$3$b$.$ A stream which can be approximated to a parabolic section channel with longitudinal bed slope of $9{10}^{-3}$ carries a flow with a top width of $3\mathrm{.}25m.($a$)$ Determine whether the channel slope is mild, steep, or critical when the discharge is $5\mathrm{.}80\frac{m^3}{s},$ and $($b$)$ Estimate the range of depths at which the profile will be of type $1,2$ or $3$ respectively. Take Manning's $n$ for the stream channel $=0\mathrm{.}024.$