Problem $1(10$ points$)$

The $10-$year IDF curve for Baton Rouge is given as

$i=\frac{60\mathrm{.}86}{(t+6\mathrm{.}78{)}^{0\mathrm{.}73}}$

where $i$ is the rainfall intensity in in$/hr$ and $t$ is the rainfall duration in minutes. Let $K_s=10m\frac{m}{h}r,n=0\mathrm{.}453,{}_i=0\mathrm{.}1375,$ and soil suction head at wetting front ${}_f=114mm.$

For a $10$ year $2-$hour storm with uniform intensity, use the Green$-$Ampt method to calculate cumulative infiltration $)$ at $t=2$ hour