# Terminal Velocity Equation in vertical cylinder with some fluid

• B
• yejin
In summary, the speaker asks if an equation can be made to express terminal velocity based on the condition that when diameter increases, velocity decreases. They mention that the velocity should change depending on the diameter of both the cylinder and sphere, and that they have all the necessary variables. They clarify that the situation is for free-fall in a fluid and ask for help with their research on Stokes law. They mention the need for this information in the design of subway tunnels in South Korea. The speaker also shares an equation they have found relating terminal velocity to variables, but notes that it does not account for changes in cylinder diameter.
yejin
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...)

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:

## 1. What is the terminal velocity equation for a vertical cylinder with some fluid?

The terminal velocity equation for a vertical cylinder with some fluid is given by vt = √(2mg/ρACD), where vt is the terminal velocity, m is the mass of the cylinder, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the cylinder, and CD is the drag coefficient.

## 2. How is the terminal velocity affected by the mass of the cylinder?

The terminal velocity is directly proportional to the mass of the cylinder. This means that as the mass of the cylinder increases, the terminal velocity also increases.

## 3. What is the role of the drag coefficient in the terminal velocity equation?

The drag coefficient represents the resistance to motion of the fluid. A higher drag coefficient means that the fluid is more resistant to the motion of the cylinder, resulting in a lower terminal velocity.

## 4. How does the cross-sectional area of the cylinder impact the terminal velocity?

The cross-sectional area of the cylinder is directly proportional to the terminal velocity. This means that as the cross-sectional area increases, the terminal velocity also increases.

## 5. Can the terminal velocity equation be applied to all fluids?

No, the terminal velocity equation is specifically for fluids with a constant density. It cannot be applied to non-Newtonian fluids or fluids with varying density.

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