M. Thiruvengadam ¹, G. N. Pradeep Kumar ², D. Sivakumar ¹, C. Mohan ¹

Affiliations
1 Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Chennai - 600062, Tamil Nadu, IN
2 S.V.U. College of Engineering, Tirupati - 517502, Andra Pradesh, IN

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.

Keywords

Darcy, Friction Factor, Hydraulic Gradient, Porous Medium Flow, Reynolds Number, Velocity

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M. Thiruvengadam ¹, G. N. Pradeep Kumar ², D. Sivakumar ¹, C. Mohan ³

Affiliations
1 Department of Civil Engineering, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Chennai - 600062, Tamil Nadu, IN
2 Department of Civil Engineering, S.V.U. College of Engineering, Tirupati - 517502, Andra Pradesh, IN
3 Department of Mathematics, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Chennai - 600062, Tamil Nadu, IN

Abstract

Objectives: Since 1856, Darcy's equation is used to analyse the ground water flow. This equation can be applied only in laminar regime of flow. No suitable equation is available to analyse other regimes of flow. During the pumping the water from well, the water around well flows in converging pattern towards well. The analysis of flow of water around wells is a problem in converging boundary through porous soils or sands. Generally, Dupuit's equation is used to analyse the flow around the well. One of the drawback in Dupuit's equation is it can be used only in laminar flow, since, this equation used Darcy's concept. No equation is available to analyse other than laminar flow in converging pattern towards well. Therefore, this situation motivated to think to design a sector of well model to conduct experiments on porous medium flow in converging boundary for all regimes of flow to estimate the discharge of a well. Methodology: In order to achieve the objective, a converging permeameter (a sector of a well model) is planned, designed and experimented. In this study, experiments have been conducted on porous medium in converging flow permeameter for all regimes of flow. From the experimentation of converging boundary, data like discharge, hydraulic gradient and velocity are calculated. Further, a new non-dimensional form of equation is also derived relating hydraulic gradient with Reynolds number. Findings: A set of graphs are drawn between hydraulic gradient and velocity, using Darcy's range of velocities and corresponding hydraulic gradient. These graphs are compared with Darcy's graph and the validity of Darcy's equation is verified. The trends of the present graph is coinciding with that of Darcy's graph such that the validation of this experimentation is checked. Another set of graphs are also drawn with hydraulic gradient versus velocity for all regimes of flow. A polynomial second degree equation (i=a1 Vb 2 +k'Vb) has been proposed relating hydraulic gradient with bulk velocity in laminar and turbulent regimes. Hence this project result proves that, using this equation and corresponding constants discharge of a well can be estimated even if the flow is laminar and turbulent. Applications: The relation between hydraulic gradient and Reynolds number is obtained as i=0.0004 Re0.5. Substituting hydraulic gradient in this equation from field observations, Reynolds number can be find out. From the Reynolds number seepage velocity can be find out and corresponding discharge may be calculated in a well for any regime of flow which superfluous Dupuit's equation.

Keywords

Darcy’s Equation, Hydraulic Gradient, Porous Medium, Reynolds Number, Velocity of Flow.

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