Estimation of seepage losses in an ephemeral multibranched stream by simultaneously solving for seepage and unsteady flow

Due to transmission losses and absence of initial flow prior to flood occurrence، it is impossible to estimate seepage losses and flow routing for an ephemeral stream with several branches and complex connections by using common routing methods، and it is necessary to develop a routing method for such streams. To this end present research prepared a computer for irregular stream cross section، in which partial differential equation for non-uniform unsteady flow (saint- Venant equation) are solved by using finite difference method and alternative technique (staggered method) after being linearized. Water flow elevation at fluvial connection is determined at any time step completely implicitly by using influence line method. Model accuracy was examined in terms of programming، its ability to simulate uniform flow، and to satisfy continuity relationship by using a loop stream consisted of 8 open channels. The results of verification showed 0. 7 and 0. 0209 percent as maximum calculation error for discharge and flow depth، respectively. With very high accuracy، therefore، present model estimates discharge and water surface profiles at each branch. Employing Lane hydrograph and characteristics of Hughes Wash River، prediction of flow behavior and transmission losses showed that compared to other experiment relationship، Muskat’s estimates seepage losses and peak flood better. Under seepage condition، a highly complex system of open channel with 24 branches and low slopes was employed، in which the flow of any branches is sensitive to small changes in flow depth. Also، in this network، the model is able to detect flow direction at any branches. For steady flow، the results showed a 1. 127% decrease in system output discharge due to seepage losses. For unsteady flow، with the present seepage، system output hydrograph volume is 6. 37% less than that of input hydrograph volume.