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These people inhabit an underwater city.

In the city there are pools that connect the dry habitat with the outside ocean, this of course mean that the habitat is unpressurized and therefore the internal atmospheric pressure is the same as the pressure at the bottom of the sea.

So my question is: how deep can the city be?

I do not care what they breath as long as the air mix can let them live as deep as possible without any major problem. I also know that they cannot simply go back to the surface; to do that they need to undergo decompression, but that's ok, they are supposed to live there!

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  • $\begingroup$ the aquarius research facility is at 196.1 kilopascals. You can look at some of the other facilities en.wikipedia.org/wiki/Underwater_habitat $\endgroup$ – John Dec 23 '16 at 17:11
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    $\begingroup$ Currently about 700 m. Look up "saturation diving". $\endgroup$ – jamesqf Dec 23 '16 at 19:34
  • $\begingroup$ This needs to be clarified. There are two different questions, the one in the title and 'how deep can the city be?' in the answer. Which question do you want answered? Those are both very different questions. $\endgroup$ – kingledion Dec 24 '16 at 6:43
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    $\begingroup$ @kingledion depth and pressure are correlated in this case. $\endgroup$ – SilverCookies Dec 24 '16 at 10:49
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The change in pressure below the ocean is approximately $$\frac{dp}{dz}=\frac{1\text{ atm}}{10\text{ m}}$$ where $z$ is measured from the surface of the water downwards. We also have to add in the one atmosphere of pressure from the atmosphere, meaning that the pressure is really $$p(z)=1+\frac{1}{10}z$$ where $p$ is in atmospheres. According to Wikipedia, 100 meters under the surface leads to pressures dangerous to even the most experienced divers. We know that $p(100)=11\text{ atm}$, where nitrogen narcosis becomes extremely hazardous, and could lead to death. A much better depth, in terms of narcosis, is about 40 meters, where $p(40)=5\text{ atm}$.

That said, there's no reason for your city to have the same pressure as the outside ocean. It should absolutely be pressurized, with the correct mix of gases. Pure oxygen can lead to oxygen toxicity.

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    $\begingroup$ There must be some confusion between meters and another unit of measurement. 1 atm is about 10 meters column of water. $\endgroup$ – AlexP Dec 24 '16 at 19:04
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    $\begingroup$ @AlexP I did make an embarrassing conversion error. Thank you. $\endgroup$ – HDE 226868 Dec 26 '16 at 19:17
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A lot depends on the air mix - very deep diving can involve helium instead of the usual gases, as the partial pressure of oxygen and other gases becomes critical. As this is a technical area, the best answer would depend on the gas mixture and the community's needs. These three wiki articles should help a lot with background and resources:

https://en.wikipedia.org/wiki/Breathing_gas (Gaseous mixtures used for various depths and circumstances)

https://en.wikipedia.org/wiki/Deep_diving (Overview of breathing requirements and gas mixtures in the context of water depth, and how different depths are generally seen)

This of course excludes any acclimatisation/adaptations that may occur, or (in the medium term) evolutionary changes, which may well occur too.

https://en.wikipedia.org/wiki/High-altitude_adaptation_in_humans (May spark ideas by looking at how human biology has adapted in the communities that live permanently in the opposite environment)

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