$(20$ pts$)$ You have been tasked with designing a new section of trapezoidal canal with the following characteristics:

Moderately Sinuous

Side Slopes of $4$ Horizontal to $1$ Vertical $(m=4)$

Design Flow $=1200f\frac{t^3}{sec}$

Manning's $n=0\mathrm{.}032$

Channel Slope $=0\mathrm{.}0004f\frac{t}{f}t$

Canal Material is Very Rounded $($Cohesionless$)$ with a mean diameter of $1/2-$Inch

a$.$ Using the tractive force method, determine a design bottom width and flow depth

b$.$ Check that the Froude number is within typical design parameters

c$.$ Check the channel sides and bed for erosion

d$.$ Determine the freeboard using the US Bureau of Reclamation $(1959)$ methodology