# Use of equivalent celerity to estimate maximum pressure increase in serial pipes during water hammer – numerical simulations in MATLAB

Agnieszka Malesińska, Mariusz Rogulski, Pierfabrizio Puntorieri, Giuseppe Barbaro, Beata Kowalska

Pipe lines are useful for transporting water for drinking, irrigation and for fireing over long distances, this pipe lines are called “Transmission line” and are used to carry conveying raw or treated water from a well field or remote storage (large lake, reservoir, etc.,) facility to a treatment plant and/or distribution storage tank. In water-carrying piping systems, dangerous phenomena may occur. One such phenomenon is water hammer.

The water hammer has always been an area of study, which has captivated the minds of researchers due to its complex and challenging phenomena. Modeling the phenomenon in real conditions is extremely difficult. Due to the dimensions of the piping systems, conducting research at real scales is impossible. However, thanks to the development of numerical methods, the study of water hammer and its effects can be performed using simulation programs. Unfortunately, the simulation results are not always consistent with the actual course of the phenomenon.

One of the parameters that describes the nature of the course of a water hammer is the velocity of propagation of the pressure wave, c, which is called celerity. The transient surge pressure, p, may be calculated from the pressure celerity c, and the sudden change in fluid flow velocity, ∆ v. In a piping system, the value of the pressure wave celerity is not equal to the individual celerity, c, for a single pipeline. Therefore for piping systems for ∆p calculations the equivalent celerity shell be used.

This article presents value of the equivalent celerity calculated from equations derived using linear analysis of natural vibrations of the system. For implement of the equations, an algorithm in MATLAB has been developed that allows one to easily calculate the equivalent celerity, ce, for N pipelines connected in series with varying diameter, length and material composition.

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