QUESTION $4[5$ Marks$]$

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

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

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

sequence: $32\frac{mm}{h}r$ for $30$ minutes, $50\frac{mm}{h}r$ for $30$ minutes, and $27\frac{mm}{h}r$ for $30$ minutes.

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

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