$(1)$ Find the discharge of a rectangular channel $5$ wide with a $5\%$ slope, flowing $1$ deep. The channel has a stone and weed bank $($n$=\mathrm{.}035).(2)$ Find normal depth in a $10\mathrm{.}0-$ft wide concrete rectangular channel $($n$=0\mathrm{.}013)$having a slope of $0\mathrm{.}015$ ft$/$ft and carrying a flow of $400$ cfs$.$In Dane County, a smooth asphalt roadway includes two $12$ ft wide lanes. Runoff from the $2$ acre watershed has a time of concentration of $20$ minutes and CN $74$ and flows onto the roadway. The road is at $1\mathrm{.}5\%$ longitudinal slope and the traffic lanes with a $4\%$ cross slopes. Inlets are placed at side shoulders $100$ ft from the road high point.$(3)$ Determine the $25-$year peak rate of runoff to the first inlet on each shoulder. Assume the $2$ acre upstream watershed is split equally to each side of roadway.$(4)$ Calculate the flow spread on roadway at the inlet for n $=0\mathrm{.}013.(5)$ Using a curb opening inlet determine the length of opening needed to $($a$)$ fully $(100\%)$ intercept gutter flow and $($b$)$ half $(50\%)$ intercept gutter flow.