Question

How terminal velocity changes with radius of the tube?

Answer 1

Imagine an experiment in which you have a vertical pipe closed at the bottom and filled with a viscous fluid. How would doubling the radius of the pipe change the terminal velocity of a ball bearing dropped into the top of the pipe? And how can you explain this? Poiseuille's formula says that volume of fluid flowing per unit time increases in proportion to radius4. I thought I'd be able to use this for a situation where an object was moving and the fluid was still as I thought this would be an equivalent situation where you could imagine that in fact the ball was still and the fluid was moving as if you were an observer atop the ball bearing. However logically this cannot be the case because if a pipe were very very wide, the walls would barely affect the ball bearing and doubling the radius would have almost no affect, it certainly wouldn't multiply the terminal velocity by 16!
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Answer 2

Answer:

Imagine an experiment in which you have a vertical pipe closed at the bottom and filled with a viscous fluid. How would doubling the radius of the pipe change the terminal velocity of a ball bearing dropped into the top of the pipe? And how can you explain this? Poiseuille's formula says that volume of fluid flowing per unit time increases in proportion to radius4. I thought I'd be able to use this for a situation where an object was moving and the fluid was still as I thought this would be an equivalent situation where you could imagine that in fact the ball was still and the fluid was moving as if you were an observer atop the ball bearing. However logically this cannot be the case because if a pipe were very very wide, the walls would barely affect the ball bearing and doubling the radius would have almost no affect, it certainly wouldn't multiply the terminal velocity by 16!

Thank you

Explanation: