$(9\mathrm{.}1)($a$)$ Compute the critical depth and velocity in a trapezoidal channel with $b=6m,s=2,=1\mathrm{.}12$ and $Q=30\frac{m^3}{s}$ by $($i$)$ the trial$-$and$-$error method, $($ii$)$ the bisection method, and $($iii$)$ the Newton$-$Raphson method.

$($b$)$ Compute the critical depth and velocity in a circular channel with $d_0=3m$ and $Q=5\frac{m^3}{s}$ by the trial$-$and$-$error method, if $($i$)=1,$ and $($ii$)=1\mathrm{.}12.$