A grass lined trapezoidal channel experiences uniform flow at a normal depth of $2\mathrm{.}0$ m$.$ The base width is $7$ m and the side slopes are equal at a H:V of $1$:$3.$ Using an appropriate Manning's n and a bed slope S$0$ of $4\%,$ calculate the following:

$($a$)$ The discharge flow rate Qin m$3/$min; and

$($b$)$ Reynolds number Re and type of flow $($i$.$e$.,$ laminar or turbulent$).$