The evolution of water distribution models

Computation of flows and pressures in networks of pipes has been of great value and interest for those involved with the design, construction and maintenance of public water distribution systems. Many methods have been used in the past to compute flows in networks of pipes. Such methods range from graphical methods to the use of physical analogies and finally to the use of mathematical models. This paper will attempt to catalog and review those methods that have been developed and applied since the dawn of the "computer age" in 1957 when the original Hardy Cross method was first adapted for solution using a computer in analyzing the water distribution system of the city of Palo Alto, California. Subsequent methods have included the "simultaneous node" method, the "simultaneous loop" method, the "simultaneous pipe" method, and the "simultaneous network" method. A brief review of the theoretical framework of each method will be presented along with a short history of the origin and evolution of the computational approach.