Air (density ρ ) is being blown on a soap film (surface tension T ) by a pipe of radius R with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed v is 1 2 ρ v 2 , the speed at which the bubble formed is

Question

Air (density ρ ) is being blown on a soap film (surface tension T ) by a pipe of radius R with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed v is 1 2 ρ v 2 , the speed at which the bubble formed is, T ρ R, 2 T ρ R, 4 T ρ R, 8 T ρ R

MARKS App · Accepted Answer

Bubble detached from the look at ends of circumference, when force of dynamic pressure exceeds force of surface tension. ⇒ p dynamic × Area ≥ Force of surface tension ⇒ 1 2 ρ v 2 × π R 2 ≥ 2 2 π R T Note- that factor 2 on right hand side appears as there are two sides of film surface. ⇒ v ≥ 8 T ρ R ⇒ v min = 8 T ρ R

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