$(30$ Pts$)$ A rectangular channel with $b=6\mathrm{.}0m,n=0\mathrm{.}025,$ and $S0=0\mathrm{.}001$ carries a discharge of $28m\frac{3}{s}.$ The channel discharges over a free overfall.

a$.$ What are the critical and normal depths in the channel

b$.$ Is the channel mild or steep

c$.$ Using a starting depth of $1\mathrm{.}50$ m $,$ what is the depth upstream using the corrected Euler method without iteration for a single $-10$m distance increment.