Fluid Mechanics Viscosity Question 314
Question: Two soap bubbles of radii a and b combine to form a single bubble of radius c. If P is the external pressure, then the surface tension of the soap solution is
Options:
A) $ \frac{P(c^{3}+a^{3}+b^{3})}{4(a^{2}+b^{2}-c^{2})} $
B) $ \frac{P(c^{3}-a^{3}-b^{3})}{4(a^{2}+b^{2}-c^{2})} $
C) $ Pc^{3}-4a^{2}-4b^{2} $
D) $ Pc^{3}-2a^{2}-3b^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ \left( P+\frac{4\sigma }{a} \right)\left( \frac{4}{3}\pi a^{3} \right)+\left( P+\frac{4\sigma }{b} \right)\left( \frac{4}{3}\pi b^{3} \right) $ $ =\left( P+\frac{4\sigma }{c} \right)\left( \frac{4}{3}\pi c^{3} \right) $ $ or,,,P[a^{3}+b^{3}-c^{3}]=4\sigma [c^{2}-a^{2}-b^{2}] $ or$ \sigma =\frac{P(c^{3}-a^{3}-b^{3})}{4(a^{2}+b^{2}-c^{2})} $
BETA
