Question

Air (density p) 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 $v\text{is}\frac{1}{2}\rho v^2$ the speed at which the bubble is formed is

• A. $\sqrt{\frac{T}{\rho R}}$
• B. $\sqrt{\frac{2T}{\rho R}}$
• C. $\sqrt{\frac{4T}{\rho R}}$
• D. $\sqrt{\frac{8T}{R\rho }}$

Answer 1

The correct option is D $\sqrt{\frac{8T}{R\rho }}$

$\frac{1}{2}\rho v^2=\frac{4T}{R}$

$\Rightarrow v=\sqrt{\frac{8T}{R\rho }}$

Hence, the answer is $\sqrt{\frac{8T}{R\rho }}.$