New correlations for non-Darcy flow in porous media

In this paper, a general power form of head-loss (pressure-drop) equation and the concept of shear velocity were used to study non-Darcy filtration through coarse granular materials. Using new laboratory data, the validity of four widely-used power form pressure-drop equations were evaluated. The results indicated that for the lower size of grain diameter (d ≤ 8.7 mm) the Wilkins (in: Proceedings of the 2nd Australia-New Zealand Conference on Soil Mechanics and Foundation Engineering, Christchurch, 1956) method has predicted satisfactorily the hydraulic gradient, while for the higher size of grain diameter (d ≥ 15.6 mm), the Stephenson (Rockfill in Hydraulic Engineering, Elsevier Science Publishers B.V., Amsterdam, 1979) method predicted acceptably the pressure gradient. The results also indicated that the best estimation for the Izbash coefficient a is the Wilkins method. Finally, new correlations for friction factor, shear velocity and Reynolds number as well as new threshold limits for Darcy, partially-turbulent, and fully-turbulent flow regimes are presented and discussed.