CEE $404/604-$ Assignment $-$ Due September $27,2024$

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A horizontal trapezoidal channel has a bottom width $b_1=20$ feet and a side slope of $z=1\mathrm{.}5(1\mathrm{.}5H$:$1V).$ The

flow is $Q=800cfs$ and the velocity is $v_1=6fps.$ At a bridge abutment, the channel gradually transitions

into a double box culvert $($i$.$e$.,$ rectangular channel$)$ with a combined open width of $24$ feet.

a$)$ Determine the depth of flow $y_1$ in feet, the hydraulic depth $D_1$ in feet, and the Froude number $F{r}_1$ for

the flow in the trapezoidal channel section.

b$)$ Determine the depth of flow $y_2$ in feet and the velocity $v_2$ in feet per second $($fps$)$ within the box

culverts.

c$)$ Determine the minimum allowable combined width $b_{2\text{m}\text{i}\text{n}}$ of the box culverts to prevent choking.

Water flows at a rate of $Q=300$ cfs and a depth of $y_1=6$ feet in a horizontal rectangular channel with a

bottom width $b_1=10$ feet.

a$)$ Determine the velocity $v_1$ in feet per second $($ fps $),$ the hydraulic depth $D_1$ in feet, and the Froude

number $F{r}_1$ for the approach flow.

b$)$ Determine the depth of flow $y_2$ in feet and the velocity $v_2$ in fps if the channel width gradually increases

to $b_2=12$ feet.

c$)$ Determine the height of the bottom step $z$ in feet which would just cause choking to begin if the

channel width simultaneously increases to $b_2=12$ feet.

Water flows at a depth of $y_1=2\mathrm{.}75$ feet and a velocity $v_1=8$ feet per second $($ fps $)$ in a horizontal

rectangular channel having a width of $b_1=10$ feet. The channel gradually transitions into a trapezoidal

channel having a side slope $z=2(2H$:$1V)$ and a bottom width of $b_2=5$ feet.

a$)$ Determine the flow $Q$ in cubic feet per second $($cfs$),$ the hydraulic depth $D_1,$ and the Froude number $F{r}_1$

for the approach flow.

b$)$ Determine the depth of flow $y_2$ in feet, the hydraulic depth $D_2$ in feet, the velocity $v_2$ in fps$,$ and the

Froude number $F{r}_2$ within the trapezoidal channel section.

c$)$ Determine the height of the bottom step $z$ in feet that would just cause choking.