PROBLEM $1(25$ points$)$

A $1-$m$-$wide trapezoidal channel reach with a bed slope angle of $\backslash (0\mathrm{.}20^\{\backslash$circ$\}\backslash )$ carries water at a rate equal to $\backslash (2\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$ The side slopes of this channel are $\backslash (2$: $1\backslash ).$ The channel lining is made of finished concrete $\backslash ((\backslash$mathrm$\{$n$\}=0\mathrm{.}012)\backslash ).$ Water enters the channel at normal depth. Answer the following requests:

a$)$ Calculate the normal depth of the flow, in cm$,$ and indicate whether the flow at the channel's entrance is subcritical, critical, or supercritical.

b$)$ Use the direct step method to calculate the specific energy, in cm$,$ at a location $250$ m downstream of the channel's entrance.