To analyze flows in channel expansions and contractions, two-dimensional, depth-averaged, unsteady flow equations in a transformed coordinate system are solved numerically by using the MacCormack scheme. The non-rectangular physical domain is converted into a rectangular computational domain. This transformation allows the use of an orthogonal grid and an easier inclusion of side wall boundaries. The unsteady flow model is used to obtain steady flow solutions by treating the time variable as an iteration parameter and letting the solution converge to the steady state. The results of the mathematical model are compared with experimental data. The comparison of the computed and measured results show satisfactory agreement in cases where the assumption of hydrostatic pressure distribution is valid. The capability of the model for handling mixed super- and sub-critical flows in a channel transition is demonstrated.