Design the section for a stable trapezoidal channel so that a flow rate of $20$ m$^3/$s passes through. Mechanical properties of the in situ material give us a maximum stress at the bottom of $2\mathrm{.}51$ kg$/$m$^2$ and an angle of repose of $32\backslash$deg $.$ The channel slope S$=0\mathrm{.}0010,$ a Manning coefficient n$=0\mathrm{.}022,$ the slope is $2$:$1.($A satisfactory answer is considered with $3$ iterations$)$

$($Justify your answer$)$