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flow4 - 53:030 Class Notes C.C Swan University of Iowa...

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Period #10: Multi-dimensional Fluid Flow in Soils (II) A. Review Our objective is to solve multi-dimensional fluid flow problems in soils. Last time, mass conservation and Darcy’s Law were used to derive the so-called Laplace Equation which governs seepage in homogeneous, isotropic soil deposits. 2 h/ x 2 + 2 h/ y 2 + 2 h/ z 2 = 0 B. Possible Methods for Solving the Laplace Equation. 1) Analytical, closed form or series solutions of the PDE. quite mathematical, and not very general. 2) Numerical solution methods typically, the finite element method or the finite difference method . very powerful and easy to apply can deal with heterogeneity, anisotropy, 2D, 3D Will use finite element method in Lab 6. 3) Graphical Techniques - Flow-net Methods commonly used in engineering practice to solve 2D flow problems. the ideas behind this method are now explained. 1 53:030 Class Notes; C.C. Swan, University of Iowa
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2 C. Flow-net Methods straightforward graphical method to solve 2D seepage problems. underlying idea: solutions of Laplace Equation consist of two families of orthogonal curves in the (x,z) plane. These families of curves make a flow net.
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