How to calculate air pressure below sea level?

[Machine_Elf]

@am77494

But even if you assume a constant temperature, the ideal gas law is no longer valid at higher pressures, so the expressions break down.

Agreed, which is why I said that the results get weird very quickly. I can’t find a reference that says at what pressures air starts to deviate from the ideal gas law in a meaningful way, but as I mentioned, my model predicts 14,000 psi about 1% of the way down from seal level to the core. That’s probably already inaccurate. For the other 99% of the way down, you end up having to make some assumptions about the behavior of air at extremely high pressures.

[am77494]

@Machine_Elf

I can’t find a reference that says at what pressures air starts to deviate from the ideal gas law in a meaningful way, but as I mentioned, my model predicts 14,000 psi about 1% of the way down from seal level to the core.

For engineering purposes, we use a factor z, called the compressibility factor

PV = znRT (for ideal gases z = 1)

z at 68 F (293K ~ 300K) for Air at varying pressures can be found here :

The Ideal Gas Law

There is about 3% deviation from Ideal gas at 200 bar (~2900 psi) (68F)

Not at the link above but I have simulators that calculate z to deviate about 70% (z=1.687) at 14000 psi (68F)

[Machine_Elf]

@am77494

For engineering purposes, we use a factor z, called the compressibility factor

PV = znRT (for ideal gases z = 1)

Yeah, I remember my 1990-vintage thermo text had a Z chart in the back. Your numbers (Z=1.687 @14 ksi) show that the density will be lower than my model predicts, meaning the rate of pressure increase with depth will be slower. Instead of 37 miles down, it’ll be quite a bit further before we hit 14 ksi.

Thanks for the Engineering Toolbox link. Their Z-factor table only goes to 500 bar (7350 psi), but with your extension to 14 ksi, I can incorporate a compressibility model and get more accurate results (at least up to the point where we achieve 14 ksi).