Consider a U-tube containing some liquid. The two ends of the tube are connected to closed volumes of air with different initial pressures, such that there is some difference in the liquid levels inside the tube. Assume that the U-tube has uniform cross section, the liquid is incompressible, and there are no losses.
Now, if the U-tube is accelerated vertically, will there be any changes in the liquid level at one leg relative to that in the other, and why?
I initially thought they would change. When the tube is accelerated upwards, the liquid in the tube would tend to move from the leg with higher liquid level to the other leg. The increased pressure that drives it is given as $\rho d a$, where $\rho$ is the liquid density, $d$ is the initial difference in the liquid levels of the two legs, and $a$ is the acceleration of the U-tube. But then, I thought there should be an equal and opposing pressure increase from the leg with lower liquid level, which prevents the liquid from moving. But I am not sure.