A circular concrete pipe $($n $=0\mathrm{.}015)$ must carry $40$ cfs with flow depth at $85\%$ of the pipe diameter. The longitudinal slope is $0\mathrm{.}001.($a$)$ Determine the required diameter, $($b$)$ Specify a standard pipe size, $($c$)$ Calculate the actual depth for $40$ cfs flowing through the specified pipe, $($d$)$ Report the water velocity and Reynolds number.