Nonlinearity and Free-Surface Flowby Nazeer Ahmed, (M.ASCE), Lenox Inst of Water Technology, Lenox, United States,
Abstract: The Dupuit-Forchheimer (D-F) assumption is commonly considered a viable design criterion for water resources projects and, consequently, Darcy law is used to determine the locus of free surface for flow through a given porous medium. On the other hand, however, the physical measurements of water level in the porous medium provide the location of actual free-surface higher than that predicted by the analysis based on the D-F flow configuration. According to the D-F assumption, conditions of linear flow are assumed to exist throughout the porous medium; the effects of convective and turbulent forces as well as those of curvature of streamlines are ignored. This process introduces a permanent discrepancy into the flow phenomena and leads to approximate values of different hydraulic parameters. As a result, the analytical procedure does mask the true character of the flow field yielding unrealistic design parameters. Therefore, it is obvious that the determination of the true position of free surface is crucial to the exact determination of the required hydraulic parameters. In this paper the role of nonlinear flow in terms of convection, turbulence, and curvature of streamlines is included in the flow equation, as dictated by the Reynolds equations in cylindrical coordinates, to provide clear understanding of the flow phenomena and realistic answers to the problems of the project at hand.
Subject Headings: Porous media flow | Turbulent flow | Flow measurement | Free surfaces | Water flow | Free flow | Parameters (statistics) | Overland flow
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