Considerable effort has been expended on the theoretical aspects of the applicability of the unsteady flow equations to natural overland flow. The major difficulty when these equations are used to simulate watershed flow lies in estimating the friction factor for natural situation. In this paper a generalized friction factor is introduced and a kinematic relationship which describes the »kinematic state« of the watershed surface is proposed. The resulting equations for unsteady free surface flow is a kinematic wave approximation. These equations are solved analytically and the solution obtained in the form of integral series.

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