Pressure Depth in a Cave

[boat sju]

Originally Posted by Drewski

So, regardless of what else is going on, the depth on your gauge IS the depth you are AT.

Good thing too - because that's what your second stage is thinking also.

 

[Melicertes]

As far as I can tell, my two mistakes are:
a. Ignoring A and E which make it an open system; and
b. Ignoring the weight of the water column from B to C which would have the effect of decreasing the pressure the same amount as the weight (at least that is my take away of this)

This is exactly the way I took to understanding the scenario also, and yes I agree these were the exact same two mistakes I made in this discussion. In my mind the air columns above A and E were as good as pressurized plugs that "closed" the system at A & E and contributed to introducing pressure into the system between points B and D.

Another mistake I made was assuming that the water was entirely contained within the cave space between ABCDE meaning that it would not seap through the walls to connect with the surrounding ground water and air, which also makes the system most definitely "open."

Blackwood's explanation of the styrofoam cup upside down in the sink started to crack the ice for me on this.

I'm definitely no physicist or mathematician so I do not proclaim to truly know anything as any kind of expert. Galileo wrote: "I never met a man so ignorant that I couldn't learn from him." This is how I approach life. I'm not bothered with trying to convince people of my opinion so that I can get them to say "Yeah you're right." I'm rather concerned about challenging my understanding of things and putting them to the test by exposing them to good old public scrutiny. This way I learn where the weaknesses are in my understanding of things.

A final note: being an instructor does not mean I'm perfect. I've never looked at it that way. In fact it's in many ways only the start of yet another learning curve. I just take exception to certain people's judgments in arrogance and their sense of superiority. The condescending tone of certain comments shows a lot about their character. The rest who spent time to challenge and argue respectfully, thank you; again I learned a lot

 

[phunk]

Another mistake I made was assuming that the water was entirely contained within the cave space between ABCDE meaning that it would not seap through the walls to connect with the surrounding ground water and air, which also makes the system most definitely "open."

It doesn't really matter where the system is open, either through cracks in the rock or through the mouth of the cave at point B. As long as it's all one body of water the pressure at C only depends on its depth below the surface at A.

 

[Seadeuce]

Have not done any serious cave diving, but I can see a quick connection to answer the original question.

I have done much wreck diving, with many penetrations. When diving through a wreck it sometimes can be the same as the profile described by the original poster. You leave the surface, enter the wreck at point A, descending to the floor of the engine room at 66ft.
If I need to ascend again before I can make another deep excursion, say to the forward hold, I am still in my "tube" within the wreck going from one end - at depth - to the other, through a corridor that matches the profile described.

In my experience the pressure dropped when I ascended, and increased again on going back down.

Therefore I would have to agree that the pressure at 33ft in the example would be 2atms.


Seadeuce

 

[Blackwood]

My answer is "indeterminate", because water is neither truly incompressible, nor is the container truly rigid.

This isn't just semantics, it really is one of those cases where small 2nd order effects start to dominate. In that sort of system the pressure can vary widely from things like expansion of the water due to temperature changes. Things like gases dissolved in the water going into or out of solution also have big effects.

If the container is very close to rigid, then just a tiny amount of dissolved gas coming out of solution will keep the average pressure of the water at the same average pressure it was when sealed up.

Yes. I deliberately used the word "average". When sealing up a bunch of water, I'm pretty sure what is going to dominate is the pressure of the gases dissolved in the water, so the average depth is what counts (assuming a constant liter/ata solubility with pressure changes).

If you are going to the extremes of considering density changes of liquids over minor changes of depth, dissolved gases, and geometric changes of a container hundreds of orders of magnitude stronger than any of the forces at play, then sure, the total pressure inside the container is indeterminate.

Blackwood's explanation of the styrofoam cup upside down in the sink started to crack the ice for me on this.

Did you try it?

I started off thinking of a different experiment involving filling the glass with water, holding it vertically (facing down) under the surface, and then draining the sink (to watch the water level in the glass fall accordingly). Then I thought: naw, just punch a hole in it.

 

[Charlie99]

If you like doing experiments with styrofoam cups in the sink, here's another experiment that you might find interesting. It demonstrates how external pressures can effect air space and buoyancy.

(I just linked to the first website that popped up on a Google search on "Cartesian Diver". There are many others.)

 

[TeddyDiver]

Possible solution to Thalassamanias dialemma with the aquariums.
The environment is sealed so that observers do not notice it.
1. totally sealed and the air space above the surface is pressurized or
2. tubes are sealed and both of them form their own environment and have higher pressure than the aquariums at "subjectively" same level.

 

[jponline77]

If that container holds water, I disagree.

Would a container containing 1L of air have a different reaction than a container carrying 1mL of air?
How would this water in this ideal container know that it has been lifted above the surface? The internals of an ideal container would not feel the outside effects of the change in pressure.

 

[reefnet]

This is exactly the way I took to understanding the scenario also, and yes I agree these were the exact same two mistakes I made in this discussion. In my mind the air columns above A and E were as good as pressurized plugs that "closed" the system at A & E and contributed to introducing pressure into the system between points B and D.

Another mistake I made was assuming that the water was entirely contained within the cave space between ABCDE meaning that it would not seap through the walls to connect with the surrounding ground water and air, which also makes the system most definitely "open."

I still sense some misunderstanding here. You must divorce yourself from this notion of a "closed" system. Whether the holes are plugged or the rock is porous does not change the result of the problem in any way. As long as the system is in equilibrium on Earth (under the influence of gravity), point C will always experience 2 atmospheres LESS pressure than points B/D. No exceptions.

For instance, you could plug the holes with pistons and weigh them each down with 1000 elephants and point C would still be 2 atmospheres less than points B/D. sealing the system and applying pressure to it simply increases the pressure everywhere in the system, it doesn't change the pressure differential of one point relative to another.

Does that help?

 

[ClayJar]

Regarding the open vs. closed at A&E part. That actually isn't relevant in and of itself.

You have this cave system sitting there, full of basically stagnant water, and all of the sudden, you close the sliding hatches at A and E (you did read the sign that said the cave closes at dusk, eh?). It should be pretty clear that the pressures above and below the sliding hatches do not magically change in the instant the doors seal, right?

Okay, now let's say that only the middle of the W closes at dusk. At the moment you slide the doors at B and D closed, what happens to the pressure on either side? Well, nothing happens.

In the case of this example, whether the system is open or closed is irrelevant. The only relevant information is:

1. The pressure at a given vertical coordinate (i.e. 1 ata at point A)
2. The vertical distance between the level at that coordinate and the level of any other coordinate inside the water.

Incidentally, as the pressure above and below any water-air interface is equal (ignoring the all but immeasurably low contribution of surface tension), and as the pressure in the air in the bubble can be taken as a constant (as air has a low enough density to make the pressure changes with height negigible in a cave bubble), the pressure in any gas space can be said to be equal to the pressure in the water's surface in contact with the bubble (as determined by the height in the water column, as explained above).

(In other words, the permeability or impermeability of the surrounding rock is irrelevant to the pressure in any bubble, permanent or transient, in the cave system.)