a$)$ If the design rainfall intensity is given by $I=120\frac{T^{0\mathrm{.}175}}{T_d+27},$ then compute the design discharge for the $10-$year storm event using the Rational Method where the runoff coefficient, $C,$ has been determined to be $0\mathrm{.}6$ and the catchment area is $174,240f{t}^2.$ Inlet time $T_d$ has been determined to be $10$min.

b$)$ Determine the required diameter of a drainage pipe $)=(0\mathrm{.}015$ to convey the design discharge from part a if the upstream invert elevation is $498\mathrm{.}43$ and the downstream invert elevation is $495\mathrm{.}55.$ The length of the pipe needed is $450ft.$