A rectangular channel is $3\mathrm{.}9$ m wide has a Manning$$s number $=0\mathrm{.}025,$ a longitudinal bed slope of $1$ in $130$ and conveys X m$3/$s of water.

Showing the steps in your answer as clearly as possible, determine

$($a$)$ The normal depth of flow

$($b$)$ The critical depth of flow

$($c$)$ Whether the channel flow is sub$-$ or super$-$critical

$($for X$,$ take the sum of the digits of your student number$)(42)$