Mathematical Modeling of water surface at Unsteady Flow in Al-Msharah River

Abstract

This study is concerned with unsteady flow in open channels in boundary conditions that may exist in river or channel system. A software Hydrologic Engineering Center-River Analysis System (HEC-RAS) was used for a case study. The software contains a hydrodynamic model for simulating the unsteady flow in open channels based on a one-dimensional form of the Saint-Venant equations, by formulating a discrete form using the implicit finite difference scheme, then solving using the Newton-Raphson iteration procedure and the modified Gaussian elimination technique. The case study adopted with the help of HEC-RAS application was applied to a reach of Al Msharah River (channel) between AL Msharah Barrage (upstream)and Al Malah Bridge (Downstream), for a length of (49 Km) divided to (52) cross sections. Model runs and the comparison of results with actual field data indicate that the accuracy of the results obtained for(θ=1 and ∆t=5 minute) is quite acceptable, where θ is a weighting parameter and ∆t is the time interval. The paper covers the case of normal depth of flow and observed water stage data within the period ( from January 2006 to July 2006) . The results demonstrate that the area at Al Am'arah city at distance 17.5 Km from upstream(cross section 30)could be subjected to flooding at High Flow, therefore, it is recommended to adjust cross sections to prevent the flooding in this area. At last , Calibration of the hydrodynamic model is achieved in a study reach using the observed data (water stage) along AL Msharah River and show that a good agreement.