Exercise - Darcy's Law in 2D
Assume you have a 2D domain with bedding planes declining at a sharp angle as shown below.
Recall the following equations:
\[
k_{xx} = k_r cos_{\alpha}^2 + k_s sin_{\alpha}^2
\]
\[
k_{yy} = k_r sin_{\alpha}^2 + k_s cos_{\alpha}^2
\]
\[
k_{xy} = k_{yx} = -\frac{1}{2}\left(k_r - k_s\right) sin(2\alpha)
\]
Assume the following:
| variable | value | units |
|---|---|---|
| \(k_s\) | 0.001 | cm/sec |
| \(k_r\) | 0.005 | cm/sec |
| \(\alpha\) | -60 | degrees |
(a) Calculate the hydraulic conductivity tensor for the given domain assuming \(\alpha\) = -60 degrees.
(b) Let alpha range from 0 to -90 degrees. Calculate and plot \(k_{xx}\) and \(k_{yy}\) as a function of \(\alpha\).
Excel starter file: darcy2d.xlsx
Excel solution: darcy2d_KEY.xlsx
Python starter file: 
Python solution: