Q$1)$ Water flowing in a rectangular channel encounters a smooth upward step as shown in the

figure. The flow has just the enough energy to pass through Section $(2)$ without choking.

Assuming no loss in total energy:

a$)$ Find the flow depth at section $2$ if $E_2=3m.$

b$)$ Find the unit discharge of the flow.

c$)$ Find the depth of the flow at Section $(1)$ if the flow is subcritical at this section.

d$)$ Draw the longitudinal water surface profile on the sketch given.