A rectangular channel carries a flow of $12$ m$^3/$s and has a width of $6$m$.$

a$)$ Create a plot of the specific energy diagram for $0<$ y $<4$m$.$ Use excel to show how you plot the specific energy diagram.

b$)$ Determine the critical depth and minimum specific energy. Indicate on the plot the location of the critical point.

c$)$ Determine the two possible flow depths when the flow has a specific energy of $2$m$.$ Indicate on the plot the location of this condition.

Show work as well. Thank You.