nominal closing time is not what counts: many valves throttle the flow only over the last part of their stroke, so the effective closing time is much shorter.

The pressure rise is only half the loading. While the pressure wave passes through a straight run between two bends, the pressure at its two ends differs for a short time. The difference times the flow area gives a force along the pipe axis that tries to shift the run.

These forces tear lines off their supports and supports out of the steelwork. They are taken by anchors and axial stops and determined in a dynamic analysis – or, simplified, as an equivalent static load with a dynamic load factor, which is up to 2 for a suddenly applied load.

Fast-closing valves are not the only cause. When a pump trips, the liquid column separates downstream of it; when it rejoins, high pressure peaks occur. In steam lines, entrained condensate causes hammer. The measures address the respective cause.