Pressure at the top of a mountain...
Atmospheric pressure reduces with altitude for two reasons, both of which are related to gravity.
The gravitational attraction* between the earth and air molecules is greater for those molecules nearer to earth than those further away — they have more weight — dragging them closer together and increasing the pressure (force per unit area) between them.
Molecules further away from the earth have less weight (because gravitational attraction is less) but they are also ‘standing’ on the molecules below them, causing compression. Those lower down have to support more molecules above them and are further compressed (pressurised) in the process.
* Strictly speaking, it is the gravitational force minus the effect of the Earth's spin (an effect that is greatest at the equator).
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Air pressure changes with altitude.
Air is all around us, but we cannot see it. Gravity from the Earth pulls air down - this is called air pressure. We don't feel this pressure because our bodies push an equal amount of pressure outward. This graph shows how air density and air pressure changes with altitude (the distance above sea level). Barometers are used to measure air pressure in millibars.
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I am looking to find the reason: why air pressure decreases with altitude? Has it to do with the fact that gravitational force is less at higher altitude due to the greater distance between the masses? Does earth’s spin cause a centrifugal force? Are the molecules at higher altitude pushing onto the molecules of air at lower altitudes thus increasing their pressure? Is the earths air pressure higher at the poles than at the equator?
Qmechanic♦
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asked Dec 21, 2020 at 8:33
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The air pressure at a given point is the weight of the column of air directly above that point, as explained here. As altitude increases, this column becomes smaller, so it has less weight. Thus, points at higher altitude have lower pressure.
While gravitational force does decrease with altitude, for everyday purposes (staying near the surface of the Earth), the difference is not very large. Likewise, the centrifugal force also does not have significant impact.
answered Dec 21, 2020 at 8:50
SandejoSandejo
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I edited this question on the first day, in response to a few comments that pointed out a misunderstanding, but it didn't register. I sincerely apologize for that.
As pointed out by other answers, the pressure due to any fluid, compressible or not, increases with depth. This is due to the greater mass and thus weight of the fluid above.
What's interesting is that the pressure of water increases linearly with depth, while that of air does not.
The gravitational field strength drops down to only 88% even at the height of the ISS. The drop in pressure has more to do with the fact that unlike water, air is a compressible fluid. As you move further down the atmosphere, there is a greater weight of air above pushing down on the air below, so the density, and thus the air pressure, increases. Basically, the density $\rho$ is a function of $h$. so you have to integrate density over the height instead of simply multiplying.
$$P=g\int\rho\mathrm{d}h$$
or $$P=\int g\rho\mathrm{d}h$$ if you want to account for the change in gravitational field, however small
answered Dec 21, 2020 at 8:49
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As you go higher, there are less air molecules (less weight) on a given area this is basically one reason why it decreases.
From the barometric formula, one can get the relation between the pressure and altitude. It's defined as
$$P = P_{0}e^{-\frac{mgh}{kT}}$$
so the relation between pressure and altitude is $P\propto e^{-h}$. Thus, as we go to higher altitudes pressure will exponentially decrease.
answered Dec 21, 2020 at 8:54
MonopoleMonopole
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Has it to do with the fact that gravitational force is less at higher altitude due to the greater distance between the masses?
The gravitational force does decrease as you go higher up, but that's not the reason. The pressure would still be greater at the bottom even in some weird physics where gravity got stronger further from the surface.
Does earth’s spin cause a centrifugal force?
It does, but again, that's not part of the reason.
Are the molecules at higher altitude pushing onto the molecules of air at lower altitudes thus increasing their pressure?
Yes. That is exactly the answer.
Is the earths air pressure higher at the poles than at the equator?
No. Even if the effective gravity is different, air at sea level will flow from where there is more pressure to where there is less until it balances out. Of course, pressure changes due to weather but over time I believe seal level pressure is the same around the world.
answered Dec 22, 2020 at 3:10
Mark FoskeyMark Foskey
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Edit: After researching a bit more, I've edited my answer to be significantly more accurate.
In short - air pressure is the result of the cumulative force that air molecules act on objects below them due to Earth's gravity. The higher the altitude, the less air molecules there are to act a force below them, and therefore, there's less air pressure at higher altitudes.
So, even though
Molecules further away from the earth have less weight (because gravitational attraction is less) ... they are also ‘standing’ on the molecules below them, causing compression. Those lower down have to support more molecules above them and are further compressed (pressurised) in the process. [Source]
A more technical way to approach the question would be looking at the general formula for pressure: $$p=\frac{F}{A}$$ Where $p$ is the pressure, $F$ is the force that causes the pressure, and $A$ is the area of the surface on contact, we can understand that (assuming $A$ is constant), as $F$ increases, so does $p$.
As for the effect of Earth's spin on air pressure, it is miniscule, as explained here.
answered Dec 21, 2020 at 8:59
uriyabauriyaba
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You can check the following link from Wikipedia this is what I learned during the undergraduate education in thermodynamics course. You can relate ideal gas law and Bernoulli's principles without introducing kinetic terms (hydrostatic approximation only). Thus, you get an equation that also depends on the temperature. Gravitational acceleration is fairly the same considering the depth of atmosphere. So, it can only be a correction to the atmospheric model rather than the main principle.
I guess also you can include centrifugal force in the gravitational acceleration, because they are in the opposite direction (Be aware that centrifugal force is just an imaginary force that you may add to the equation.). You can imagine the radius of Earth and compare it to the depth of atmosphere to guess if the radius dependent terms such as gravity or centrifugal force is important with respect to other changes in your equation. If you want to do a precise calculation to compare two regions, the poles and the equator, you can add the centrifugal acceleration part too.
The air certainly pushes down the other air molecules, thus increase the pressure. It is the same principle (Bernoulli's) that is applied also in the pressure change in liquids.
answered Dec 21, 2020 at 9:13
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