Network Linear Programming as Pipe Network Hydraulic Analysis Tool

Abstract

An accurate network linear programming (NLP) algorithm for the hydraulic analysis of water pipe networks is developed and compared with direct equation solving techniques. Accuracy is achieved by the use of a novel iterative scheme in which successive linear approximations to the nonlinear head loss equations are refined for each pipe in the region of the emerging solution. The use of primal-dual and simplex method NLP solvers in the iterative strategy is investigated, with a hybrid scheme being shown to reduce execution times by an order of magnitude. Nevertheless, the direct equation solving algorithm of Todini and Pilati remains much more efficient than the best NLP algorithm. A new algorithm for the analysis of locally controlled feedback devices is developed for inclusion in the NLP strategy. The uniqueness of pipe network hydraulic solutions is also investigated. Although some doubt has been expressed regarding uniqueness of solutions to networks that contain locally controlled feedback devices, evidence of nonuniqueness has not been forthcoming. Arguments in support of unique solutions for such networks are presented.