Pressure Transients in Hydraulic Pipelines

Equations of motion for a cylindrical tube containing a fluid are developed from a consideration of the forces and moments in the tube wall. These equations are solved for boundary conditions representing the situation where the fluid is flowing steadily through a horizontal pipe and a valve at the downstream end is closed instantaneously. The solution gives theoretical results for the usual water-hammer wave but also predicts the existence of a precursor wave. Expressions are derived for the velocities of propagation of both transients and their associated pressure changes. A comprehensive series of experiments has been carried out. Some interesting and probably unique results were obtained, which demonstrate the behavior of both transients. Measurements of velocity and pressure change have been made. The effect of axial restraint on the pipe is demonstrated.