Thought experiment: Rising bubble in rigid container

[chingel]

I understand that this would be the scenario since there doesn't seem to be another explanation. But if the fluid column is of the same height, the gas exerts the same pressure, where does the extra force come from to the bottom?

 

[K^2]

Reaction force to the increased force on the top.

 

[sophiecentaur]

Only if at the beginning of experiment the top of the fluid was not under pressure, and all of the pressure was accounted for by the gradient. That's not necessarily the case. Say, I start with a 1m tall cylinder filled with air at 1atm and sealed, with exception of a small inlet valve. Through that valve, I start forcing in liquid until the cylinder is 90% filled with liquid. I then allow the temperature in the cylinder to equalize with room temperature. The pressure of the gas is now 10atm. The pressure gradient in fluid is just under 0.1atm. If I now quickly invert the cylinder, perhaps by the top end so that centrifugal effect helps me to end up with bubble almost perfectly at the bottom, I have the setup for our problem. Bottom of the cylinder is at 10atm, while top is at 9.9atm. Once the bubble rises, the top is at 10atm, and the bottom is at 10.1atm. Increase of only about 1%.

Yes, I agree. The fractional pressure increase is less and less as the pressure goes up. Actually, what you wrote gets it all in proportion. Good comment. I wish you'd made it ten pages back.

 

[chingel]

Oh, I see. When the bubble is at the bottom, the force felt at the top is the bubble pressure minus the pressure of the fluid column and at the bottom is the bubble pressure, when the bubble is at the top, the pressure at the bottom is the bubble pressure plus the fluid column pressure and at the top is the bubble pressure.