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.