# Atmospheric pressure below sea level

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

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.