Water content, head, and flow analysis in a profile $(115)$

Consider a sandy soil with the unsaturated properties of the drying curves on the following

page.

The elevation of the ground surface at a site of interest is $300$ cm $($your datum$).$

Draw, quantitatively $($with accurately labeled and scaled axes$),$ a set of vertical profiles of

moisture content, pressure head, elevation head, and total hydraulic head versus depth for a

$200-$cm deep profile under the following conditions:

a$.$ The volumetric moisture content is $20\%$ throughout the profile

b$.$ The pressure head is $-50$ cm throughout the profile

c$.$ Which way $($if any$)$ is water flowing in a$)$ and b$)?$ Calculate the flow rate via Darcy's law

for each profile.

d$.$ Draw the set of vertical profiles of moisture content, pressure head, elevation head, and

total hydraulic head versus depth for a $200-$cm deep profile for a profile with no vertical

flow and a moisture content of $10\%$ at the top of the profile $($pick five points spaced

equally with depth for the moisture contents$).$

$*$You will want to draw three different profiles $($one for a$,$ c$,$ and d$).$