# How to calculate air pressure below sea level?

**URL:** <https://boards.straightdope.com/t/how-to-calculate-air-pressure-below-sea-level/969089>\
**Category:** Factual Questions\
**Created:** [August 4, 2022, 2:26pm UTC](https://boards.straightdope.com/t/how-to-calculate-air-pressure-below-sea-level/969089 "2022-08-04T14:26:22Z")\
**Posts on this page:** 3\
**Page:** 2

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**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\
**Post date:** [August 5, 2022, 2:23pm UTC](https://boards.straightdope.com/t/how-to-calculate-air-pressure-below-sea-level/969089/21 "2022-08-05T14:23:21Z")

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 But even if you assume a constant temperature, the ideal gas law is no longer valid at higher pressures, so the expressions break down.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

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**Author:** ![am77494](https://avatars.discourse-cdn.com/v4/letter/a/d2c977/32.png) [@am77494](https://boards.straightdope.com/u/am77494)\
**Post date:** [August 5, 2022, 3:25pm UTC](https://boards.straightdope.com/t/how-to-calculate-air-pressure-below-sea-level/969089/22 "2022-08-05T15:25:56Z")

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> [@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](https://www.engineeringtoolbox.com/ideal-gas-law-d_157.html)**
>
> The relationship between volume, pressure, temperature and quantity of a gas, including definition of gas density.

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)

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<div class="post-metadata">

**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\
**Post date:** [August 5, 2022, 6:25pm UTC](https://boards.straightdope.com/t/how-to-calculate-air-pressure-below-sea-level/969089/23 "2022-08-05T18:25:43Z")

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> [@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).

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