Question $1$:

A rectangular channel has a width of $15$ ft and carries $300$ cfs of water. The channel lining has an estimated Manning $n$ of $0\mathrm{.}018.$ For a uniform flow depth of $3\mathrm{.}0$ ft calculate the following. To get full points show all calculations with results at least up to five decimal places. $(30$ points$)$

$($a$)$ Calculate normal slope of the channel corresponding to uniform depth $(7$ points$)$

$($b$)$ Calculate critical depth $(6$ points$)$

$($c$)$ Calculate critical slope of the channel $(6$ points$)$

$($d$)$ Classify channel slope and why $(3$ points$)$

$($e$)$ Classify the water surface profile at a gaging station where depth is $2\mathrm{.}0$ ft and why $(3$ points$)$

$($f$)$ Calculate Froude number at the gaging station $(5$ points$)$