Problem $5(10$ points$)$

A box culvert with a rectangular cross$-$section is to be designed to pass storm discharge

underneath a roadway. At the upstream end, the culvert is fed by a rectangular open channel

with width $B_1=3[m]$ and a design water depth of $h_1=2[m].$ The design discharge is

$Q=15[cms].$ The proposed height of the culvert barrel is to be $1\mathrm{.}75[$m$].$ The elevation

difference between the entrance $($point $2)$ and exit $($point $3)$ of the culvert is $z=1[m].$

Assignment $1$

Figure $1\mathrm{.}4$: Left: top$-$down $($plan$)$ view of culvert. Right: side $($profile$)$ view of culvert.

Concrete wingwalls will be used to gradually reduce the width of flow to $B_2=2\mathrm{.}75[$m$]$

at the entrance of the culvert barrel. What is the water depth $h_2$ in $m$ at the culvert

entrance? Is the proposed culvert barrel tall enough such that water passes below the

ceiling of the culvert at the upstream end?

Find the width of contraction $B_2$ such that the critical depth is achieved at the entrance

of the culvert barrel.

Assume that the width of the culvert entrance $B_2$ is designed such that critical depth is

obtained at the entrance to the culvert. The culvert is steep enough that supercritical

flow occurs inside the culvert barrel. The flow exits the culvert into a rectangular

stilling basin with width $B_3=3[m]$ and a horizontal bottom. What is the supercritical

depth $h_3$ at the entrance of the stilling basin $($point $3)?$ Assume that frictional and

minor losses are negligible.