CE 4358_5346 Assignment 1_ solution
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Aerospace Engineering
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Jan 9, 2024
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Uploaded by SuperHumanRockWren8192
1 CE4358/5346 Open Channel Flow Assignmnet #1 1.
Classify each of the following flows as steady or unsteady from the viewpoint of the observer: (Sturm P1.1) (10 Points)
Flow Observer (
a
) Flow of river around bridge piers: (1) Standing on bridge (2) In boat, drifting (
b
) Movement of flood surge downstream: (1) Standing on bank (2) Moving with surge Solution (a)
Over relatively short time intervals, the observer standing on the bridge will see a steady flow even though the flow may be unsteady over longer time intervals; however, the observer drifting in the boat will see an unsteady flow as the boat passes under the bridge because the velocity increases around the bridge piers even if the approach flow is steady. (b)
An observer standing on the river bank will see an unsteady flow as the surge passes but a steady flow while riding on the surge if the flow is uniform in the direction of movement.
2 2.
If the lake level upstream of the spillway in the following figure is 55 m above the channel floor at the base of the spillway just upstream of the hydraulic jump, estimate the depth and velocity there for a flow rate of 1,000 m
3
/s and a spillway width of 30 m. What is the value of the Froude number? Neglect the approach velocity in the lake and the head losses on the spillway. (Sturm P1.6) (15 Points)
Solution. Writing the energy equation from the water surface upstream of the spillway where the velocity head is negligible to the floor of the stilling basin downstream of the spillway, and neglecting head losses, we have Solving by trial and error for the supercritical solution (see Chapter 2), the result is y
2 = 1.024 m and V
2 = q
/
y
2 = 33.33/1.024 = 32.55 m/s
. The Froude number becomes: 55 m
3 3.
A sluice gate controls the flow in a 6.6-ft wide rectangular channel. If the discharge is 17.7 ft
3
/s and the upstream water depth is 4.95 ft, calculate the downstream depth and velocity. Assume no energy loss at the gate. (25 Points)
𝐻𝐻 = ℎ +
!
!
"#$
!
%
!
= ℎ +
&.(("
%
!
The upstream depth h
1
= 4.95 ft gives 𝐻𝐻 = ℎ +
&.(("
%
!
= 4.95 +
&.(("
).*+
!
= 4.955 𝑓𝑓𝑓𝑓
(dominated by
ℎ
(
) Hence, 4.955 = ℎ +
&.(("
%
!
Rearrange for the shallow, supercritical solution: 4.955 ℎ
"
= ℎ
,
+ 0.112
or ℎ
,
+ 0.112 − 4.955 ℎ
"
= 0
Solving this equation by trial and error gives ℎ
"
= 0.153 𝑓𝑓𝑓𝑓
𝑉𝑉
"
=
!
-.-×&.(+,
= 17.5 𝑓𝑓𝑓𝑓/𝑠𝑠
Answer:
downstream depth = 0.153 ft; velocity = 17.5 ft/s
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4 4.
A 10-ft wide rectangular channel is very smooth except for a small reach that is roughened with angle irons attached to the bottom of the channel. Water flows in the channel at a rate of 200 cfs and at a depth of 1 ft. Assume frictionless flow except over the roughened part where the total bottom shear force (for all angle irons) is assumed to be 2000 lb. Determine the depth at the end of the roughness elements for the assumed conditions. (Midterm Exam Fall 2017) (25 Points)
5 5.
Water passes under a sluice gate in a 2-m wide rectangular channel. The depths of flow before and after the sluice gate are 1.8 m and 0.3 m, respectively. A hydraulic jump occurs at a short distance downstream. Assuming no energy loss at the gate, calculate the force on the gate. (Midterm Exam Fall 2016) (25 Points)
6.