Forces on a falling sphere in a liquid

In summary, the conversation is about designing a model for falling spheres in a Newtonian fluid and ensuring all applicable forces are included. The three formulas mentioned are for Stokes' drag, buoyancy, and gravity. It is noted that the velocity in the first equation represents the falling sphere's velocity, while in the second equation it represents the volume of the sphere. Additionally, there is a mention of a correction for Stokes' law based on Robert Millikan's Oil Drop experiment if the sphere size is comparable to the gap between air molecules.
  • #1
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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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  • #2
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.
 
  • #3
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
 

Related to Forces on a falling sphere in a liquid

1. What is the force acting on a falling sphere in a liquid?

The force acting on a falling sphere in a liquid is known as buoyant force. This force is exerted by the liquid in an upward direction, opposing the weight of the sphere and causing it to experience a net acceleration.

2. How is the buoyant force related to the weight of the sphere?

The buoyant force is equal to the weight of the displaced liquid, which is known as Archimedes' principle. This means that the buoyant force will be greater for larger and denser spheres, and will be less for smaller and less dense spheres.

3. What factors affect the buoyant force on a falling sphere in a liquid?

The buoyant force is affected by several factors, including the density and volume of the sphere, the density of the liquid, and the acceleration due to gravity. It is also influenced by any other forces acting on the sphere, such as drag or surface tension.

4. How does the buoyant force affect the motion of a falling sphere in a liquid?

The buoyant force will cause the sphere to experience a net upward acceleration, which will decrease as the sphere falls deeper into the liquid. This will result in the sphere reaching a terminal velocity, where the upward buoyant force is equal to the downward weight of the sphere.

5. How can the buoyant force on a falling sphere in a liquid be calculated?

The buoyant force can be calculated using the formula Fb = ρfl * V * g, where Fb is the buoyant force, ρfl is the density of the liquid, V is the volume of the displaced liquid, and g is the acceleration due to gravity. This formula assumes that the sphere is completely submerged in the liquid.

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