Why is Force of Bubble Given by 2(2πR)σs?

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SUMMARY

The force exerted by a bubble is accurately represented by the formula 2(2πR)σs, where R is the radius of the bubble and σs is the surface tension. This formula simplifies the calculation by disregarding the negligible difference between the inner and outer circumferences due to the bubble wall's thickness being significantly smaller than the bubble's radius. Additionally, the pressure on the concave side of the bubble is higher because the curvature increases the pressure exerted on that side, a consequence of the principles of fluid mechanics.

PREREQUISITES
  • Understanding of surface tension in fluids
  • Basic principles of fluid mechanics
  • Familiarity with geometric properties of circles
  • Knowledge of pressure differentials in curved surfaces
NEXT STEPS
  • Study the effects of surface tension on bubble formation
  • Learn about pressure differentials in curved surfaces using the Young-Laplace equation
  • Explore the relationship between curvature and pressure in fluid dynamics
  • Investigate the implications of bubble wall thickness on pressure calculations
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Students studying fluid mechanics, physicists interested in surface tension phenomena, and anyone analyzing the behavior of bubbles in various fluids.

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Homework Statement


why the force of bubble is given by the formula of 2(2 pi R ) σs ? why not (2 pi R ) σs + (2 pi R+ ΔR) σs ? Since the radius of th outer circumfernece and inner circumference are the different ?

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Because for most purposes the difference is too small to worry about. The thickness of the bubble wall is usually far smaller than the radius of the bubble.
 
haruspex said:
Because for most purposes the difference is too small to worry about. The thickness of the bubble wall is usually far smaller than the radius of the bubble.
i have one more question here . I was also told that the pressure at the concave side of the bubbles is higher ... why is it so ? is it because of the circumference of the pressure at the concave side is higher?
 

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