Matrix Method for Analysis of Hydraulic Networks

A new matrix method is developed for the steady-state and transient analyses of incompressible flow networks. It is shown that the branch pressure drop versus nodal pressure, nodal continuity, and branch momentum equations can be expressed in matrix form for networks with any arbitrary configuration. These equations are solved simultaneously to obtain explicit relations for the unknown nodal pressures and branch mass flow rates. This new technique is applied to the analysis of a water distribution network. To ascertain the accuracy of the solution, a numerical stability and convergence analysis is performed which provides an estimate for the upper bound of time increment needed for a stable and convergent numerical integration. The transient and steady-state behavior of incompressible flow networks with arbitrary configurations having nodal sources and sinks as well as branch transducers are determined by the time-integration of the network dynamic equations with a comparatively smaller computer running time.