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From an hydrostatic point of view, the pressure in a fluid should be the same at the same depth/altitude.

Obviously, in our atmosphere that does not happen. I am guessing that the main reason is the fact that the atmosphere cannot be regarded as hydrostatic.

Is this the reason? How exactly can we explain these pressure differences?

I understand that a higher pressure region must have a higher density, and therefore it would take time for reducing such density gradient. But how fast is this? In the order of the speed of sound? Or it has nothing to do with it?

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    $\begingroup$ The pressure in a fluid should be the same at constant altitude because if it wasn't you'd have... wind? $\endgroup$
    – Emilio Pisanty
    Commented Oct 16, 2015 at 22:07
  • $\begingroup$ @EmilioPisanty In you opinion, is "Wind" the "cause" or the "effect"? $\endgroup$
    – cinico
    Commented Oct 18, 2015 at 15:10
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    $\begingroup$ The reason that horizontal pressure differences cannot occur in equilibrium is that the air in the middle will feel a net force and will therefore be blown sideways, which is what we want to rule out for a system in equilibrium. For the atmosphere, this sideways motion is known as wind, which I'm sure you've experienced, so I'm just really wondering why on earth you thought the atmosphere is an equilibrium system. $\endgroup$
    – Emilio Pisanty
    Commented Oct 18, 2015 at 21:36
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    $\begingroup$ @EmilioPisanty And still you didn't answer my question. I also didn't assume that the atmosphere is an equilibrium system. I was just trying to better understand the mechanisms behind the differences in pressure, which others have explained very well. Your last comment somehow felt a bit ungracious since you stated obvious facts suggesting my ignorance about them, and not contributing for an healthy discussion. Please avoid that. Thank you $\endgroup$
    – cinico
    Commented Oct 18, 2015 at 22:17

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You asked a number of questions in this question.

From a hydrostatic point of view, the pressure in a fluid should be the same at the same depth/altitude.

That "should be" assumes hydrostatic equilibrium. That is a simplifying assumption. It's a reasonable starting point, but it's not a hard and fast rule. The Earth's atmosphere, it's oceans, and even its interior are approximately in hydrostatic equilibrium.

I am guessing that the main reason is the fact that the atmosphere cannot be regarded as hydrostatic. Is this the reason?

Significant deviations from hydrostatic equilibrium do occur. This is an effect, not a cause.

How exactly can we explain these pressure differences?

Ultimately, it's because the Earth

  • Is round,
  • Is lit by the Sun,
  • Rotates about its axis once per day,
  • Has distinct rotational and orbital axes, separated by about 23 degrees,
  • Has a fairly clear atmosphere, and
  • Is covered by lots of liquid water.

These result in climate and weather, which in turn result in the Earth's atmosphere being only approximately in hydrostatic equilibrium.

Equatorial regions receive a lot more sunlight than do polar regions. The resulting temperature gradient is one of the key drivers of the climate. On Venus, which rotates slowly, this energy transfer occurs in a pair of Hadley cells that reach from the equator almost to the poles. On Titan, which rotates in about 16 days, the Hadley cells breaks up at about 60 degrees latitude. Jupiter and Saturn are so large and rotate so quickly that they have bands instead of Hadley-type cells.

On the Earth, which rotates once per day, the Hadley cells extend to only 30 degrees. Polar cells form around the poles, and the Ferrel cells act as intermediaries between the Hadley and Polar cells.

http://www.metoffice.gov.uk/media/image/f/s/Figure-4-Global-cells(edit)2.jpg

But how fast is this? In the order of the speed of sound? Or it has nothing to do with it?

The speed of sound has nothing to do with it. Winds do, and winds generally move much slower than the speed of sound. The fastest winds recorded are inside tornados, and even there things only move at about 40% of the speed of sound.

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  • $\begingroup$ Very detailed answer, thank you David. Overall, you explain why we have weather in our planet. And while it is, obviously, the explanation for my question, I feel that it should be more clear on the effect of how the air convections produces different pressure zones. That is why I will accept Mike's answer instead. But again, thank you so much for all the precious information. $\endgroup$
    – cinico
    Commented Oct 18, 2015 at 15:07
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The air moves in great swirls.

In places where the air is being warmed from below it moves up. That causes air to be sucked in from below, and spread out at the top. What it sees as the reason to be sucked in is a lower pressure pulling it. When any fluid is pulled in to a center, its angular momentum is conserved (and it has plenty of that because it is spinning with the earth), so it spins faster. (Coriolis force is another way to describe this.)

So, you have meteorological low pressure areas, where the air is spinning the same direction as the earth, only faster, and high pressure areas, which are the opposite.

So that's why you can see different pressures at sea level or any other altitude. (By the way, a low atmospheric pressure at sea level causes the water itself to be pulled up, resulting in "storm surge".)

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A very simplified explanation: because the temperature is not everywhere the same. Why is the temperature not uniform? There are various reasons, the most important reason for temperature and pressure differences at locations not too far from each other is that the ground below is not the same everywhere. Depending on whether it's a forest, a lake, a field, or rocks below you, the ground absorbs and reflects heat differently. The humidity will also be different, depending on what is on the surface.

This local variation in temperature leads to air getting warmer and rising up at one location, and getting colder and moving downward at another location, leading to pressure differences. Air then moves around to equalize these pressure differences, this is what we call "wind".

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Another example (in the question and not clarified by any response) of treating compressible and on-compressible fluids the same. Once they are separated the problem is simplified and for me at least sorts itself out.

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    $\begingroup$ Quite short - this should go to comments $\endgroup$
    – jaromrax
    Commented Apr 28, 2017 at 20:33
  • $\begingroup$ The question my answer addresses is so full of paradoxical confusion it is impossible to answer and the only solution is to correct the confusion, which is what I am suggesting the questioner does. $\endgroup$
    – john
    Commented Apr 30, 2017 at 2:35

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