Statistical evaluation of mathematical methods in solving linear theory problems: Design of water distribution systems

Abstract

Water distribution is an important factor in the development of a community. As a follow up on authors previous studies on water supply, access to safe water, water, sanitation and health (WASH) and network analysis, this paper presents evaluation of various methods (statistical and numerical) in use to solve Linear Theory equations in pipe network analysis. Three practical pipe network analyses were conducted using Guassian and Gaus-Jacobian eliminations, Microsoft excel solver, least squared and numerical methods. The flow obtained using the methods were evaluated using model of selection criterion MSC, coefficient of determination CD, reliability RD and errors. The study revealed that flow in pipe network analysis varied with the method. The flow was a function of the method used, length and diameter of the pipe; and withdraws from the node. The values of model of selection criterion and  coefficient of determination varied from 1.2195 to 24.5549 and 0.7912 to 0.9751 respectively. Statistical evaluation revealed that least squared, elimination, Microsoft excel solver and numerical methods had MSC of 1.7519, 2.8709, 24.5549 and 1.2195, respectively. It was concluded that Microsoft excel solver, elimination and least squared methods were better methods for solving linear theory equations in pipe network analysis than numerical method based on CD,MSC, reliability and errors, while Microsoft excel solver was the overall best method based on MSC (24.5549), reliability (99.99 %), CD (0.9751) and errors (0.0000).

Keywords: Water Distribution, Linear Theory Equations, Eliminations, Least Squared, Numerical