Question $2(20$ points$)$

You are designing a pipe to convey a flow rate of $19\mathrm{.}3f\frac{t^3}{s}$ at a slope of $0\mathrm{.}001$ and with the depth that is $75\%$ of the diameter.

$(1)$ Determine the necessary diameter, if the pipe is made from smooth$/$troweled concrete.

$(2)$ Determine the necessary diameter, if the pipe is made from corrugated metal.