ESTION $4[5$ Marks$]$

Infiltration data from a precipitation experiment yield an initial infiltration rate of $3\mathrm{.}8$ cm$/$hr and a

final equilibrium infiltration rate of $0\mathrm{.}7$ cm$/$hr$.$ The value of the empirical constant k was estimated

to be $0\mathrm{.}225/$hr$.$ Determine the total volume of infiltration for the following storm$/$precipitation

sequence: $32$ mm$/$hr for $30$ minutes, $50$ mm$/$hr for $30$ minutes, and $27$ mm$/$hr for $30$ minutes.

$($hint: calculate the precipitation and infiltration volume for first $30$ mins$($total time $($t$)$ in infiltration

equation $=0\mathrm{.}5$ hr$,$ second $30$ mins $($t $=1\mathrm{.}0$ hr$),$ and third $30$ mins $($t $=1\mathrm{.}5$ hr$)).$