Calculate the Output Flow Depth from a Coarse-Grained Porous Media with Radial Flow

Coarse-grained gravel (rockfill material) has numerous applications in engineering including filtration, gabion construction, channel lining, stilling basins, ponds, and cobble stone dams as well as flood control. In the fine-grained media, there is a laminar flow with a linear relation between hydraulic gradient and flow velocity so that the flow follows Darcy law (Eq. 1) (McWhorter and Sunada, 1977). However, in the coarse-grained media, due to the presence of voids, flow velocity is high with a tendency to the turbulent flow formation (Hansen et al. 1995), and there is a nonlinear relation between hydraulic gradient and flow velocity and flow follows non-Darcy law. Hydraulic gradient equations in the non-Darcy media considering steady flow condition are classified into two groups of power and binomial equations, according to Eqs. 2 and 3 (Forchheimer, 1901; Leps, 1973; Stephenson, 1979).