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A numerical model is introduced for solution of shallow water flow equations with negligible physical dissipations due to canal roughness and turbulence effects. Two-dimensional velocity distribution and water depth of the flow field are computed by solving the depth average equations of continuity and motion. The equations are converted to discrete form using cell vertexfinite volume method on triangular unstructured mesh. The formulation of the added numericalviscosity is chosen in such a way that preserves the accuracy of numerical results. The accuracy ofthe model is assessed by computing the challenging case of inviscid frictionless flow in a canal with a 1800 bend. The computed results are compared with analytical solution which is obtainedfrom potential flow theory. Simulation of frictionless free surface flow in a constant width meandering sinusoidal canal is considered as an application of the model. The algorithm produced encouraging results.