Analysis of water distribution systems using a perturbation method

Abstract

The analysis of a water distribution network requires the solution of a set of nonlinear equations. The current methods are all iterative and require a good initial estimate to reach the solution quickly without any convergence problems. In this study a perturbation expansion is applied to the set of nonlinear equations to obtain a series of linear equations that can be solved easily using matrix methods. The advantage of the proposed approach is that the solution is obtained directly without iterations, initial estimates, and issues of convergence. The method of solution is simple and straightforward to implement because it requires only one matrix inversion and four matrix multiplications. Hence the solution process is fast and efficient, which could prove useful in the optimization of water distribution systems wherein the network is solved for every trial set of design parameters. The solution is expressed in an explicit fashion which might be of use for further mathematical manipulation and implementation in an optimization algorithm. The method has been tested on various networks and the results obtained show a relatively high degree of accuracy.