This induces the first wave reflection and it occurs at time t1.įigure 4 shows the conditions after the first reflection. So now the fluid needs to move in the reverse direction from the high pressure pipe into the lower pressure tank. This condition is unstable as the pipe inlet pressure is set by the head of fluid in the inlet tank h. The pipeline pressure has been raised by ρCU i and the fluid velocity is 0 throughout. The rate of pipe volume change and fluid compression is the same as the flow rate upstream of X.įigure 3 shows the conditions when the pressure wave reaches position A at time t1. Downstream of X the velocity is 0.īetween X and B the fluid will be compressed and the pipe will be expanded. Upstream of position X the velocity is the initial velocity U i. The pressure rise across the wave is ρCU (Joukowsky equation). A pressure wave at position X is traveling up the pipe with velocity C (the sonic velocity). The other end of the pipe at position B is open to atmosphere and its pressure is P 0įigure 2 shows the pipe and flow conditions just after the pipe end at B has been instantaneously closed at time t0. The pipe inlet at position A is connected to a header tank which provides the pressure P 1 to drive the flow in the pipe. This can liberate dissolved air from the water which forms air bubbles reducing the effective bulk modulus and so reducing the wave speed.įigure 1 shows the initial conditions in the pipe. Often with water hammer sub atmospheric pressure and cavitation can also occur (as explained below). This can make a significant difference to the effective bulk modulus and so to the sonic speed. Often microscopic size bubbles can be seen suspended in the fluid. The bulk modulus (k) of water is 2.19x10 9 Pa however this assumes that the water has no air bubbles in it. But in some plastic pipe the wave speed can be lower than 200 m/s. The sonic velocity is also the speed at which the pressure waves generated by water hammer travel in the pipe.įor water in very stiff pipes the sonic speed could be as high as 1480 m/s. The sonic velocity is the speed of sound in the pipe and is determined by a modified hooks law formula which takes into account the stiffness of the fluid and the pipe wall. The magnitude of the water hammer pressure rise can be calculated using the Joukowsky equation which is Water hammer can generate very high pressure transients which could burst a pipe and can generate pipeline vibrations. Usually this occurs when a valve closes quickly. It is the special case when there is a sudden change in flow velocity. Water hammer is part of the larger subject of transient flow or surge analysis.

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