What happens to the pressure of some gas, air for example, that is in a container almost full of liquid, some hydraulic fluid for example, when the liquid is pressurized?

The air is at 0 PSIG at the beginning, the container is rigid, a pump is connected to its bottom.

This is what I think: after the pump pressurize the hydraulic fluid, supposedly incompressible, the liquid now has an increased overall pressure that exerts to all directions. Since the air is compressible, it now has a smaller volume, and increased gage pressure that is equal of the increased overall liquid pressure. Is this correct?

If so, how does the new gage pressure of the air compare to the increased overall liquid pressure if there was no air at all in the container but full of liquid?

  • $\begingroup$ All the air is deliberately bled out of hydraulic systems, so this will not happen in practice. Nevertheless, go for it @Gert. $\endgroup$ – David White Sep 7 at 4:06
  • $\begingroup$ @DavidWhite Sure, but in a hypothetical setting like this, what would happen? $\endgroup$ – Yulin Z Sep 9 at 21:42
  • $\begingroup$ The air bubble will be under the same pressure as the oil. $\endgroup$ – David White Sep 10 at 2:51
  • $\begingroup$ Is my assumption that the pressure would also be less than that of the hydraulic fluid if there is no air correct? @DavidWhite $\endgroup$ – Yulin Z Sep 10 at 19:15
  • $\begingroup$ Yulin, that all depends on the conditions of the problem. If you have a cylinder/plunger setup, and you try to push the plunger the same incremental distance for both cases, then yes, the liquid full system will end up at the higher pressure. $\endgroup$ – David White Sep 10 at 19:29

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