On gradually varied flow profiles in rectangular open-channels

This technical note presents the equation for one-dimensional gradually-varied steady flow profiles with constant discharge, in a rectangular-section prismatic channel of constant roughness and small longitudinal slope. The flow profile differential equation was transformed by means of a polynomial approximation and then, by an algebraic procedure followed by the integration of the equation, the solution was obtained. This solution was applied to a particular case which, through a comparative analysis, allowed to verify a satisfactory accuracy. The solution obtained here, though rather complex from an algebraic point of view, is easily programmable; its major merit consists in its contribution to the mathematical knowledge of flow profiles.