Curious Question about Atmospheric Pressure.

  • #26
olivermsun
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Take a body of air. It can be doing whatever you like within itself. If it is in equilibrium with its surroundings (not rising, falling or moving) then it is no more than a hot air balloon with no envelope... In the end, the total forces on it must be zero. All of the downwards (weight) forces must balance all of the upwards forces (caused by pressure on the ground. If this is not true then it must be accelerating upwards or downwards (outwards or inwards).

That's a big if, around which the entire disagreement pretty much revolves.

The cold air flowing downslope in a katabatic wind isn't in equilibrium with its surroundings. That's why the katabatic wind happens.
 
  • #27
sophiecentaur
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That's a big if, around which the entire disagreement pretty much revolves.

The cold air flowing downslope in a katabatic wind isn't in equilibrium with its surroundings. That's why the katabatic wind happens.

That's why i said that you must take a bigger body - even the whole of the Earth's atmosphere, which is not moving, rising or falling. It's just easier to consider an ideal - bite sized bit - first. How about a nice stable cumulus cloud with the outside layers pretty well stationary and loads of turmoil inside it, sitting on a cushion of cool air?
However big you choose, I think you'd have to agree that Newton 1 must apply.
 
  • #28
olivermsun
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However big you choose, I think you'd have to agree that Newton 1 must apply.

But what does this have to do with the disagreement in the thread?
 
  • #29
sophiecentaur
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It resolves the disagreement about whether atmospheric pressure is due to the weight of the atmosphere. I must admit that I don't always read every post either. Haha
 
  • #30
russ_watters
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Oy, this keeps getting worse. I need to go back and correct some errors right from the start, but first I am going to give another thought experiment that clearly illustrates the error (not that you responded to the last two....):

Imagine you are holding a cup of cold air and there is no wind to disturb it. The bottom of the cup is negligibly thin, but flat. There is pressure pushing up on the bottom of the cup due to the air around it and there is pressure pushing down on it due to the air above it. Are the pressures equal and if not, which is greater? Hint: punch a hole in the bottom of the cup and air will pour out as if it were water.
 
  • #31
russ_watters
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Ok, first some definitions:

There are a few ways to measure pressure, but ultimately all pressure is measured as a differential, using a gauge. So differential pressure and gauge pressure measure the pressure difference between two different points. For absolute pressure, one of those points (the reference) is a vacuum.

In terms of the way pressure acts on things (a surface, other air), there are three possibilities: Static pressure is what you have when there is no movement. Dynamic (velocity) pressure is what you get due to movement, perpendicular to the movement of the air. Total pressure is the sum of these two.

So:
Atmospheric pressure is the pressure exerted on any exposed surface by the impact of air molecules upon that surface. It is the simple product of the number of impacts per square meter per second and the mean impulse per impact.
No. That description includes velocity pressure. Atmospheric pressure is the static pressure of the atmosphere. Mistakenly capturing velocity pressure in the measurement would crash airplanes.
When the wind is blowing, that approximation becomes increasingly less accurate.
No. The wind does not affect the approximation, just the measurement accuracy of certain instruments.
If the wind is blowing then it must be from a higher pressure region to a lower pressure region.
Important point of clarification. We vs klimatos are talking past each other here a little bit, but only because the typical description above is usually sufficient. But when those "regions" become separated vertically, it isn't quite right anymore. That's not your fault, as I know that's what you meant: klimatos threw a non sequitur into the mix that confuses the issue.
There are lots of winds that do not blow from areas of high pressure to areas of low pressure. Virtually all gravity winds blow from areas of low pressure to areas of high pressure. If you think of winds as three-dimensional phenomena (the only rational perspective, in my opinion) then all areas when the air is sinking represent movement from low pressure areas to high pressure areas.
So these "vertical winds" break the simplification. But:
No. Air cannot flow through an increasing pressure gradient. Gravity causes the pressure gradient that moves the air in the case of gravity winds.
Pressure gradient. I've clarified the situation to be more precise. You then later misused the term, so I was right that you don't realize what it means and why the distinction is important. A gradient is a vector field showing the variations in a scalar field. In other words, the difference between two widely spaced areas is not a gradient: a gradient only exists at a point. If the pressure variation between two widely spaced areas were continuous, then you could average it and get a gradient at every point, but that isn't the case here and that's where your error lies. As my cup example demonstrates, there is a discontinuity in the pressures. The pressure just above the bottom of the cup is higher than the pressure just below the bottom of the cup, so when you punch a hole in the cup, the gradient at the point between them is high->low is above->below. So air spills out of the cup due from an "area" of higher pressure to an "area" of lower pressure despite the fact that two widely separated parcels of air will appear to show an opposite pressure gradient.

So how do we explain this or expand it more generally. Well consider that the air spills into another cup below. As it spills into the cup below, the higher ambient pressure compresses it, making it more dense and still a higher pressure than the air around it. So essentially, the falling parcel of cold air carries with it, follows or creates its own pressure gradient as it falls.
Under isobaric conditions, cold air will flow towards warm air. At 1000 hPa, the flux rate for air at -25°C is 3.11 x 10^27 molecules per square meter per second. At +25°C, the flux is 2.84 x 10^27. This flux differential will manifest itself in a flow of air from the colder to the warmer. This is the genesis of the very common daily alternations of "land breezes" and "sea breezes".
No. There can't not be a pressure difference between warm and cold parcels of air next to each other: the cold parcel is heavier, so its pressure is greater. Land and sea breezes are and example of this, not a counterexample.
Finally, there will be a net flow of air away from evaporating surfaces and toward condensing surfaces.

These are all common illustrations of isobaric winds.
Evaporation causes local pressure differences.
Every time there is subsidence in the atmosphere (the downward leg of a Hadley Cell, for instance) you have air moving from an area of lower real pressures (not pressure reduced to sea level) to an area of higher real pressures.
It's not pressure reduced to sea level that matters here, it is absolute pressure or pressure differential: pressure with the normal atmospheric pressure gradients removed.
The vertical pressure gradient IS the issue. The wind is blowing from the source area at a lower ambient pressure to the destination area at a higher ambient pressure. Ergo, it is blowing from a point of lower pressure to a point of higher pressure. Because there is a vertical pressure gradient, these winds are called katabatic winds; i. e. downslope winds. That vertical gradient is the essence of the issue.
No. It's a non-sequitur that you've added, which is confusing you and the issue.
 
  • #32
olivermsun
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Pressure gradient... A gradient is a vector field showing the variations in a scalar field. In other words, the difference between two widely spaced areas is not a gradient: a gradient only exists at a point. If the pressure variation between two widely spaced areas were continuous, then you could average it and get a gradient at every point, but that isn't the case here and that's where your error lies.

An exceedingly small time after you opened the hole in your coffee cup, there would no longer be a pressure discontinuity but only a very steep gradient, and yet the flow would continue for a while longer. Hence the discontinuity is not really the sticking point.

The pressure just above the bottom of the cup is higher than the pressure just below the bottom of the cup, so when you punch a hole in the cup, the gradient at the point between them is high->low is above->below. So air spills out of the cup due from an "area" of higher pressure to an "area" of lower pressure despite the fact that two widely separated parcels of air will appear to show an opposite pressure gradient.

This thought experiment seems a bit misleading as described.

You could very well imagine the same experiment, but with water in the cup. Most observers would agree that the water at the bottom of the cup is at higher pressure than the air at the same height outside the cup, and thus the water would be pushed out under some pressure. However, the "last" parcel of water would still fall out of the hole (let's assume a large hole here), even with no additional weight of water above it. This would happen solely due to the weight of the parcel itself, which is heavier than air.
 
  • #33
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This thread has gone badly off post. The OP asked the question of why atmospheric pressures were omni-directional when the weight-force hypothesis used to explain such pressures was uni-directional. That question has been answered; and the discussion has since fragmented.

I intend to abandon this thread and initiate a new thread on the most interesting of these fragments: the question of whether fluids can naturally flow from areas of lower pressure to areas of higher pressure.

Please join me there if the subject interests you.
 

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