The water hammer or Zhukowski pulse (named after the Russian engineer Nikolai Zhukovsky) is, along with cavitation, the main cause of breakdowns in pipes and hydraulic installations.

Water hammer occurs because the fluid is slightly elastic (although in various situations it can be considered a non-compressible fluid). Consequently, when a valve or a tap installed at the end of a pipe of a certain length is closed suddenly, the fluid particles that have stopped are pushed by those that come immediately behind and are still in motion. This causes an overpressure that moves through the pipe at a speed that can exceed the speed of sound in the fluid. This overpressure has two effects: it slightly compresses the fluid, reducing its volume, and it slightly dilates the pipe. When all the fluid circulating in the pipe has stopped, the impulse that compressed it ceases and, therefore, it tends to expand. On the other hand, the pipe that had widened slightly tends to return to its normal dimension. Together, these effects cause another pressure wave in the opposite direction. The fluid moves in the opposite direction but, when the valve is closed, a depression occurs with respect to the normal pressure of the pipe. As the pressure is reduced, the fluid can change to a gaseous state, forming a bubble while the pipe contracts. Upon reaching the other end of the pipe, if the wave is not dissipated, for example, in a tank at atmospheric pressure, it will be reflected and progressively mitigated by the compression resistance of the fluid and the expansion of the pipe.

If the closing or opening of the valve is abrupt, that is, if the closing time is less than the time it takes for the wave to travel through the pipe round trip, the maximum overpressure is calculated as.

In turn, the speed of the wave is calculated as:.

For the particular case of having water as a fluid:

From this expression we arrive at the Allievi formula (named after Lorenzo Allievi (1856-1941), the Italian engineer who developed it):

where a variable (lambda) is introduced that depends on the pipe material, and as a reference the following value is given:.

The water hammer problem is one of the most complex problems in hydraulics, and is generally solved using mathematical models that allow the behavior of the system to be simulated.