Pressure Depth in a Cave

[Charlie99]

Which is it? Sealed or unsealed? You just contradicted yourself in the same sentence.

I think he is thinking in terms of whether air introduced at point C would leak out into the surrounding soil.

A well constructed pipe running from A to E with the profile shown could be described as a "completely sealed system with only points A and E open to the atmosphere".

 

[Charlie99]

If its not vacuum sealed, then the water will move. If it is vacuum sealed, then you've got a water barometer there and you'll be at less than one atmospheric pressure.

Somewhere recently in the past few days I read an article about diving in a water barometer... I can't remember where I came across it though...

You'd run into that situation if diving in a siphon. Not a siphon as used by cavers, but a true siphon where the shape is an upside down U, with the top of the U above the main body of water, but less than 33' feet (or local atmospheric pressure) above it.

Extra credit question: How long can you stay at -25' depth (25' of water above sea level) without getting bent?

Spoiler

My bet is just 10 or 20 minutes, and you would have to be breathing close to pure O2 in order to avoid going hypoxic.

 

[Scubakevdm]

For extra credit, how long can you stay at -25' depth (25' of water above sea level) without getting bent?

Wrap yourself tightly in an ace bandage.

 

[lamont]

Lamont -- IF you have a BIG bottle of water (cap on, sealed vessel) are you saying the pressure at the bottom of the bottle is greater than the pressure at the top? I thought that one of the characteristics of a fluid was that it exerted pressure equally in an enclosed vessel? What am I missing here?

Neglecting gravity, fluids and gasses will exert pressure equally in an enclosed vessel.

When you are dealing with columns of water that are 33 feet high, though, you can't neglect gravity. You also need to add up the column of air resting on the water as well, which is what gives the 1 ATA at the surface.

BTW, I thought the answer was that C was at 4 ATA because it was 4 ATA at both "ends" of the "vessel."

Nope. It is 4 ATA at the bottom, but you *must* take off the 2 ATA of pressure sitting on top of that as you rise up through the water column going from B to C. That water column is a huge piston which is pushing against the piston of the water column coming from A to B. As you travel up both pistons, though, the pressure decreases because there is less mass above pressing down because of the action of gravity upon it.

Alternatively the way to look at it is if it was 4 ATA at C then the water just below C would push down on the water below it with a force slighly above 4 ATA because of the addition of the weight in that thin layer. You add up the weight of all those thin layers and you would get 6 ATA at C -- which would not be opposed by the 4 ATA water column coming from A and the water would move.

 

[lamont]

You are confusing a liquid with a gas. Gas in a closed vessel exerts an equal pressure in all directions.

nope... gas has mass and weight as well -- otherwise we wouldn't have 1 ATA at the surface caused by the column of air over the divesite. the density of gas makes the weight of the column of gas negligible though for all practical purposes with containers of reasonable size (although the density of gas in a scuba tank should mean that the pressure differential between the top of the tank and the bottom would be much greater than an empty scuba tank -- 10 lbs over the cross sectional area of the inside of the tank in square inches would give the psi differential for an HP130).

 

[H2Andy]

guys, this is really easy

your pressure gauge measures water above your head, period

you could be 100 feet underground, but if there's only 33 feet of water above you, the gauge is going to show 33 feet. if you are 100 feet underground, but out of the water, your depth will show as zero. it takes 50 miles of air to create one atmosphere of presure. 100 feet of air extra is not going to even register.

at 33 feet depth, you add one ATM for the air pressure, and your "true" pressure is 2.0 ATM

 

[lamont]

You'd run into that situation if diving in a siphon. Not a siphon as used by cavers, but a true siphon where the shape is an upside down U, with the top of the U above the main body of water, but less than 33' feet (or local atmospheric pressure) above it.

Extra credit question: How long can you stay at -25' depth (25' of water above sea level) without getting bent?

You run into the same problems that NASA does with astronauts going EVA. You'd want to prebreathe a bunch of pure O2 to wash the N2 out of your system first.

I just read an article on the net about this a few days ago, but I can't turn it up in google now..

 

[Blackwood]

guys, this is really easy

/thread

 

[Melicertes]

Which is it? Sealed or unsealed? You just contradicted yourself in the same sentence.

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.

If you want, you can prove it to yourself. Go fill up the sink. Take a styrofoam cup and put it face down into the water. Position it so that it's halfway into the water. Poke a hole in the top. See if water fills the cup or if it just fills halfway (so that it's at the same level as the rest of the water in the sink).

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.

 

[lamont]

Peter are you thinking of the fact that water/fluids are incompressible? So if you have a tube of water that is horizontal and press on one end with a piston the pressure throughout the entire tube will increase, but with rigid walls around the rest of the tube the water will not move...

That one is highly useful since we're mostly water/fluids and means that we don't get crushed when we go diving -- all that we have to worry about is equalizing airspaces...