Mathematical model for the analysis of unsteady flow during a pressure pipeline break using the method of characteristics

Abstract

The goal of developing a mathematical model to analyze the occurrence of non-stationary flow is to conduct an analysis of an existing pressure pipeline - specifically, a siphon from an irrigation system in Macedonia. In this system, when a defect occurs in the pipeline, particularly in the section experiencing the highest pressure, the phenomenon of non-stationary flow arises - creating a significant vacuum within the pipeline, leading to a massive breakdown. Specifically, this concerns a steel pipeline with a diameter of D=1640 mm, operating at a maximum working pressure of 8.2 bar in the lowest part of the siphon. When non-stationarity occurs, a substantial negative pressure (vacuum) emerges, resulting in complete destruction of the pipeline over a length of 500 m.