Transient flow routing in channel networks

The formulation of a mathematical model to predict transient flows in hydraulic networks is presented. The network formulation consists of breaking the network up into a series of connected reaches; reducing the finite difference equations for each reach into two ‘reach’ equations; forming an exterior matrix consisting of the reach equations, external boundary conditions, and interior compatibility conditions; solving the external matrix for the end values of discharge and water surface elevation for all reaches; and back‐substituting for all interior values. Examples presented include the James River, USA, estuary model (24 nodes and 26 reaches), the Cork Harbor, Ireland, estuary (13‐reach double‐looped network), and the Rio Bayamon basin, Puerto Rico. Results are very satisfactory when they are compared to known data.