Pressure Depth in a Cave

[SteveC]

This is a very interesting question. I can see how some people think the answer is 4 ata. or even 1 ata. But even for a dive instructor this is not surprising. I had an instructor tell me that your regulator could free flow from looking up at the surface. Makes since doesn’t it? You have all the weight of the water column pressing down on your purge valve. But I would hope that a cave diver would know the answer from experience

 

[markr]

To clarify, when I am saying "sealed environment" I am refering to the fact that the walls of the cave/tunnel system in which the water and possible trapped air pockets reside are impermeable, i.e. they do not allow any water to be forced through them and therefore act as solid, impermeable barriers. Thus the only open areas exposed to atmospheric pressure are those at A and E at which atmospheric pressure according to he original diagram is at 1ATA. I realize that in reality cave walls are in fact permeable and in that way in direct contact with the water table and the air spaces in between rock and dirt particles which are in turn in direct contact with atmospheric pressure and this therefore does not constitute a sealed environment by a strict definition of that term. The pressure inside the cave system indirectly equalizes with atmospheric pressure because it is affected by the pressures outside of the actual cave space that contains the water. In that way it's basically the same as what Blackwood explained below.

My argument is that in a lab environment, and yes clearly non-practical and totally theoretical, if we were to construct a pipe system in the shape of a giant W where the outer points of the W is at 1ATA (A&E) and the bottom of the legs where the W touches the ground is at 4ATA(B&D,) the inner peak in between the legs that points upwards (C) will then be at 4ATA also because the pipes are providing an impermeable, and in my words albeit being a somewhat inaccurate choice of wording, "sealed" environment. This will be the case because Pascal's laws state that in a sealed container an increase in pressure introduced into a liquid will result in that pressure force to be equally exerted everywhere throughout the whole "sealed" system at right angles at every point where it encounters a barrier - in this case the sides of the pipes. The atmospheric pressure of 1ATA then at points A&E will act as plugs that could just as well have been watertight weighted plugs that exert 1ATA pressure on the water at A&E (hence my thoughts about a "sealed" system - because the water cannot go anywhere outside the pipe system.

If your explanation of Pascal's law were correct if you took a 66' long rigid tube and stuck in the water vertically there would be a two atmosphere difference in pressure as long as the ends of the tube were open. But as soon as both ends of the tube were sealed all the water would be at the same pressure over the length of the tube. Next you'll be trying to prove perpetual motion works.

If you go back and re-read Pascal's law pay attention to the word "additional". Even if the cave were a sealed environment, which it isn't, Pascal law states that if you increased the pressure by an additional two atmospheres at any point in the container, the pressure would increase by an additional two atmospheres at every point in the container. If the container is 66' tall, the pressure at the top is going to be two atmospheres less then the pressure at the bottom. There is always a pressure differential between different depths in a water column, assuming you remain on the planet.

 

[Melicertes]

I just did in this post. There's no nice way to say the following, but realize it's nothing personal:

If you can't follow the article I linked to or the alternate explanation I offered, you probably shouldn't be diving. Furthermore, your status indicator suggests that you are an instructor. If that's true, then I would not hesitate to report your lack of understanding to your certifying agency.

That may sound hostile, but I'm honestly concerned for your safety. I'd hate for you (or a student) to get hurt because you made a mistake like this.

I made a mistake. If you wish I will PM you my instructor number and you can report me to PADI with my blessing. I nevertheless learned a lot from this thread (thnx Blackwood, your post was enlightening) which is why I enjoy chatting on Scubaboard

 

[Melicertes]

If you go back and re-read Pascal's law pay attention to the word "additional". Even if the cave were a sealed environment, which it isn't, Pascal law states that if you increased the pressure by an additional two atmospheres at any point in the container, the pressure would increase by an additional two atmospheres at every point in the container. If the container is 66' tall, the pressure at the top is going to be two atmospheres less then the pressure at the bottom. There is always a pressure differential between different depths in a water column, assuming you remain on the planet.

Point well taken

 

[JeffG]

I made a mistake. If you wish I will PM you my instructor number and you can report me to PADI with my blessing. I nevertheless learned a lot from this thread (thnx Blackwood, your post was enlightening) which is why I enjoy chatting on Scubaboard

Some good has happened in this thread.

 

[TSandM]

Something tells me that Lynne is posting as Peter Guy

No, Lynne knew the answer when she read the question.

 

[reefnet]

I made a mistake.

"To err is human". As long as it's clear to you now, then there's no problem. It's the stubborn folks who refuse to admit to being wrong that bother me.

Dive safely...g'night.

 

[Dive-aholic]

This thread is absolutely shocking. Anyone who is convinced that the answer is 4 ATA should be flogged with his C-card.

The original poster's question is really just a convoluted version of the Hydrostatic Paradox.

You mustn't let looks deceive you...the pressure at point "C" has NOTHING to do with the solid rock above. It is defined solely by the height of the free water surface, and is therefore 2 ATA. You could replace the rock with marshmallows or pixie dust and the answer would be the same.

If you are still not convinced, consider the point 33ft down from the cave system entrance. The pressure there is certainly 2 ATA. If the pressure at C were anything other than 2 ATA there would be a pressure differential and the cave system would become an underwater river. For the system to be in equilibrium, point C MUST be at 2 ATA.

Class dismissed.

Actually, Florida cave systems are underwater rivers. They flow from sinkhole to sinkhole. In fact, there are several caves in Florida where you can enter through one opening and exit through another. The water flows through the systems.

I'm not arguing your hydrostatic paradox argument. I agree, it is 2ATA. I've also been there and confirmed it. Okay, now there's really no way for me to know that I was exactly 34ft below the surface, but I do know where I traveled through the caves and whether I was ascending or descending in the caves. And the depths my computer registers seem to coincide with my travel through the system.

 

[Coldiver1]

(Decrease of pressure on ascencion) Now I know why when I shake up a can of beer, pop it open while it is in my mouth, only a little bit flies out of my nose!

 

[victor]

Generally, though, you just ignore all the rock and look at the height of the water column...

So, the correct answer at C is 2 ATA. And we know that C is not exposed to the atmosphere, otherwise there would be a net force at C (air would push down with 1 ATA and the water would push up with 2 ATA) so the water and air would move and water would push upwards until it reached a zero water column height (if the displacement of water caused the level of water at other areas in the system to drop, the water would rise until those heights were equal).

It is definitely *not* 4 ATA at C, because you take that 4 ATA and add another 66 fsw column of water as you head towards B so that there would be 6 ATA pushing on the water at B from the direction of C, while there is only a 100 fsw column of water (4 ATA) pushing on B from the direction of A so 4 ATA != 6 ATA and the water would move until equilibrium was reached...

Thanks Lamont I was trying to think of a clear way to explain this but you have beaten me to it.