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If I go up in the air the amount of oxygen decrease and the atmospheric pressure gets lower.

What would happen if i dig a hole 100 km down? does atmospheric pressure go up?

  • when is the pressure so big that I could not breath (do to lung capacity to displace the air)
  • when do certain gases become liquid, if at all.
  • when would i notice a change in pressure on my skin.
  • if there is less oxygen on Mount Everest, would there be more oxygen 8 km down?

I ask because water gets heavier real fast as you go lower. an

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At any point above or below the Earth's surface the atmospheric pressure is equal to the weight of air above a square metre surface. So if you go down a mine the atmospheric pressure goes up because there is more air above you.

If the density of the air varies with height as some function of height as $\rho(r)$ then the pressure at a height $h_0$ will be given by:

$$ P(h_0) = \int_{h_0}^\infty \rho(h)g(h)dh $$

where $g(h)$ is the gravitational acceleration. Although this looks simple enough the density of the air varies in a complicated way because it's affected by temperature differences. As you down e.g. a mine the temperature goes up and the air density goes down. I found some calculations of the pressure change in this paper, though the authors bemoan the fact that no actual experimental measurements exist in the literature.

Re your other questions, I believe the upper pressure limit is due to the toxicity of nitrogen at high pressures rather than your ability to breath. The proportion of oxygen in the air wouldn't change (much) and since the density is increasing the amount of oxygen per cubic metre of air would indeed increase with depth. I doubt pressure changes would be detectable on your skin, though most of us have detected pressure changes when our ears pop.

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