Excess Pressure of a Underwater Airbubble?

Question

An underwater air bubble has an excess inside pressure of 12.2 Pa. What is the excess pressure inside an air bubble with twice the radius?

Answer 1

Underwater air bubble inside pressure P₁ = 12.2 Pa

Inside air bubble radius = R₁

Underwater air bubble inside pressure when twice the radius P₂ = ?

When twice the radius R₂ = 2R₁

Pressure inward due to surface tension at the circumference P = 2πσR

σ = surface tension of the liquid.

Keep σ is constant for underwater.

P = 2πσR

P/R = Constant

P₁R₁ = P₂R₂

12.2R₁ = P₂(2R₁)

P₂ = 12.2/2 = 6.1 Pa

Underwater air bubble inside pressure when twice the radius is 6.1 Pa