$2.(30$ points$)$ Sketch all longitudinal profiles that can occur for all the headwater and tailwater heights given in the figures. In Figure a$,$ the slope is mild, and in Figure b$,$ the upstream slope is steep, and the downstream slope is mild. Label all controls, profiles, hydraulic jumps, and normal$/$critical depth lines. Be neat! You should assume that each section is long enough so flow at least approaches normal depth.