$(24$ points$)$ Consider a $50$ cm long, vertical, homogeneous sand$-$filled column undergoing steady state

flow. The elevation datum is located at the base of the column. The top boundary has a Type I

boundary condition with a hydraulic head of $50$ cm $.$ The bottom boundary has a Type II boundary

condition with a downward flux equal to $0\mathrm{.}9$ K $,$ where K is the hydraulic conductivity of the medium.

$($a$)$ What are the pressure and hydraulic heads at the top and bottom boundaries of the column?

$($b$)$ Using the axes provided, draw and label a plot that shows the elevation, pressure and hydraulic

head values $($ x $-$axis$)$ as a function of the height above the base of the column $($ y $-$axis$)$ using solid

lines. Label the lines and the axes.

$($c$)$ On the same plot you used for question $5$b$,$ draw the new steady state pressure and hydraulic

head lines if the bottom boundary is changed to zero flux using dashed lines.