High School Terminal Velocity Equation in vertical cylinder with some fluid

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The discussion focuses on deriving an equation for terminal velocity in a vertical cylinder containing fluid, emphasizing that as the diameter of the sphere increases, its velocity decreases. Participants clarify that the terminal velocity is influenced by both the diameters of the sphere and the cylinder, with all relevant variables known. The original poster is studying Stokes' law and is interested in its application in tunnel design for subway systems in South Korea. They express difficulty finding specific information on how terminal velocity changes with the radius of the cylinder. The conversation highlights the need for a clear mathematical representation of these relationships.
yejin
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I just have a question that could you guys make an equation that expresses the terminal velocity based on followed condition?
- When diameter increase, velocity decrease
- velocity should change depending on both cylinder and sphere's diameter
- We know every variable
- The sphere is in situation follow:
1. Net Force is ZeroCd = Drag coefficient
d = diameter of sphere
D = Diameter of cylinder

I hope you guys help me...
I really need you guys' help!

Sorry for grammar or something Langauge mistake (English is not my first language...)
 
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Welcome to PF.

Do you mean terminal velocity in free-fall in a fluid? If so, there are lots of web pages that should give you the formulas. What have you found so far with your Google searches?

Also, is this for schoolwork? If not, what is the application?
 
Thank you for your response! I meant the terminal velocity in free-fall in a fluid!

I am just studying stokes law and trying to research it myself. I am wondering how tunnel designers consider these kinds of issues when they are building the subway. Because South Korea, where I am living, has developed a subway system.

I tried to search from Google, but there is no information about the change of terminal velocity depending on the radius of cylinder changes and I could make the equation that
Vt = {24(viscosity)}/{(Drag coefficient)(Fluid density)(diameter of the ball)} -> When d increase, Vt decrease
 
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