PROBLEM $2$:

A $120-$acre watershed is $55\%$ impervious area and $35\%$ grass in good condition and $10\%$ forest. The minimum infiltration rate of the soil is $0\mathrm{.}20i\frac{n}{?}$ hour. The average slope of the watershed is $0\mathrm{.}01f\frac{t}{f}t.$ The longest flow path in this area is $200ft$ of sheet flow over a grass area $($lawns$)$ with a slope of $0\mathrm{.}01f\frac{t}{f}t,$ followed by $4300ft$ of flow in a grassed waterway $(n=0\mathrm{.}095)$ with a slope of $0\mathrm{.}01f\frac{t}{f}t$ and a hydraulic radius of $1\mathrm{.}0ft.$ The rainfall intensity$-$duration$-$frequency relation for this area is:

$i=\frac{100T_r^{0\mathrm{.}2}}{t_d+40},$ where $T_r$ is the design return period $($years$)$; $t_d$ is the rainfall duration $($minutes$)$; and $i$ is the rainfall intensity $($in$/$hr$).$ Use the rational method to determine the peak discharge that you would use to design a culvert draining this area? Assume that the design calls for a $10-$year design event. Show your work and assumptions.