Approximate modelling of 2D curvilinear open channel flows

The common treatment of open channel flow involves the hydrostatic pressure approach. However, many flows are curvilinear and a higher-order approach is needed to deal with the non-hydrostatic pressure distribution. The current models are based on linear relationships for the variation of streamline curvature and inclination along the equipotential curves of the flow net, yet this approach is not verified with 2D results. In the present study typical 2D free surface flow nets are analysed to investigate the variations of streamline curvature and inclination. From the detailed 2D information, approximate relationships describing the curvature and inclination are proposed. It was found that streamline curvature and inclination do not vary linearly in general. The higher-order energy and momentum curvilinear equations are improved with this approach, thereby approximating the real flow net geometry. The implications of these findings on curvilinear flow modelling are discussed using several test cases.