Graph-Theoretic Models for Pipe Network Analysis

Graph-theoretic models were developed for the analysis of nonlinear pipe networks. Both symbolic formulation procedures as well as illustrative examples were presented. The topological information contained in the continuity equations together with the component characteristics are used to derive the minimum set of independent equations in a systematic manner. In contrast to conventional methods, the nonlinearities associated with components in the network are treated as an integral part of the formulation procedures and thus they do not require any special treatment. One of the main advantages of the graph-theoretic approach is that the formulation procedure is independent of the numerical technique used to solve the resulting set of nonlinear equations. In other words, once the equations are formulated, a suitable numerical method for solution can be chosen. The graph-theoretic formulation procedures are highly computer worthy.