Darcian, Transitional, and Turbulent Flow through Porous Media

The study of flow through media consisting of large-sized grains is important in a number of civil engineering applications. Employing the square root of permeability as the characteristic length in defining friction factor and Reynolds number, theoretical curves, relating friction factor and Reynolds number—similar to the Moody diagram used in pipe flow to estimate the friction factor—have been developed using the ratio of characteristic length d and square root of permeability $\mathit{k}$ as the third parameter. The existing experimental data on flow through porous media have been sorted based on the $\mathit{d}\mathit{k}$ ratio and are used to verify the theory developed. The agreement is good. From the set of theoretical curves so obtained, the Reynolds number at which the friction factor–Reynolds number relationship deviates from Darcy's law and the Reynolds number at which turbulent flow is fully established are identified. Empirical equations for these Reynolds numbers in terms of media parameters have been obtained. The factor affecting linear parameter a and nonlinear parameter b have been brought out. The empirical power law applicable for high Reynolds number flows is given a theoretical justification.