The expression used to calculate water hammer pressure p_w is:

Explanation:

When the water flowing in a long pipe is suddenly brought to rest by closing the valve or by any similar cause, there will be a sudden rise in pressure due to the momentum of the moving water being destroyed.

This causes a wave of high pressure to be transmitted along the pipe which creates noise known as knocking.

This phenomenon of the sudden rise in pressure in the pipe is known as a water hammer or hammer blow.

Water hammer pressure rise can be calculated using the Joukowsky equation

P = ρCU  (Pa)

Where

P is the change in pressure, ρ is the fluid density

U is the change in fluid velocity, C is the sonic velocity in the pipe

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.

\(C = V\;\sqrt {\frac{\rho }{{\left( {\frac{1}{K} + \frac{D}{{Et}}} \right)}}}\)