A self-similar solution for transient flow in a pipeline

Abstract

In this study, we examine the classical problem of unsteady fluid flow in a long pipeline, induced by reduction/growth in the fluid head. This problem was solved by using the symmetry properties of the water hammer equations, which enable us to transform the time and the space coordinates into one independent coordinate. In other words, the two partial differential equations which are characterized by the unsteady flow in a long pipeline were reduced to one nonlinear ordinary differential equation.In general, self-similar solutions are an effective tool for describing transient phenomena in various flow fields, where the problem lacks a characteristic length or time scale. The development of self-similar solutions simplifies the physical problem and changes the partial non-linear differential equations to the level of ordinary differential equations. As a result, a closed form analytical solution for the governing equations (continuity and momentum) is derived for several transient situations. Based on data of heads, collected from the pipeline for transient situations, the model was calibrated and its applicability to predict head distribution in the pipeline has been shown.