Forces on a falling sphere in a liquid

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SUMMARY

The discussion focuses on modeling the forces acting on a sphere falling through a Newtonian fluid. Key forces identified include Stokes' drag, buoyancy, and gravity, with specific formulas provided for each. It is crucial to differentiate between the velocity of the sphere in Stokes' drag and its volume in the buoyancy equation. Additionally, when the sphere's size approaches the mean free path of air molecules, corrections based on Robert Millikan's Oil Drop experiment must be applied to Stokes' law.

PREREQUISITES
  • Understanding of Newtonian fluid dynamics
  • Familiarity with Stokes' drag formula
  • Knowledge of buoyancy principles
  • Awareness of Robert Millikan's Oil Drop experiment
NEXT STEPS
  • Research Stokes' drag in detail, focusing on its applications in fluid dynamics
  • Study buoyancy calculations and their implications in various fluid scenarios
  • Explore the effects of particle size on fluid dynamics, particularly in relation to mean free path
  • Investigate the historical context and significance of Millikan's Oil Drop experiment in modern physics
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Physicists, engineers, and students studying fluid dynamics, particularly those interested in the behavior of particles in fluids and the application of classical mechanics principles.

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I want to design a model for falling spheres in a Newtonian fluid and I just want to make sure I've got everything right. Are these all of the forces that apply on an object in a liquid?

4ca08f628070e-fluid.png


I have the following formulas:

[URL]http://upload.wikimedia.org/math/7/2/2/722eecf17cc922626c36f3488ca290e9.png[/URL] (Stokes' drag)
[URL]http://upload.wikimedia.org/math/4/c/b/4cbadb68d4f9eade03797f90f99eae0a.png[/URL] (Buoyancy)
[URL]http://upload.wikimedia.org/math/e/5/1/e51111b22ad80b2b72ef52dccc810409.png[/URL] (Gravity)
 
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Yes but be careful.
The V in the first equation is the velocity of the falling sphere, but in the second it's the volume of it.
 
Yes, don't forget that if the sphere size is comparable with the gap between the air molecules then you will have to make a correction for stokes law based on Robert Millikians Oil Drop experiment
 

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