$4.$ A rectangular channel, which is $50$ ft wide, has a roughness coefficient n $=0\mathrm{.}015.$

$($a$)$ Determine the channel bottom slope if the normal depth is $1\mathrm{.}50$ ft at the discharge of

$200$ cfs$.$

$($b$)$ Determine the critical slope and the corresponding normal depth when the discharge is

$200$ cfs$.$ Note that the critical slope is the bottom slope of the channel at which the

normal depth is equal to the critical depth.

$($c$)$ Determine the critical slope at which the normal depth is $1\mathrm{.}50$ ft$,$ and compute the

corresponding discharge.