This flow in rivers is concerned with unsteady flow in open channel and it mathematically governed by the Saint Venant equation, using a four-point implicit finite difference scheme. For a one-dimensional applications, the relevant flow parameters are functions of time, and longitudinal positions. Considering the equations for the conservation of mass (continuity) and conservation of momentum. The mathematical method is empirical with the computer revolution, numerical methods are now effective to develop the hydraulic model. Conventional methods used to compute discharge, such as stage-discharge and stage-fall discharge relationships has been inadequate. Further research is recommended to include tributaries in rivers.