$4.(15$ pts$)$ As the result of flooding in Boise$$s north end due to a thunderstorm you previously analyzed, you have determined the $25-$year design peak flow for the storm drainage line to be $30$ ft$3/$s$.$

a$.$ The existing pipe is a $30$ inch inside diameter corrugated metal storm drain pipe at a $\mathrm{.}0035$ ft$/$ft slope.$$ Is this pipe adequate for the design flow without surcharging $($assume surcharging occurs if the design flow is greater than the full pipe capacity$)?$ Show your analysis.

b$.$ What diameter of concrete pipe $($assume a concrete sewer with manholes, inlets, etc. $$ straight$)$ would you recommend replacing it with if the design flow depth over diameter $($y$/$D$)$ is $0\mathrm{.}75$ and the inside pipe diameters are only available in $0\mathrm{.}5-$foot increments $(2,2\mathrm{.}5,3,$ etc.$)?$ The new pipe will need to be constructed at the same grade $($slope$)$ as the existing pipe.