Mathematical Modeling of Unsteady Flow

The study of the river flow predictions in open channels is an important issue in hydrology and hydraulics . Consequently, this paper is concerned with studying the unsteady flow that may exist in open channel , and its mathematically governed by the Saint Venant equation using a four-point implicit finite difference scheme. From many hydrologic software, HEC-RAS (Hydrologic Engineering Center – River Analysis System) is a good choice to develop the hydraulic model of a given river system in the south of Iraq represented by Al- Kahlaa River by a network of main channel and three reach and a total of 57 cross sections with 3 boundary sections for one of the applications . The model was calibrated by using the observed weekly stage and flow data . The results show that a good agreement was achieved between the model predicted and the observed data by using the values Manning's(n=0.04) for over bank with the values of Manning's ( n=0.027) for main channel and also with using time weighting factor ( θ ) equal one .