The triangular channel has the dimension shown below. The channel slope $(S_o)$ is $0\mathrm{.}01$ and a Manning roughness $n$ is $0\mathrm{.}020.$

$A=y^2$

$P=2\sqrt[\phantom{2}]{2}*y$

$R=\frac{y}{2\sqrt[\phantom{2}]{2}}$

$T=2y$

If the flow rate in the channel is $16\mathrm{.}0\frac{m^3}{s},$ then determine:

a$)$ The normal depth $($in $m)$

b$)$ The critical depth $($in $m)$