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The construction of sewer systems has proven to be challenging. It has been noted that the margin between safety and optimality is small and as such it is not so easy to predict the efficiency of sewer design. This paper tries to
look for a model to describe the motion of water in a channel. A coupled surface runoff-water flow approach is applied to model the water transport from the catchment areas. The Saint-Venant’s equations have been employed and the Lax-Friedrichs scheme has been used to numerically solve the nonlinear system of equations.