presentation on research analysis of flow around a river bend (horseshoe bend) in 180 degrees

1. Prepared by
Brendan Gallahue and Tushar Dange
Guided by
Dr. David J. Willis

2. Index
 Intro
 Pictorial View
 Brief History of Canyon
 Assumptions
 Equations Used and Flow Properties
 Graphs
 Future Work
 References

3. Horseshoe Bend

4. Phenomenon Being Examined
 How does water flow around a 180° bend?
 The real life example of this phenomenon 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 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

5. Brief History of the Canyon
 Over millions of years the flow of water through the canyon has caused the
sedimentary rock to break down and erode away leaving a massive canyon in
its place.
 The erosive action of the Colorado has been severely constrained by the
building of the Glen Canyon Dam, which ended the annual spring floods, but
there is still a lot of water flowing relatively quickly through a very narrow
gorge.
 Before building the dam the Colorado River had spring floods that would
exceed a flow rate of 100,000 CFS. All of that snow melting in the Colorado
Rockies came pouring down through the Grand Canyon causing a lot of rapid
erosion.
 Today spring floods are only producing 8,000-10,000 CFS with a maximum of
about 20,000 CFS in some parts of the river.

6. 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.

7. Horseshoe Bend
Picture: Google Maps

8. Equations Used
Conservation of Mass
Streamline Bernoulli
Normal Bernoulli
Used to verify that mass is conserved (obvious). Also used to find the surface height at the inner wall of the bend.
Used to find an equation relating the velocity at some radial distance along the bend.
Used to determine the surface height at some radial distance along the bend. Taken on top(red line) and bottom (green
line) surfaces.

9. Horseshoe Bend Flow Properties
Average volume flow rate of
1100
𝑓𝑡3
𝑠
over a period of
105 years.
Ref: http://waterdata.usgs.gov/usa/nwis/uv?site_no=13247500

10. Horseshoe Bend Flow Properties
Average height of water is 3.5 ft.
Ref: http://waterdata.usgs.gov/usa/nwis/uv?site_no=13247500

11. Water Surface Height
The change in the depth of the water from the inner surface to the outer
surface of the bend is about 1.2 ft.

12. Water Velocity Around Bend
The velocity of the water around the bend goes from 6.25
𝑓𝑡
𝑠
at the outer radius to a
value of 0.728
𝑓𝑡
𝑠
.

13. Interesting Future Work
 If the flow was not assumed to be invicid then the velocity distribution and the
water surface height would be different.
 The no slip boundary condition would come into effect at the inner and outer
walls of the bend as well as the floor of the river.
 It would be interesting to calculate the amount of sediment removed by the
flow of the river to create this Wonder of the World.
 By utilizing the equations learned in this course and with more allotted time
we could also calculate the rate at which the river eroding the canyon today by
calculating the shear stresses caused by the flow of the river.

14. References
 Google Maps
 2013 Advanced Fluids Midterm
 USGS (United States Geological Survey)
 http://waterdata.usgs.gov/usa/nwis/uv?site_no=13247500

15. THANK YOU

16. ANY QUESTIONS?