Author(s): Oscar Castro-Orgaz; Subhasish Dey
Keywords: Curvilinear coordinates; free surface flow; hydraulics; open channel flow; steady flow
Abstract: The one-dimensional (1D) momentum equation for free surface flow over curved boundaries has so far been traditionally developed integrating the Reynolds equations across the flow section in a boundary-fitted system of coordinates, such as flows over spillways and round-crested weirs. The formulation of the Reynolds equation was performed in a Cartesian coordinate system instead of boundary-fitted coordinates. Consequently, the traditional free surface flow equations do not strictly apply to the flow over curved boundaries. In this study, a novel generalized (1D) momentum equation for steady free surface flow over curved boundaries is developed by considering a modified formulation of the boundary-fitted coordinates. In an application of the present model, the singular-point of a round crested weir is found to be closer to the crest than as predicted by the traditional theory. A generalized expression for the pressure distribution is also proposed.