Q:$9$ A $60cm$ diameter sewer is required to flow at $0\mathrm{.}4$ depth on a grade ensuring a degree

of self$-$cleansing equivalent to that obtained at full depth at a velocity of $65c\frac{m}{sec}.$

Find the required grade, associated velocities and rates of discharge at full depth and

$0\mathrm{.}4$ depth. Take a uniform value of $N=0\mathrm{.}015$ at all depth of flow.