Comparison of Binomial and Power Equations in Radial Non-Darcy Flows in Coarse Porous Media

Abstract

Analysis of non-laminar flows in coarse alluvial beds has a wide range of applications in various civil engineering, oil and gas, and geology problems. Darcy equation is not valid to analyze transient and turbulent flows, so non-linear equations should be applied. Non-linear equations are classified into power and binomial equations. Binomial equation is more accurate in a wide range of velocity changes in comparison to power equation and its validity has been verified by dimensional analysis and Navier–Stokes equations. But since velocity changes are rather limited in engineering problems, power equation would be accurate enough. Non-Darcy flow analysis for the cases in which streamlines are almost parallel has been investigated by numerous investigators in pressured and free surface conditions. Radial flows are accompanied by streamlines contraction. Contracted streamlines in free-surface radial flows result in flow inflation, i.e. flow depth through the path increases significantly in comparison to parallel flows. This phenomenon makes free surface radial flows behave completely different from other types of flows. To investigate the behavior of free-surface radial flows in coarse porous media, power and binomial equations are analyzed in this paper. Furthermore, several experiments have been conducted by setting up a semi-cylindrical experimental device with a diameter and height of 6 and 3 meters, respectively. Results indicate that free-surface radial flows behave different from pressured radial flows and Non-Darcy flows in which streamlines are relatively parallel.