Naked Science Forum
Life Sciences => Marine Science => Topic started by: CS_SJ on 18/12/2021 00:50:03

Hello,
Something I’ve wondered about is those amazing air bubbles that are sometimes found in underwater caves. In particular, I was wondering how the depth of the water does or does not affects them.
In my Figure 1 example, the water is 50 feet deep and air bubble in the cave has 3 feet of air from the top of the cave to the water, and the air pressure in the bubble is the same as sea level.
Well, what would happen if the same cave was 1000 feet deep? (see Figure 2.) Would the bubble still have 3 feet of air from the top of cave to the water? Or would the tremendous weight of the water make the bubble much smaller like just 3 inches tall or something? And what about the air pressure? Would the air be super compressed?
If this is the wrong place to ask this question, I apologize in advance, and if you could direct me where I could get an answer for this, I would appreciate it.
Thank you,
 SJ

In my Figure 1 example, the water is 50 feet deep and air bubble in the cave has 3 feet of air from the top of the cave to the water, and the air pressure in the bubble is the same as sea level.
No it isn't. The pressure there is about 40 psi, 25 more than at sea level. It's 50 feet down. The water there is well over twice the surface pressure.
Well, what would happen if the same cave was 1000 feet deep? (see Figure 2.) Would the bubble still have 3 feet of air from the top of cave to the water?
Probably, yes, because it holds more air when more compressed. It's the height of the cave that determines the thickness of the bubble, not the pressure. But given the same mass of air as the cave above, it would be compressed more down there, yes. The pressure down there is about 450 psi.
Would the air be super compressed?
Yes, more than 30 times the compression at the surface.
If this is the wrong place to ask this question, I apologize in advance.
Probably, yes. Marine Science is in lifescience. It's about fish and such. I'm not worried about it.

the water is 50 feet deep and air bubble in the cave has 3 feet of air from the top of the cave to the water, and the air pressure in the bubble is the same as sea level.
No, it is not unless somehow the system has only just been set up and water is still rushing into the cave.
Once it settles down the air pressure will be significantly higher if my memory and arithmetic serve me well ( somewhat dubious at 1 on a Saturday morning) the pressure at 50 feet will be a little under 2 atmospheres higher than "normal" air.

The deeper you go, the greater the pressure and thus the smaller the air pocket would be (assuming equal masses of air, and take note that's exactly what I'm assuming for the following calculations. As soon as you discard that, then the volume changes I speak of don't apply).
According to this website, every 33 feet you descend results in an increase in pressure of 1 atmosphere: https://oceanservice.noaa.gov/facts/pressure.html#:~:text=The%20deeper%20you%20go%20under,at%20all%20with%20high%20pressure.
So at 50 feet down, the air pressure would be 50/33 = 1.515 additional atmospheres plus the original atmosphere equals 2.515 atmospheres of total pressure. At a given temperature, gas volume decreases linearly in step with the increase in pressure. We can thus tell that the volume of air in that cave would be 1/2.515 = 0.3976 x 100 = 39.76% of what it would be at sea level.
At 1,000 feet down, the pressure in such a cavern would be 1,000/33 = 30.3 + 1 = 31.3 atmospheres total. The volume of air would be 1/31.3 = 0.0319 x 100 = 3.19% of what it would be at sea level.
The actual height of the air pockets is harder to estimate, given that the shape of a cave is irregular.

@CS_SJ
One advantage of the metric system.
Atmospheric pressure 1bar at surface, for every 10m you descend in water add 1bar ie 2bar pressure at 10m = half the air volume compared to surface.

what would happen if the same cave was 1000 feet deep?
The above calculation assumes the ideal gas law: Volume α 1/Pressure
But there is an additional factor here: solubility of oxygen and nitrogen increases with pressure (but by different amounts).
 At a pressure 31 times atmospheric pressure, almost all the air would be dissolved in the water
 If there were circulation of the water, all of the air would dissolve
 So no bubble for divers to pop up into...
See: https://en.wikipedia.org/wiki/Henry%27s_law

@CS_SJ
One advantage of the metric system.
Atmospheric pressure 1bar at surface, for every 10m you descend in water add 1bar ie 2bar pressure at 10m = half the air volume compared to surface.
Sadly, no. Time was that you could talk about bars and millibars, but just to make it interesting, standard sea level pressure was actually 1.01325 bar.
Nowadays we have to use the official SI unit pascal, so the practical unit for barometric measurements and altimetry has changed from the friendly millibar to the absurd hectopascal except in the USA where "inches" (of mercury) remains the reporting standard. Flying the plane is the easy bit: navigation involves solving 4dimensional differential equations with a bizarre historic mixture of units: knots, statute miles, gallons/liters/pounds per minute/hour, feet, kilometers, hectopascals /inches, minutes/"decimal hours", degrees (circular/fahrenheit/centigrade)....and a significant unknown  wind velocity.

standard sea level pressure was actually 1.01325 bar.
If you are doing your calculation to half a dozen sig figs, then you need to include the humidity. That gives you a few more units to include.
Fortunately, you aren't, so you don't.

.....but just to make it interesting, standard sea level pressure was actually 1.01325 bar.
True, but most of us use 1bar in decompression tables and make adjustments for local pressure and altitude where lots of accuracy is needed. Works quite well for the example given, but as @Kryptid says, you need to know details of the cave shape to work out the actual height.