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Pressure $1$ meter under water is approx $1.1$ atm ($1$ atm due to air, $0.1$ atm due to water), and pressure $1000$ meters above water is approx $0.9$ atm.

So, roughly speaking, is it correct to say that $1$ meter of water (indipendently from cross-sectional area) weighs as much as $1000$ meters of air?

For example, a cubic metre of water weighs $1000$ kg, while a column of a square metre base and $1000$ meters height weighs $1225$ kg (using constant air density at 15°C, which is wrong since temperature will decrease with height)

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    $\begingroup$ Yes. But since "1 meter of water (independently from cross-sectional area)" is long winded and confusing, it might be better to say "the density of water is 1000 times bigger than the density of air" (The actual values are 1000 kg/m^3 and about 1.2 kg/m^3 at sea level atmospheric conditions). $\endgroup$ – alephzero Jul 5 at 11:21
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    $\begingroup$ Your phrasing implies a dimensional inconsistency, so others will not immediately understand what you are trying to say. $\endgroup$ – David White Jul 5 at 18:50
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Mostly yes.

The air density varies with altitude and temperature but for 1000m the effect is still relatively small. Density at ground level is $1.22kg/m^3$ and at 1000m it's still $1.11kg/m^3$ (see https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html) so it's closer to 850m of air but it's in the right ballpark

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