Air-Entrapment Issues During Draining Processes in Water Supply Systems: Towards an Analytical Solution for pressure in Inclined Pipelines

Abstract

This study examines the challenges associated with air entrapment during the draining process in water supply systems, focusing on developing an analytical solution for the dynamics of the pressure in inclined pipelines. Air pockets trapped in water columns can lead to various operational issues, such as water hammer, flow reduction, pressure oscillations, and potential structural damage. This research builds on previous numerical models that describe air-water interactions in a single inclined pipe with a sealed upper end. The model was initially formulated using a system of three equations: two ordinary differential equations (ODEs) and one algebraic equation. The primary objective of this study is to derive an analytical solution for the case where the air pocket remains closed. To achieve this, the initial model is reduced to a system of two first-order nonlinear ODEs, allowing for an analysis of the existence and uniqueness of solutions. It is then further transformed into a second-order nonlinear ODE to facilitate an intuitive examination of its oscillatory behavior. A numerical validation of this model confirms its accuracy in predicting the physical system's behavior. Additionally, through a variable transformation, the second-order ODE is converted into a first-order linear ODE, potentially simplifying the derivation of an explicit analytical solution. This research extends the understanding of transient hydraulic dynamics during the draining process in pipelines with air-water interaction. The findings provide an analytical framework that complements previous numerical solutions, offering valuable insights for optimizing hydraulic system design and performance.