Some basic theory about drag coefficients of spheres.

In summary, the conversation revolved around a lab where three spheres of different sizes and densities were dropped into two different fluids and their velocities and drag coefficients were measured. The participants also discussed some theory questions, specifically about the behavior of the spheres during their descent. The first question involved the oscillating path of low density spheres and the second question was about why some spheres bounced along the sides of the wall before falling. The group theorized that vortex shedding and lift generation may play a role in these phenomena. The third question focused on the ability of streamlined bodies to fall at an angle instead of straight down. The participants shared a helpful link for further information on vortex-induced vibration. Finally, they requested assistance with the second question and described the significant effect
  • #1
Vidatu
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We did a lab where we dropped three spheres into two different fluids, measured their velocities, and found drag coefficients. We were also asked some theory questions, and these are what I need help with.
Spheres:
3.175 mm, 0.05 g Teflon
6.35 mm, 0.375 g, aluminum
12.7 mm, 8.36 g, steel
Fluids:
Water (density 998 kg/m^3)
Sugar water (density 1230 kg/m^3)
Questions:
1 - Why did some of the spheres of low density plastic follow an oscillating path as they fell?
2 - Explain why some spheres tended to bounce along the sides of the wall as they fell. In particular, explain what drew the spheres into the wall, and pushed them away after contact.
3 - Explain why a streamlined body can fall at an angle, rather than straight down.

I would guess that vortex shedding has something to do with the first two, but don't really know. Any help (or links to some sites with relevant theory) would be much appreciated. Thanks.
 
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  • #2
#1 Think about the pattern of Kármán vortex streets and the forces that would be created on a low density sphere.

#3 Think about how lift is generated.
 
  • #3
Thanks, I got pretty good answers for those two now, just needed to prodded in the right direction.
As an FYI for anyone interested, I found some good info on this wiki page http://en.wikipedia.org/wiki/Vortex-induced_vibration. We were introduced to vortex shedding, but never learned about the lateral forces it can generate (those it makes sense intuitively).

Anyone have any help for question 2? It was a very pronounced effect, with the heavier balls at least. The steel sphere hit the wall before descending 15 cm, and hit hard enough to produce clicks audible across the room.
 

FAQ: Some basic theory about drag coefficients of spheres.

1. What is a drag coefficient?

A drag coefficient is a dimensionless quantity that describes the resistance of an object moving through a fluid, such as air or water. It is a measure of how much the object's shape affects the fluid flow around it.

2. How is the drag coefficient of a sphere calculated?

The drag coefficient of a sphere can be calculated using the formula Cd = 24/Re, where Cd is the drag coefficient and Re is the Reynolds number. The Reynolds number is a measure of the ratio of inertial forces to viscous forces in a fluid and is calculated by dividing the object's velocity by its size and the fluid's viscosity.

3. What factors affect the drag coefficient of a sphere?

The drag coefficient of a sphere is affected by several factors, including the size and shape of the sphere, the speed at which it is moving through the fluid, the density and viscosity of the fluid, and the roughness of the surface of the sphere.

4. Why is the drag coefficient of a sphere important?

The drag coefficient of a sphere is important because it helps engineers and scientists understand and predict the aerodynamic or hydrodynamic behavior of objects moving through fluids. It is also used in the design and optimization of vehicles, sports equipment, and other objects that need to minimize drag.

5. Can the drag coefficient of a sphere be changed?

Yes, the drag coefficient of a sphere can be changed by altering any of the factors that affect it. For example, changing the shape of the sphere or the roughness of its surface can significantly impact the drag coefficient. Additionally, using specialized coatings or adding fins can also alter the drag coefficient of a sphere.

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