$3.(30$ Pts$)$ A trapezoidal channel with a bottom width of $10$ meters and side slopes of $2$ horizontal to $1$ vertical $($m$=2)$ has a Manning$$s n $=0\mathrm{.}022$ and a channel slope So $=0\mathrm{.}003.$ The canal conveys a flow of $50$ m$3/$s$.$ A downstream weir creates a pool with a depth of $3\mathrm{.}0$ m$.$

a$.$ What is the critical and normal depths in the canal

b$.$ What kind of water surface profile $($using the standard letter and number scheme$)$ occurs where the canal approaches the pool

c$.$ Using the direct step method, starting at the $3\mathrm{.}0-$meter depth, how far up stream $($in meters$)$ does the depth of $2\mathrm{.}99$ occur using a single step.