This paper presents a numerical model in two dimension (2D) for flow simulation in open channels. For this purpose, the shallow water (SW) equations are first transformed into boundary fitted coordinate (BFC) system, for the model to be applicable for real rivers. The transformed governing equations are then discretized utilizing a simple explicit based Finite Difference Method (FDM). The FDM-based scheme used here is Lax-Friedrichs scheme. This scheme features first-order accuracy in temporal discretization with second-order accuracy in spatial discretization. The main advantage of this one-step numerical technique is its simplicity, less computational time requirement and ease in programming. The inherent dissipation error of this technique is minimized here using a weighting coefficient. The numerical model is then applied to simulate two classical test cases with known experimental solutions. The accuracy of numerical results is additionally assessed using the performance metric Index of Agreement (IA). The results obtained are found to be approximately mimicking the available experimental results, with less computational effort.