Problem $4)30$ points

Water flows at a rate of $20\frac{m^3}{s}$ in a rectangular channel of $6m$ wide. The profile of the channel is shown in the figure below:

Determine the uniform flow depth in different parts of the channel. $(15$ points$)$

Determine the critical depth, $y_c$ and the critical slope of the channel $S_c(9$ points$)$

Determine the slope type in each part. $($Mild or Steep$).(6$ points$)$