Equivalent Celerity in Water Hammer for Serially Connected Pipelines
Agnieszka Malesińska, Mariusz Wojciech Rogulski, Pierfabrizio Puntorieri, Giuseppe Barbaro, Beata Elżbieta Kowalska
The purpose of this study is to analyze the effect that inserting an elastic tube into a pressure pipeline has on the water hammer phenomenon. This research draws upon theoretical analysis, experimental testing, and numerical simulations. Assuming perfect elastic behavior of the system, the formula for the constant pressure wave velocity in a pipeline with an inserted tube was derived. Experimental tests were carried out, aimed at reducing the pressure increase in the pipeline due to inserting a silicone rubber tube in it. A significant reduction of the pressure increase has been achieved. Theoretical values of the pressure wave velocity were significantly lower than measured. Numerical calculations were performed, the purpose of which was to simulate the course of pressure changes in the pipeline with inserted tube. An approximate model of unsteady flow was used, which relates elastic behavior of water, pipeline, and tube materials to the continuity equation via the variable pressure wave velocity. By taking into account the variable celerity of the pressure wave and diffusive term, it was possible to obtain an acceptable compliance between the experimental data and the results of the numerical calculations.