Increase in rising air bubble's terminal velocity

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Discussion Overview

The discussion centers on the behavior of rising air bubbles in water, specifically focusing on the relationship between buoyancy, terminal velocity, and the changing volume of the bubble as it ascends. Participants explore the theoretical and experimental aspects of this phenomenon, seeking equations and methods for calculation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Experimental/applied

Main Points Raised

  • One participant notes that as an air bubble rises, the decreasing pressure leads to an increase in its volume, which in turn affects buoyancy and suggests that terminal velocity should increase proportionally.
  • Another participant questions the conditions of the water, asking whether it is air-saturated, air-free, or super-saturated, which may influence the bubble's behavior.
  • A different participant proposes conducting an experiment using a pipette to create bubbles in tap water or oil, suggesting that oil may produce rounder bubbles due to surface tension.
  • One participant advises looking up the coefficient of drag for spheres, noting that while an air bubble is not a perfect sphere, the drag coefficient is relevant and varies with velocity and bubble size, indicating the need for numerical solutions.
  • Another participant expresses enthusiasm for the experiment, highlighting its feasibility and the potential for comparing theoretical and measured speeds.

Areas of Agreement / Disagreement

Participants express varying views on the conditions of the water and the implications for the experiment. There is no consensus on the best approach or the specific equations to use, indicating that multiple competing views remain.

Contextual Notes

Participants do not fully resolve the assumptions regarding the type of water or the exact nature of the bubble's behavior, leaving open questions about the experimental setup and theoretical calculations.

Who May Find This Useful

This discussion may be useful for students and researchers interested in fluid dynamics, experimental physics, and the behavior of bubbles in liquids.

PhyVibDsics
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Hi! As we know air bubble in the water rises due to buoyancy and quickly reaches its terminal velocity. What is more, as bubble rises the pressure decreases, consequently the volume of the bubble increases resulting in buoyancy becoming larger. So the terminal velocity doesn't remain constant, but should increase proportionaly (like a linear function). And the difficult part here is that velocity (speed of rising) depends on buoyancy, but buoyancy depends on the velocity as well.. Sooo..

Does anybody know any useful equations, ways to calculate this? As far as I know, it is only solvable with a computer simulation. Does anybody know where to find any articles adressing this problem? I want to/am planning to do an experiment for a research (so called extended essay in my educational program) and I would like to have some more theory on this..

Thanks for your help, I hope I wasn't too long, but in my opinion it is really interesting haha.. Even though I'm looking for this because of school, I think I wouldn't classify this thread as HW, exercises.. (am a new forum user so don't want to break no rules haha).
 
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Air saturated water? Air-free water? Super-saturated?
 
Bystander said:
Air saturated water? Air-free water? Super-saturated?
Imagine producing a bubble with pippete or something similar into a normal tap water at the bottom of a 2m high cylinder. Or maybe even oil; that would result in in bubbles being rounder even at little bit bigger radiuses because of surface tension if I'm correct (easier to conduct an experiment)
 
Look up coefficient of drag for spheres. An air bubble is not really a sphere, but the the drag coefficient will be close enough for your purposes. You will see that the drag coefficient is a function of velocity and bubble size, so that pretty much forces you to use a numerical (computer simulation) solution.

It should be a fun experiment. Easy to do, easy to measure velocity, easy to change bubble size, and a good chance to compare theoretical speed to measured speed.
 

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