Pressure Depth in a Cave

[Thalassamania]

Wiki is considering siphons that have reservoirs at two different height with "final end of the tube lower than the liquid surface in the (first) reservoir" as well as with the final end open to atmospheric. Give that special case, everything said is correct, however, that was not the special case I was asking about. In the case that I'm interested in the two reservoirs are at the same level and both ends of the tube are at the same level, but there is no flow, just water held above the height of the surface of the two reservoirs.

Permit me to describe again: Two identical reservoirs 33 feet deep at the same level. Two siphons each connecting the two reservoirs. One siphon just slightly below the surface of each reservoir and another siphon that extends to almost the bottom (33 feet) of both reservoirs.

 

[Charlie99]

Let's say we have two vertically identical, very large aquaria tanks that are open on the top and are 33 ft deep. These tanks are connected together by two "true siphons," one at just below the surface of the water and at the bottom of the tanks. ... My first guess would be that the shallow origin siphon is approx 1 ATA all the way through (ignoring the fine point of siphon's diameter) and the deep one would be approx 2 ATA all the way through

What you are missing is that the pressure in the siphon connected to the bottom of the tank is 2ata at the connection point, but as you rise upward through the siphon the pressure is reduced. By the time you get even with the top of the tank, you are down to 1ata.

You could easily verify that by drilling a hole in the side of the siphon at that point. It it really was 2ata as you hypothesized, you'd have water squirting out under pressure. It won't though.

It isn't anything all that mysterious. Water has mass. Gravity pulls it down, creating a force. Once you think about it in those terms, then you can start understanding what would happen if you replace the water with mercury or if gravity had a higher or lower value. If you think hard about it, you will also see that statements like "the pressure of gas inside a tank is the same throughout" is just an approximation (although very, very close) if the gas has weight.

 

[boat sju]

I don't think this is right, I've seen teleost fish swim through such a siphon and they did not have their swim bladders expand, that is why I suspect that the pressure stays constant, though I can't explain why from first principles

I wouldn't want to get into a debate about the actual numbers but I believe markr is essentially correct - you'll go through increasing and decreasing pressure areas through the siphon and depending on the height it won't work because the water would cavitate/boil/separate do to the low pressure. You can only suck water so high through a straw. I believe you about the fish swimming through a siphon but it probably wasn't 33ft above the free water surface right?

Oh, on the cave debate, we're not talking a closed system because a diver entered from sea level and swam through the sytem which means it's open to the atmosphere. Pressure is directly related to depth below sea level in this example. A schock absorber is a good example of a closed system, you can increase pressure inside it - by compressing the air in it which can't escape. A hyperbaric chamber might be an example of a closed system that we might "dive" in but not a cave system.

 

[Thalassamania]

What you are missing is that the pressure in the siphon connected to the bottom of the tank is 2ata at the connection point, but as you rise upward through the siphon the pressure is reduced. By the time you get even with the top of the tank, you are down to 1ata.

You could easily verify that by drilling a hole in the side of the siphon at that point. It it really was 2ata as you hypothesized, you'd have water squirting out under pressure. It won't though.

It isn't anything all that mysterious. Water has mass. Gravity pulls it down, creating a force. Once you think about it in those terms, then you can start understanding what would happen if you replace the water with mercury or if gravity had a higher or lower value. If you think hard about it, you will also see that statements like "the pressure of gas inside a tank is the same throughout" is just an approximation (although very, very close) if the gas has weight.

Right you are and clearly correct, thanks for the example of drilling a hole that anwers the "whole" thing.<G> I guess the vertical displacement of the siphon in the aquarium was not greater than the fish could handle.

 

[Rick Murchison]

I do not agree, if the area between A&E were excavated to expose C to the surface, and thus the atmosphere, the 4ATA water pressure between A&B and E&D respectively would force water out of the newly exposed area C, and probably flood the excavated basin; the water levels in A&B and E&D would drop to the same level as the water level above the now flooded area C thereby decreasing the pressure at B and D from 4ATA to somewhere slightly over 2ATA depending on the depth of the water above C. The water surface above C would then be at 1ATA.

You may not agree but the pressure in the example will nevertheless be 2ATA.
Perhaps another view will be helpful.
Imagine swimming into a wreck, into a room... ascend to the ceiling and look at your depth gauge. Would it show the depth you are, or the depth of the door you came through to get there? Would the pressure measured in your exhaust bubbles trapped on the ceiling be the pressure of their actual depth, or would that pressure change by moving the depth of the door into the room around?
Rick

 

[The Horn]

Water pressure is related to the height of the water colum, gravity and the specific gravity of the water. Or P= Specific gravity X 9.81 m/s^2 X height of the water colum.

So for the initial example taking fresh water in the cave the presssure at 33 feet (c) or roughly 10 meters is 1000 kg/m^3 x 9.81 m/s^2 x 10 m = 98.1 Kpa or about 1 BAR or about 1 atmosphere on top of the normal atmospheric pressure so therefore 2 ATM.

If the cave was exerting any force on the water and the water was exposed to atmosphere the cave would collapse and water would be forced out. If it was a closed system and there was internal pressure built up you could not dive it anyway, if you tried the first time you opened the cave to get in the pressure would reduce to zero at the entrance and internal pressure would be based on the above formula. This is why Hydrostatic tests are completed vs straight air, as soon as the cylinder is exposed to atmosphere the internal fluid pressure drops to zero.

Things that affect the pressure: height above sea level changes gravity coefficient slightly and the atmospheric pressure will also change as the air density changes. Sea water vs fresh water Fresh specific gravity =1000 kg/cubic meter and sea water is about 1025 kg/ cubic meter depending on salinity, contaminates etc.

 

[phunk]

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

Not that simple. If there was air in that cave at point C, and you climbed out of the water there, your depth would still show as 33ft. If not there wouldn't be air there, the water would rise.

Given the picture in the initial post, your depth would be equivilent to 33ft at point C, there is no way for it to be anything else.

 

[H2Andy]

Not that simple. If there was air in that cave

well, that's not the scenario presented

the scenario presented was a flooded tube

as for the "air pocket" scenario, an air pocket could only exist at 1 ATM or "above" 1 ATM. at 1.1ATM, the water would "push up" the air back to 1 ATM.

so, even with an air pocket above you, you still calculate as i indicated:

[water depth/33] + 1 = ATM

 

[Drewski]

Without reading this entire thread (my apologies if someone else made this point, I stopped reading on page 4) someone please answer this:

If you are using a depth gauge that measures depth by pressure, regardless of the physics of your "position" in the cave or water column, wouldn't your profile be accurate throughout the dive?

What's the point other than academic?

 

[Drewski]

Oh, and BTW, when you ASCEND in an underwater cave, doesn't your depth guage indicate a SHALLOWER depth?

How could it do this if the pressure was the same?

Just wondering....