csh_lecture3_flow equations

# csh_lecture3_flow equations - CWR 6537 Subsurface...

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CWR 6537 Subsurface Contaminant Hydrology Lecture 3 1 WATER FLOW IN POROUS MEDIA A. Historical Highlights: 1805 P. Laplace Differential equation operator 1822 C. Fourier Heat Flow 1822 L. Navier Viscous Flow of Fluids 1827 G. Ohm Electricity 1842 J. L. Poiseuille Fluid flow in a capillary 1845 G. G. Stokes Generalized Navier-Stokes law 1856 H. Darcy Saturated water flow in porous media 1907 E. Buckingham Capillary potential, Darcy equation for unsaturated flow 1931 L. A. Richards Transient water flow in porous media Textbooks 1972 Jacob Bear Dynamics of Fluids in Porous Media 1979 A. Freeze and J. Cherry Groundwater 1980 C.W. Fetter Applied Hydrogeology 1993 C.W. Fetter Contaminant Hydrogeology 1990 Domenico and Schwartz Physical and Chemical Hydrogeology 2000 R. Charbeneau Groundwater Hydraulics and Pollutant Transport Stochastic Texts 1989 Gedeon Dagan Flow and Transport in Porous Formations 1990 W. Jury and K. Roth Transfer Functions and Solute Movement through Soil 1993 Lynn Gelhar Stochastic Subsurface Hydrology [Eulerian] 2003 Yoram Rubin Applied Stochastic Hydrogeology [Lagrangian] (1) A series of linear flux laws were proposed over a period of four decades (1820-1860), all of which state that the flux (of heat, electricity, fluids, or mass) is proportional to the driving force, i.e., the gradient in potential (temperature, voltage, water potential, or chemical potential). (2) Nonlinear flux laws, where the proportionality constant is a strong, nonlinear function of the state of the system are needed to describe transient water flow in porous media; e.g., soil hydraulic conductivity as a function of soil-water matric potential ( R ). Water Flow Saturated Unsaturated - steady - steady - unsteady - transient

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CWR 6537 Subsurface Contaminant Hydrology Lecture 3 2 Buckingham (1907) extended the applicability of Darcy's law to unsaturated flow conditions, with conductivity [ K ( R )] as a function of R (or 2 ). Richards (1931) combined Darcy- Buckingham equation with the continuity expression to obtain the governing equation for transient, unsaturated flow. (3) The study of the hydraulics of groundwater flow began to be integrated with geology and geochemistry in the 1970s. At the same time, stochastic approaches emerged. B. Soil-Water Potential The amount of work that must be done per unit quantity of water in order to transport irreversibly and isothermally an infinitesimal quantity of water from a pool of pure water (chosen as the reference) at a specified elevation and atmospheric pressure, to specified position in soil. Potential Energy:
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csh_lecture3_flow equations - CWR 6537 Subsurface...

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