Theoretical question about incompressible fluid

[robertogrramos]

Hi all!


I'm trying to get my head around something... on a pressure vessel with an ideal gas when there is a 'leak', or any output of the stored gas, if there is no inlet, the pressure inside the tank decreases (PV=nRT), right?

But with a pressure vessel filled with water, that is incompressible, what happens to the pressure then?
I'm thinking that if there is only one nozzle, even if it is open, if there aren't any other nozzle to enter new water or air, there will be no 'leak'. The water will remain on the vessel, right?

But imagine a situation where you have a vessel that is pressurized at 200 kPa and on the inlet nozzle there is a check valve. If the pressure drops at the upstream to 100 kPa, the pressure at the vessel will remain 200 kPa, because of the check valve.
On this case, with the pressure at the upstream lower than the pressure at the vessel, if we try to open a valve at the outlet whats going to happen?
A)Will the water remain on the vessel like if there weren't an inlet nozzle?
B)OR will we have a flow on the outlet, new water coming from the inlet and the pressure on the vessel drops to 100 kPa?
C)If B is correct does this depends on the pressure difference, or will this happens disregardless the pressure at the upstream?

 

[DriveMeNuts]

Applying theory directly to the real-world doesn't work.

When thinking in real-world mode there is no such thing as a non-compressible liquid and therefore pressure will be retained upon closing the valve even after disabling the pressure source. Also the vessel will elastically expand like a balloon, temporarily increasing in volume while pressure is applied. When the valve is then opened the water will expand and the vessel will shrink, causing a volume of water to flow about of the valve as the pressure drops.

If you remain in theory mode, then I would say that Newtons 3rd law applies to your problem. The incompressible liquid only retains pressure while a force is being applied to it. The valve being open or closed is irrelevant. If the valve is open then the pressure source pushes directly on the non-compressible liquid. If the valve is closed the the pressure source pushes on the valve which in turn pushes on the non-compressible liquid. If the pressure source is disabled, then the pressure of the non-compressible liquid drops irrespective of the valve being open or not.

 

[JStephen]

There is some water compressibility, there is some vessel expansion due to elasticity, there is some finite opening and closing time for valves, and some backflow possible while closing.

 

[davefitz]

some other observations:
- nearly all check valves leak, the assumption that it prevents 100% of all backflow is rarely correct
-As the pressure drops in the water filled pressure vessel, some amount of liquid will evaporate, filling the ullage with water vapor

"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick