TITLE: In which direction will air flow?
QUESTION [0 upvotes]: Here is a problem:
I am having trouble with deciding between choices B and D. The sub-hemispherical bubble will have lesser volume than the hemispherical one for a given radius of the tube, and therefore Boyle's Law dictates that air will flow from end 2 to 1.
Another explanation I can think of is the following: The excess pressure in a soap bubble due to surface tension is inversely proportional to the radius of curvature, which is greater for the sub-hemispherical bubble. According to this reasoning air will flow from end 1 to 2.
Which explanation is correct and why?

REPLY [0 votes]: $$P_i = P_o+4\frac{\gamma}{r}$$
Where $\gamma$ is the surface tension, and $r$ is the radius of the bubble.
As $r_2$ > $r_1$, $P_2$ < $P_1$. Therefore, air will flow from end 1 to end 2.
Boyle's law states the relationship between pressure and volume of a fixed quantity of a gas at a fixed temperature and is not applicable in this case. It is not right to assume that the amount of air on both sides of the valve is the same.