Air (density rho) is being blown on a soap fi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The bubble detaches from the film when the force exerted by the dynamic pressure exceeds the force due to surface tension along the circumference

Vedclass · Accepted Answer

$\sqrt{\frac{8 T}{\rho R}}$

Vedclass · Answer

(D) The bubble detaches from the film when the force exerted by the dynamic pressure exceeds the force due to surface tension along the circumference of the pipe.The force due to dynamic pressure is given by $F_{	ext{dynamic}} = P_{	ext{dynamic}} 	imes A = (\frac{1}{2} ho v^2) 	imes (\pi R^2)$.The force due to surface tension acts along the circumference of the pipe. Since a soap film has two surfaces,the total surface tension force is $F_{	ext{surface tension}} = 2 	imes (T 	imes 2 \pi R) = 4 \pi R T$.For the bubble to detach,the dynamic force must be at least equal to the surface tension force:$\frac{1}{2} ho v^2 	imes \pi R^2 = 4 \pi R T$Simplifying the equation:$\frac{1}{2} ho v^2 R = 4 T$$v^2 = \frac{8 T}{ho R}$$v = \sqrt{\frac{8 T}{ho R}}$Thus,the minimum speed at which the bubble is formed is $v = \sqrt{\frac{8 T}{ho R}}$.

Similar Questions

Two glass plates of area $10^{-2} \,m^2$ have a $10 \,cm$ thick water film between them. The surface tension of water is $70 \times 10^{-3} \,N/m$. The force required to separate the two glass plates from each other is (in $\,N$)

Small liquid drops assume a spherical shape because

Give two practical illustrations of surface tension.

The work done in increasing the size of a soap film from $10 \, cm \times 6 \, cm$ to $10 \, cm \times 11 \, cm$ is $3 \times 10^{-4} \, J$. The surface tension of the film is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module