Hydraulic network analysis using (generalized) geometric programming

Abstract

Abstract The problem of determining the flows (and pressures) in the pipes of a general hydraulic network, for given input and output flows and/or given input and output pressure heads, is shown to be equivalent to either of a pair of convex programming problems with linear constraints. This is accomplished via the theory of (generalized) Geometric Programming. The equivalence of these problems is exploited to prove existence and uniqueness of the flow solution under certain conditions as well as to derive an algorithm which calculates this solution. Computational aspects of implementing the algorithm are considered in some detail and results obtained for a general example problem are presented. A brief discussion of the application of the methods of the paper to problems in electrical network analysis, transportation network analysis and the elastic analysis of structural trusses, is also given.