Question

2) You have three inverted columns of water. A is completely filled with water. B has an air bubble at the top. C has oil trapped at the top. Rank the points according to their pressures. Least to greatest.) Explain your reasoning.

Answer 1

Let the pressures at the points be $P_A$, $P_B$ and $P_C$.

Atmospheric pressure $P_{atm}$ can be expressed as

$P_{atm}=P_A+\rho gh_A$

$P_{atm}=P_B+\rho gh_B$

$P_{atm}=P_C+\rho gh_C$

Since the points are at the same height $h$ from the free surface of liquid in vessel,

$h_A=h_B=h_C=h$

Hence

$P_A=P_{atm}-\rho gh_A=P_{atm}-\rho gh$

$P_B=P_{atm}-\rho gh_B=P_{atm}-\rho gh$

$P_C=P_{atm}-\rho gh_C=P_{atm}-\rho gh$

Hence $P_A=P_B=P_C$