A simple approach to the prediction of waterhammer transients in a pipe line with entrapped air

The pressure histories within entrapped air bubbles in a pipe line during a waterhammer transient are treated theoretically. A convenient integral method is introduced, which takes full account of air/water interface movement and liquid compressibility. The significance of the method is that it provides a simple equation set for approximating, with good accuracy and with a small degree of conservatism, the solution to a problem that otherwise involves coupled partial differential equations on time dependent domains with non-linear boundary conditions. The accuracy of the method is defined by its comparison with available numerical-solution-predictions and measurements of the pressure within an entrapped-air-bubble at a dead end in a pipe. The method is shown to be a computationally simple and efficient way of assessing the impact of liquid compressibility on pressure rise when multiple water columns and air pockets are present in a pipe line.