Terminal Velocity Equation in vertical cylinder with some fluid

Click For Summary
SUMMARY

The discussion centers on deriving the terminal velocity equation for a sphere in a fluid within a vertical cylinder, emphasizing the relationship between the sphere's diameter (d) and the cylinder's diameter (D). The user references Stokes' Law and presents the equation Vt = {24(viscosity)}/{(Drag coefficient)(Fluid density)(diameter of the ball)}, concluding that as the diameter of the sphere increases, the terminal velocity decreases. The inquiry also touches on practical applications in tunnel design, particularly in the context of subway systems in South Korea.

PREREQUISITES
  • Understanding of Stokes' Law
  • Familiarity with fluid dynamics concepts
  • Knowledge of drag coefficients
  • Basic mathematical skills for equation manipulation
NEXT STEPS
  • Research the effects of varying drag coefficients on terminal velocity
  • Explore advanced fluid dynamics simulations using software like ANSYS Fluent
  • Study the impact of cylinder diameter on fluid flow and terminal velocity
  • Investigate real-world applications of terminal velocity in engineering, particularly in tunnel design
USEFUL FOR

Students studying fluid dynamics, engineers involved in tunnel design, and researchers interested in the behavior of objects in fluid environments.

yejin
Messages
2
Reaction score
0
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 language mistake (English is not my first language...)
 
Physics news on Phys.org
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
 
Last edited by a moderator:

Similar threads

Undergrad Force applied on sphere by turbulent flow
  • · Replies 28 ·
Replies
28
Views
2K
Undergrad Express drag force/acceleration/velocity as function of time
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad Fluid dynamics: drag coefficient and pressure at the stagnation point.
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Constant Ratio of Drag coefficient and terminal velocity
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Terminal Velocity of a Cylinder Freefalling Through a Fluid
  • · Replies 6 ·
Replies
6
Views
10K
High School Temperature-Dependence of Viscosity of a Fluid?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Sinking Object Motion Equations
  • · Replies 6 ·
Replies
6
Views
2K
Doublet flow in Fluid Dynamics between two spheres or cylinders
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Stokes Law/Drag Force corrections?
  • · Replies 1 ·
Replies
1
Views
5K
Undergrad Drag Coefficient of a 'flexible' object (e.g. a piece of paper)
  • · Replies 4 ·
Replies
4
Views
2K