The elevation of the ground surface at a soil$-$moisture measurement site is $300$ cm$.$ The soil is a sand, and its unsaturated properties are represented by the drying curves in Figure $2\mathrm{.}13($handout$).$

For each of the following scenarios $($a$,$ b$,$ and c below$),$ draw a quantitatively accurate set of vertical profiles for

$($i$)$ moisture content versus depth, $($ii$)$ pressure head versus depth, and $($iii$)$ hydraulic head versus depth for a

$200-$cm depth, as in Figure $2\mathrm{.}12($handout$).$

Each profile should contain at least $5$ data points $($at depths $0,50,100,150,200$ cm below surface$).$ You may

use the measurement depth of $300$ cm as your datum $($Z $=0).$

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

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

c$)$ The hydraulic head is $150$ cm throughout the profile $($static case$).$

d$)$ For cases $($a$)$ and $($b$),$ calculate the $($i$)$ hydraulic gradients and $($ii$)$ rates of flow through the profile $($assume area $=1$ m$2)$