Solutions of selected pseudo loop equations in water distribution network using Microsoft Excel solver

Abstract

Adequate potable water supply (quality and quantity) is relevant to the community development while water consumption per capita per day and sanitation practices of the people in a community are functions of adequate potable water supply. This paper demonstrated the use of Microsoft Excel Solver (a computer package) in solving selected pseudo loop equations in pipe network analysis problems. Two pipe networks with pumps and overhead tanks were used to demonstrate the use of Microsoft Excel Solver in solving pseudo loops (open loops; networks with pumps or reservoirs in series) equations in water distribution network from groundwater sources. Continuity and headloss equations (non linear and linear, transform into linear equations using linear theory method) were developed. These equations were solved using Microsoft Excel Solver. Pump characteristics parameters and headloss were determined from the solutions. These flows and headloss in the pseudo loops calculated were evaluated statistically using Analysis of variance (ANOVA); total error, root squared error, sum of squared error, mean squared error, model of selection criterion (MSC) and average error. The study revealed that the flows calculated were similar for the two equations and there is no significant difference between the flows expected and flows calculated as well as headloss in pipe network using the two equations (F = 5.37 x 10^-5 ; p = 0.99995) at 95 % confidence level. Total errors for linear and non-linear equations were 0.002 and 0.008 with root squared errors of 0.0459 and 0.0875, while MSC values were 10.220 and 8.926 respectively. It was concluded that solving pseudo loops using these two equations provided information on pumps characteristics and would aid in pumps selection as well as provide necessary information for water, hydraulics, mechanical and environmental engineers.

 Keywords: Microsoft Excel Solver, Pipe Network Analysis, Pseudo loops, Statistical Analysis, Headloss, Flow