Compact formulation of pipe network problems

Abstract

Solution of problems in water distribution networks usually proceeds in one of two ways: (1) analysis of flows in the links, or (2) analysis of the head at the nodes. In the former case, which is somewhat commoner and has certain computational advantages, the user is usually required to generate input data by defining the set of independent loops in the circuited network in addition to the usual node and link characteristics. Such methods are acceptable for analysis where the topology of the network remains constant. A method is presented here that allows the node and loop equations to be generated automatically from a very simple data file defining nodal stipulations and link characteristics. The equations are reduced to a small set of simultaneous equations involving only the nonbasic or redundant variables. This greatly reduces the memory requirements and also speeds solution of the equations. Either an iterative linear approximation or the Newton–Raphson method may be used to solve the simultaneous equations. The approach is useful in design and optimization studies since it allows links to be deleted and/or restored with automatic generation of the necessary equations. The method may also be used with microcomputers or even pocket computers since the order of the system of equations to be solved is reduced to the number of loops in the system.