Non-Dimensional Equation of Resistance Coefficient with Reynolds Number of Porous Medium Flow

Abstract

Objectives: To review the Darcy’s equation and ascertain the reliability of the present experimental investigations with that of the past study. To present a non-dimensional form of relation between resistant to flow with fluid and particle parameters. To analyze the relation between Reynolds numbers with resistant coefficient (lambda) in ground water flow. Methodology: In order to achieve these objectives, experimental program planned, designed and carried out. Experiments conducted on porous medium of large spread of sizes of different materials in parallel flow permeameter for all regimes of flow. Findings: Experimental results compared with Darcy’s equation and the validity of this equation is verified. A new form of Reynolds number is derived taking hydraulic mean radius as characteristic length and seepage velocity as characteristic velocity absorbing void ratio, volume diameter, and kinematic viscosity. Another non-dimensional form of resistant co-efficient is also derived and used to get unique relation between Reynolds numbers with resistance coefficient. Applications: Observed experimental data applied in Darcy’s equations, and verified in its applicability. The derived equations can be applied in porous medium flow, such that velocity of flow can be determined, from which discharge through porous medium can be estimated.