Model for hydraulic networks with evenly distributed demands along pipes

Abstract

This article shows how the global gradient method formulated by Todini and Pilati (Todini, E. and Pilati, S., 1987. A gradient algorithm for the analysis of pipe network. In: International conference on computer applications for water supply and distribution, Leicester Polytechnic, UK) can be modified in order to represent user water demand evenly distributed along pipes. It is also shown how EPANET (Rossman, L.A., 2000. EPANET 2 users manual, Cincinnati, Ohio, USA: National Risk Management Research Laboratory, Office of Research and Development, US Environmental Protection Agency), which assumes demands to be allocated to the nodes, can be used to represent this type of distributed demand. The proposed procedure is based on an original mathematical method formulated by Messina (Messina, U., 1945. Metodi approssimati per i calcoli di verifica delle reti di condotte idrauliche. L'Acqua, 1 (12), 1–11 (in Italian)). Two different numerical examples relating to networks of different topological complexity are discussed. In particular, it is highlighted that the two different ways of modelling demand lead to different nodal head values that are generally lower when demand is evenly distributed along the pipes. However, differences decrease when the piezometric surface is fairly flat over the network (i.e. low water velocities in the pipes). The article concludes with several considerations regarding the consequences that the method of representing demand has on the processes of calibration and optimal design/rehabilitation of water distribution networks and leakage estimation.