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

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The force of a bubble is expressed as 2(2πR)σs because the thickness of the bubble wall is negligible compared to the bubble's radius, making the difference between inner and outer circumferences insignificant for practical calculations. The formula accounts for the surface tension acting along the entire circumference of the bubble. Additionally, the pressure on the concave side of the bubble is higher due to the curvature, which affects the pressure distribution. This higher pressure is not directly related to the circumference but rather to the principles of fluid mechanics and surface tension. Understanding these concepts is crucial for accurately analyzing bubble dynamics.
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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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