An Analytical Solution for 1-D Non-Darcy Flow Through Slanting Coarse Deposits

In this paper, an analytical solution to solve 1-D partial differential equation is presented for fully developed turbulent flow through highly permeable sloping deposited porous medium. The present solution will be applicable for a wide range of slopes varying from zero to relatively steep slopes. To confirm the solution, the analytical results have been validated using two sets of experimental data including rounded and crushed material. To see the compatibility of solution, a Darcy-based form of the solution is derived and compared with proposed solution and experimental data. The results showed a satisfactory agreement with experimental records from water surface profiles through rock cavities for both rounded and crushed rock materials. Finally, it may be concluded that the proposed solution could be used to analyze water surface profiles and normal depth in such slanting permeable porous media. This solution provides a reliable realization of the flow profiles in porous materials which are widely used in open-channel flow concepts.