Consider the setup shown in the Figure below in which two different soil layers are located inside a cylindrical tube of $200mm.$ A constant head difference is maintained across the soil sample. The porosities and hydraulic conductivities of the two soils in the direction of the flow are as follows: $k_1=4\mathrm{.}5{10}^{-3}\frac{cm}{s},n_1=0\mathrm{.}5$;$k_2=4\mathrm{.}3{10}^{-}4\frac{cm}{s},n_2=0\mathrm{.}35.$

$($a$)$ Determine the quantity of water flowing through the sample per hour.

$($b$)$ Determine the elevation head $($Z$),$ pressure head $($hp$),$ and the total head $($h$)$ at points A$,$ B$,$ C$,$ D$,$ &E$.$

$($c$)$ Plot the variation of the elevation head, pressure head and the total head with the horizontal distance along the sample axis.

$($d$)$ Plot the variations of discharge velocity and the seepage velocity along the sample axis.