river flow around 180
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River Flow around 180° Bend (Horseshoe Bend)
Introduction
The phenomenon being examined is how water flows around a 180° river bend. The real life
example of this can be seen as a part of the Colorado River called Horseshoe bend. The Colorado
River flows through the Grand Canyon and is the reason that the canyon is as vast and deep as it
is today. In this segment we will examine some interesting things about the flow around a river
bend such as the river surface level and the velocity distribution.
Brief History
Over millions of years the canyon was formed due to a cycle of erosion and deposition. First, the
outside of the bend, where we will see that the water flows fastest,is worn away. This eroded
rock and sediment is then deposited by the slower flowing water inside of the bend. The picture
of horseshoe bend shown in Figure 1, physically shows the phenomenon of the velocity
distribution around the bend. The outer edge of the bend has clearly been affected more by the
flow of water past itthen compared to the inner edge of the bend. Before the construction of dams
across the Colorado the spring floods were capable of producing 100,000 CFS. Today the floods
only produce 8,000 to 10,000 CFS in some areas of the river.
Advanced Fluid Mechanics
Report Prepared by: Brendan Gallahue
Tushar Dange
Horseshoe Bend
Figure 1. Picture of Horseshoe Bend (Colorado River)
Assumptions
The flow of the river is at steady state.
The flow is invicid.
If the flow were truly invicid (as we know no real flow is) then there would be no
Grand Canyon because no shear stress to break down the sedimentary rock as the
water flows over it.
The flow is incompressible.
There is no vertical change in velocity.
The width of the river is an average of 400 ft across and is uniform across the bend.
The cross section of the bend is assumed rectangular when in reality it would most likely
be almost parabolic
Storyline
The segment would start with the introduction to the topic being presented which in this
case is the flow around a 180° river bend. It would then transition to the real life example
of this phenomenon which is Horseshoe Bend in the Colorado River. A brief history of
the Grand Canyon and the reasons for the way it looks today will be discussed. The
assumptions used in the analysis of the phenomenon would then be explained. The
scientific evidence of the phenomenon would be shown through the use of data obtained
by the United States Geological Survey, (USGS), and the equations learned in the
duration of this course. The results of the analysis will then be shown by the use of
graphs generated in excel and the results can be proved by observing the picture of the
actual bend in the river.
Scientific Evidence
The scientific evidence was obtained through the use of data from the USGS of the volumetric
flow rate of the river at Horseshoe Bend and the average height of the water at that location. This
data can be seen in Figure 2 and 3. The volumetric flow rate is 1100 ft3
s and the average height is
3.5 ft.
Figure 2. Volume Flow Rate at Horseshoe Bend
Figure 3. Height of Water at Horseshoe Bend
Results
Using the method in the hand calculations and using excel we were able to get the river surface
level and the velocity distribution around the bend. These results can be seen in Figure 5 and 6.
Figure 5. River Surface Level from Inner to Outer Edge of Bend
Figure 6. Velocity Distribution Across the Bend
Conclusion
When a river flows around a 180° bend it can be seen from the analysis that it affects the river
surface level and the velocity distribution around the bend. From the analysis it was shown that
the river surface level was higher at the outer edge of the bend than the inner edge. The velocity
of the water at the outer edge of the bend is higher than the inner edge. When observing the
picture of Horseshoe Bend, it can be seen that when there was a high volume flow rate through
this part of the river that the outer edge of the bend is clearly more eroded due to the higher
pressure and velocity of water at the outer edge. The higher shear stresses at the outer edge
causes more rock to break down and be deposited toward the inner edge where the velocity is
lower. This process happening over millions of years provides us with the breath-taking
landscape of the Grand Canyon today.
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