Flow characteristics were investigated theoretically and numerically, inside a diverging duct through which a periodically fully developed flow of fluid is passed as working fluid. The governing differential equations along with boundary conditions were solved by finite difference method. The discritized equations with proper boundary conditions of numerical solutions were sought by obtaining Leibmann’s Successive under Relaxation (SUR) method. It has been done on the basis of stream function and vorticity formula of the two dimensional Navier-Stoke’s equation and continuity equation for all nodes. Computations were performed for different values of the Reynolds Number and the geometric parameters. If the divergence angle is sufficiently high and for high Reynolds number the flow become unsteady. The current study is ended only for steady laminar flow. Numerical results obtained were analyzed for the effectiveness of different values of duct length and outlet diameter for a fixed inlet diameter