Problem $3(35$ points$)$: Water at $10C$ flows in a $6-$m$-$wide rectanghlar channel at a depth of $0\mathrm{.}55$ il ant flow nte of $12\frac{m^3}{s}.$ Determine the followings:

$($a$)$ the critial depth, $($b$)$ whecther the flow is subcritical or supereritical, and $($c$)$ the alternate depth