$(10$ points$)$ A rectangular canal has a channel slope of $0\mathrm{.}015$ with a bottom width of $2m$ and a Manning's $n$ of $0\mathrm{.}03.$ The channel carries a flow of $25m\frac{3}{s}.$ Answer the following:

a$.$ What is the normal depth of the flow in the channel? $(3$ points$)$

b$.$ What is the critical depth of the flow in the channel? $(2$ points$)$

c$.$ Classify the water surface profile of the channel if the depth of flow at the gaging station is $3\mathrm{.}0m(2$ points$)$

d$.$ Compute the water surface slope $($i$.$e$.,d\frac{y}{d}x)$ at the gaging station $($consider the relationship between $d\frac{y}{d}x$ and $y,y_c$ and $y_n$ for the rectangular channels$).(3$ points$)$