#$3.$ A new residential development has an overland flow length of $700ft$ to the curb$/$gutter system which then connects the local $($development$)$ storm pipe system. The development is $120$ acres with hydrologic soil group B and the land surface will be graded to an average slope of $1\mathrm{.}5\%.$ The development is $25\%$ asphaltic surfaces $($driveways$,$ roads$),20\%$ roofs and $55\%$ grass areas $($yards$,$ parks, assume "dense grass"$)$ in good condition. Using a $10-$yr design storm:

$($a$)$ Compute the overland flow time using:

i$.$ FAA equation, and

ii$.$ Kinematic wave equation.

$($b$)$ Compute the flow time for the channelized flow in the gutter and storm pipes within the development to the outlet $($which then connects to the city storm sewer$).$ Assume a $250ft$ spacing for the inlets along the gutter, and $4000ft$ for the storm pipes. Assume an average velocity for the gutter flow of $4f\frac{t}{s}$ and the storm pipe of $12f\frac{t}{s}.$

$($c$)$ Compute the time of concentration for the development, using the overland flow time from $($a$)-$ii $($kinematic wave method$)$ and the channelized flow time from $($b$).$

$($d$)$ Using the Rational Method, compute the peak flow rate for the $10-$year design storm that will enter the city storm sewer at the outlet of the development.