Steady free-surface flow in porous media: generalized Dupuit–Fawer equations

Abstract

Steady free-surface flow in open channels may be analysed by the reduction of the two-dimensional (2D) potential flow problem to a quasi-2D potential flow approach by inclusion of streamline curvature and inclination effects following Fawer's theory. Flow of water in open channels and groundwater flow with a free surface can be characterized by potential functions and stream functions both obeying Laplace's 2D equation, provided there is isotropy and homogeneity. It is thus natural to expect the transfer of ideas from the open channel to the groundwater flow. A novel approximate model based on Fawer's theory for steady open channel flows with curved streamlines, coupled with Darcy's law, is proposed for groundwater flow with a free seepage surface. The seepage surface is described by a second-order differential equation which is applied to flow through both rectangular and trapezoidal dams, resulting in good agreement with the full 2D potential flow methods and test data.