$1\mathrm{.}0(20$ marks$)$

Consider a simple water filter system that consists of two soil filters, connected in series as shown in Figure

$1\mathrm{.}0.$ two soil filters, connected in series. Each filter traps different size contaminants and thus contains soil:

the upper filter traps coarse particles; the lower one traps finer ones. The cross$-$sectional area of each filter

is $1\mathrm{.}2$ m $2.$ The length of the upper filter $(L_1)$ is $1\mathrm{.}0$ m ; the length of the lower filter $(L_2)$ is $2\mathrm{.}0$ m $.$ The

permeability of the upper filter $(k_1)$ is $0\mathrm{.}40\frac{m}{h}$; the permeability of the lower filter $(k_2)$ is $0\mathrm{.}18\frac{m}{h}.$

Determine the following:

a$)$ The total head at points $A,B,C,$ and D $.$

b$)$ The water pressure at points A$,$ B$,$ C$,$ and D$.$

c$)$ The discharge through each filter $($i$.$e$.,$ Q$1$ and Q$2)$ in units of $m\frac{3}{h}.$

d$)$ Is there potential for soil "heave" $($boiling$)?$ If so$,$ where will this heave occur?