$(30$ pts$)$ The figure below shows the channel profile for a wide, rectangular channel. Water enters

the upstream section at a depth of $0\mathrm{.}5$ m $.$ The channel carries a discharge per unit width, $q,$ of $2$

$\frac{m^3}{m*s}$ and has a roughness, n $,$ of $0\mathrm{.}014.$ Determine the following:

a$)$ The normal and critical depths for all three sections $(10$ pts$)$

b$)$ A hydraulic jump will occur in Section B$.$ If the depth upstream of the jump is the normal

depth for Section A$,$ calculate the depth after the jump. $(8$ pts$)$

c$)$ Sketch and clearly label all gradually varied flow profile types that exist within the three

sections. Note, this sketch should accurately show relative shapes for the profiles but should

not need any additional calculations. $(12$ pts $)$