A rectangular channel has three segments, which have the same critical depth but different normal

depths. The upper and lower segments have a steep slope, whereas the mid segment has a mild slope.

$(1)$ Sketch and label all possible water surface profiles in the channel for an approaching water depth

of less than yc and larger than the normal depth in the upper segment $($i$.$e$.,$ yn$,1$ y$0$ yc$)2)$ For an approaching water depth of less than the normal depth in the upper segment $($i$.$e$.,$ y$0$ yn$,1),$

the possible profiles are shown in the following figure. Label the profiles for each segment