Consider transient flow in a homogeneous vadose zone. The van Genuchten properties de$-$

scribing the medium are $\backslash$Theta $\_($r$)=0\mathrm{.}078$c$($m$^(3))/($c$)$m$^(3),\backslash$Theta $\_($s$)=0\mathrm{.}43$c$($m$^(3))/($c$)$m$^(3),$a$=0\mathrm{.}036$cm$^(-1),$n$=1\mathrm{.}56,$

m$=1-(1)/($n$),$ and K$\_($s$)=0\mathrm{.}00029$c$($m$)/($s$).$

$($a$)$ If the medium has an initial water content of $\backslash$Theta $\_($i$)=0\mathrm{.}10$c$($m$^(3))/($c$)$m$^(3),$ and if infiltration occurs

at a constant rate equal to the saturated hydraulic conductivity, K$\_($s$),$ write an expression that

describes the rate of advance of the wetting front. Using $($some of$)$ the soil properties given,

what is the rate of advance of the wetting front in c$($m$)/($s$)?$

$($b$)$ What is the velocity of the newly added water front?

$($c$)$ After one day of infiltration, how far will the wetting front and the added water front be

separated?