$($a$)$ A rectangular channel $3$ m wide discharges $13\mathrm{.}5\frac{m^3}{s}.$ Construct a specific energy carve and state when:

$($i$)$ Depth of flow is $0\mathrm{.}6$ m

$($ii$)$ Depth of flow is $2\mathrm{.}4$ m

$($iii$)$ Determine their corresponding specific energies and the bed slope required to maintain the Take Manning's $n=0\mathrm{.}014.$