Mathematical Modelling for Some Flow Problems in Water Distribution Pipe Line Network

Abstract

newline newline newlineMathematical models for chlorine concentration decay in the water pipe line network, in reservoir and water hammer problems due to transient pressure are studied in this thesis. The thesis consists seven chapters. The first chapter is introductory in nature and deal with historical background of water treatment and various methods for disinfecting the drinking water such as boiling of water, adding excessive lime to water, treatment by ozone, bromination and chlorination etc and fundamental concepts of flow and transfer process of heat mass and energy. A brief idea of water hammer or surge pressure which is a very high pressure in the pipe line due to change in velocity when a valve is closed suddenly is also given. A relation for transient pressure due to gradual closure of valve and Jouskowsky equation for transient pressure are also discussed. The Laplace Transformation technique, separation of variables, Hankel transformation technique, explicit central difference method and some analytical methods are used to obtain the solution of the problems included in the next chapters. All the numerical values for the results of the problems and their graphical representation are obtained with the help of Mathematica and MATLAB. newlineIn chapter 2, an analysis has been carried out to discuss the chlorine concentration decay in drinking water pipe line network. The unsteady state one dimensional mass transfer equation together with source term is solved analytically by Laplace transform technique and numerically by explicit central difference method .The results obtained for both these methods are plotted in the form of graph and chlorine concentration decay together with time, distance and with diffusivity etc are discussed. We have also discussed a mathematical model that accounts for transport of chlorine by diffusion in the radial direction, by convection in the axial direction and that incorporates chlorine decay within the bulk flow and transport of chlorine from the bulk flow to the pipe wall is deve