A rectangular open channel carries water at a flow rate of $90$ cubic feet per second and exhibits a

channel width of $80$ feet. The rectangular open channel has a slope of $0\mathrm{.}15\%$ and a Manning's

coefficient of approximately $0\mathrm{.}035.$

a$)$ Compute the critical depth, in feet, of this rectangular channel.

b$)$ Compute the normal depth, in feet, of this rectangular channel.

c$)$ Determine whether the flow through the channel is supercritical, critical, or subcritical.