Effect of longitudinal displacement of the piping on the pressure variation in a water hammer

As a result of longitudinal deformation and displacements of the piping, the pressure in a water hammer can exceed by several tens of a percent the value predicted by Zhukovskii's theory. A pipe of finite length reinforced at the ends is considered, it being assumed that the velocity of propagation of perturbations in the pipe wall can be as much as four times as great as the velocity of a shock wave in the liquid. The reinforcing elements are modeled as concentrated masses. Equations are derived for the motion of these masses, where the longitudinal stresses in the pipe and the flow parameters at the end of the pipe are connected by the appropriate Riemann parameters. Solution of these equations gives the time variation of pressure at the end of the pipe, where the hydraulic hammer effect occurs. Experimental data were used to corroborate the theoretical results.