Nonmatrix Gradient Method for the Simulation of Water Distribution Networks

Abstract

A new method is presented for the steady-state analysis of water supply networks. This method is based on the same fundamental concepts as the gradient method, with the difference that for each element in the network, two approximations are made for the energy equation, one disregarding the head variation in the upstream node and the other doing the same for the downstream node. These equations, together with node continuity equations, provide an explicit method for determining the desired heads and flows without the need for the solution of a system of equations, as is commonly used for this type of analysis. Because the elements (e.g., pipes, valves, and pumps) present the same type of treatment, the new method facilitates parallel processing. An illustrative example is presented for comparing the results obtained using the gradient method (implemented in