In class, we learned the expression for Darcy's Law in 3D is: q=-KVh. In an anisotropic...

 

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In class, we learned the expression for Darcy's Law in 3D is: q=-KVh. In an anisotropic medium, the hydraulic conductivity K is a tensor: K11 K12 K13 K21 K22 K23 K31 K32 K33 a) (30 points) Write down the expression for the three components q1, 92, 93 of the Darcy velocity vector q. b) (10 points) In an isotropic medium, only K₁, K22, and K33 are non-zero. How does the relationship of the Darcy velocity change in such a medium? Show mathematically, and explain in words. In class, we learned the expression for Darcy's Law in 3D is: q=-KVh. In an anisotropic medium, the hydraulic conductivity K is a tensor: K11 K12 K13 K21 K22 K23 K31 K32 K33 a) (30 points) Write down the expression for the three components q1, 92, 93 of the Darcy velocity vector q. b) (10 points) In an isotropic medium, only K₁, K22, and K33 are non-zero. How does the relationship of the Darcy velocity change in such a medium? Show mathematically, and explain in words.