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Darcys Law



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Darcy s Law Philip B Bedient Civil and Environmental Engineering Rice University Darcy s Law Darcy s law provides an accurate description of the flow of ground water in almost all hydrogeologic environments Darcy s Law Henri Darcy established empirically that the flux of water through a permeable formation is proportional to the distance between top and bottom of the soil column The constant of proportionality is called the hydraulic conductivity K V Q A v h and v 1 L Hydraulic Conductivity K represents a measure of the ability for flow through porous media K is highest for gravels 0 1 to 1 cm sec K is high for sands 10 2 to 10 3 cm sec K is moderate for silts 10 4 to 10 5 cm sec K is lowest for clays 10 7 to 10 9 cm sec Darcy s Experimental Setup Head loss h1 h2 determines flow rate Darcy s Law Therefore V K h L and since Q VA Q KA dh dL Conditions In General Darcy s Law holds for 1 Saturated flow and unsaturated flow 2 Steady state and transient flow 3 Flow in aquifers and aquitards 4 Flow in homogeneous and heteogeneous systems 5 Flow in isotropic or anisotropic media 6 Flow in rocks and granular media Darcy Velocity V is the specific discharge Darcy velocity indicates that V occurs in the direction of the decreasing head Specific discharge has units of velocity The specific discharge is a macroscopic concept and is easily measured It should be noted that Darcy s velocity is different Darcy Velocity from the microscopic velocities associated with the actual paths if individual particles of water as they wind their way through the grains of sand The microscopic velocities are real but are probably impossible to measure Darcy Seepage Velocity Darcy velocity is a fictitious velocity since it assumes that flow occurs across the entire cross section of the soil sample Flow actually takes place only through interconnected pore channels Darcy Seepage Velocity From the Continuity Eqn Q A v D A V Vs Where Q flow rate A cross sectional area of material AV area of voids Vs



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