What is Air Pressure? Understanding the Weight of the Atmosphere

[klimatos]

1) I think klimatos is actually shifting his ground from a position of 'nothing to do with weight' to one of modification of the basic principle by a dynamic situation.

2)Whether, in the overall scenario of energy balance (heat in - heat out) there is any overall modification to the 'weight' figure, is questionable.

3)I have a feeling that the presence of winds is no different, in principle to the 'internal energy' corresponding to average ambient temperatures.

4)All this stuff about needing a fixed mass of a gas in order to derive the gas LawS is only to do with the derivation and where the gas happens to be. Would no Gas Laws apply inside a gas nebula?

Sophie,

1) Not so. Read my original posting (#30) on this thread. I emphasized the dynamic component of pressure right from the start.

2) I'm not sure what you mean by energy balance. In any given second, minute, hour, day, month, year, decade, century you have in mind the energy gained by the planetary system does not balance the energy lost. This is because of storage considerations. It may well be that in the long run (like from now to the end of time) the two will balance. However, there is no evidence that they balance in any human time frame.

Those of us who prepare annual energy budgets usually assume a balance for the sake of symmetry, but we know that the assumption is false. For instance, during the onset of anyone of the many glacial epochs, the energy lost by the planetary system exceeded the energy gained. For the last 13,000 years or so, the energy gained has exceeded the energy lost.

3) I'm not sure what you mean by "internal energy". In kinetic gas theory it means the rotational, vibrational, and librational energy of the gas molecules as opposed to the "external" energy of translation that is used to measure gas temperatures. Are you referring to the enthalpy of the air?

4) Not so. It refers to when that particular gas law can be properly applied and when it cannot. As to whether a gas law can be applied inside a gas nebula--I don't know. Give me a specific gas law and I will take a stab at answering.

 

[klimatos]

If we remove the top 50 miles of the atmosphere, it will be mostly replaced as the air lower in height moves up thanks to the lack of air above it "pushing" it down correct? Does that have any relation to weight? Looking from an overall picture it looks like the air above it is weighing it down.

That's not the way kinetic gas theory views it. Remember, the distance between the air molecules is many times the diameter of the molecules. Several hundreds or thousands of times greater at high elevations. It is not the collisions that start molecules downward, it is gravity. The mean impulse transferred during collisions is about two orders of magnitude greater than the weight-force. As a molecule moves upward against the pull of gravity, its speed diminishes following the well-known formula. Eventually, it stops moving upward and starts moving downward. It doesn't do so because of collisions with other molecules. It does so purely because of gravity.

There are thought experiments in textbooks on statistical mechanics that show that if there were no molecular collisions at all, the distribution of molecules with elevation would be unchanged.

 

[klimatos]

If you wish to check my calculations (not a bad idea), Bernoulli gives the drop in pressure as equal to one-half the product of the mass density in kilograms times the square of the wind velocity in meters per second. Under the stated conditions, I used a mass density of 1.15792178 kilograms per cubic meter.

Another damn correction! I am going to have to stop doing posting in the late evening when I am tired, and do it only in the early mornings (California time).

Bernoulli's equation in the above paragraph gives the increase in pressure on a surface normal to the wind. To get the drop in pressure on a surface parallel to the wind, you divide by four and change the sign. The values given for the parallel pressure drop are correct, it's just the procedure that has to be modified.

Mumble, grumble, snarl.

 

[DaveC426913]

I am still not convinced that Bernoulli's Law applies to atmo pressure at ground level. You can quote numbers till you're blue, but that doesn't make it more right.

I could as easily suggest that Bernoulli's Law applies to the pressure at 10,000ft depth in the ocean.

Convince me why it is applicable to 100 miles of shifting, moving atmo.

 

[klimatos]

1) Air is much more turbulent and at the same time, less viscous than water, so the effects would essentially be lost in the noise. I am not convinced that Bernoulli's Law is sufficient to draw a proportionality correlation between the complex (read: noisy) movement of the air and some specific drop in pressure in a real world situation.

2) You say we would be "underestimating" the mass of atmo - i.e. consistently on the low side. I'm not convinced that margin would consistently err on the low side such that it would count as a consistent underestimation. It seems sufficient to me to conclude that, due to a shifting atmo, we would expect a margin of error +/-.

Dave,

1) Good thinking. Air is much more turbulent than water because of its lower mass density. However, the entire field of aeronautics is based on Bernoulli's Theorem being right. It is the combination of "angle of attack" and the differential pressure drop over the wing's airfoil that gives heavier-than-air craft their lift.

2) More good thinking. You are absolutely correct. I was concentrating on winds that were essentially parallel to the surface. However, in downdrafts and certain gravity winds, the net movement of air towards the surface increases the surface pressure. That is why "high pressure systems" are always areas where the atmosphere has a net downward component of movement. It is the net movement of air that changes the pressure, not the change in pressure that causes the movement.

It is interesting to note that in such downdrafts the air is moving from areas of low pressure (higher elevations) to areas of high pressure (lower elevations).

 

[olivermsun]

For all of the above reasons. Air is much more turbulent and at the same time, less viscous than water, so the effects would essentially be lost in the noise.

Is this clearly established? If you examine the Reynolds number of many typical flows, I'm not sure you would conclude that air is "much more turbulent" and "less viscous" than water

(Recall that it is the kinematic viscosity ,
\nu = \mu / \rho
that matters here, and water is a heck of a lot denser than air under typical conditions).

 

[olivermsun]

Following on to the above post:

Air is much more turbulent than water because of its lower mass density.

Actually, higher density increases the Reynolds number and would seem to lead to more turbulent behavior. The reason for this is that turbulence occurs due to motions of the fluid, while viscosity tends to damp out such motions.

 

[DaveC426913]

Is this clearly established? If you examine the Reynolds number of many typical flows, I'm not sure you would conclude that air is "much more turbulent" and "less viscous" than water

(Recall that it is the kinematic viscosity ,
\nu = \mu / \rho
that matters here, and water is a heck of a lot denser than air under typical conditions).

I'm argunig that Bernoulli is best applied to relatively simple systems if you want reliable numbers. I don't think it is enough to lead to such sweeping conclusions about what the atmospheric pressure might be at ground level under 100 miles of air. I think there's far too much chaos involved.

I'm not saying I plan to demonstrate this, I'm saying that it's klimatos' initial assertion that it does apply, and the onus is on him to demonstrate that Bernoulli has much to say to about 100 miles of atmo.

 

[rcgldr]

Now take a rushing river. The pressure on the bottom of the river does not accurately measure the weight of the overlying water because of the Bernoulli drop in pressure due to the water's density and the square of the velocity.

This would violate Newton's third law. The downwards force of gravity on the water is equal and opposite of the upwards force of the river bed. The pressure at the river bed corresponds to the force per unit area at the river bed, and that force corresponds to the weight of the water, regardless of the speed of the water. Unless there is a vertical component of acceleration of the water, the force on the river bed corresponds to the weight of the water in the river, and so does the pressure.

The Bernoulli relationship between speed and pressure only applies when acceleration of a gas or fluid is due to a pressure gradient within that gas or fluid.

Getting back on topic, water vapor, temperature, and vertical accelerations of the atmosphere can affect the pressure. Wiki articles:

http://en.wikipedia.org/wiki/Low-pressure_area

http://en.wikipedia.org/wiki/High-pressure_area

closed container

In the case of a closed container experiencing the force of gravity (acceleration at 1 g would cause the same effect), there will be a pressure differential within the container, such that the net downwards force on the container by the gas inside the container will exactly equal the weight of the gas inside the container (if there is no vertical component of acceleration of the gas within the container).

 

[sophiecentaur]

That's not the way kinetic gas theory views it. Remember, the distance between the air molecules is many times the diameter of the molecules. Several hundreds or thousands of times greater at high elevations. It is not the collisions that start molecules downward, it is gravity. The mean impulse transferred during collisions is about two orders of magnitude greater than the weight-force. As a molecule moves upward against the pull of gravity, its speed diminishes following the well-known formula. Eventually, it stops moving upward and starts moving downward. It doesn't do so because of collisions with other molecules. It does so purely because of gravity.

There are thought experiments in textbooks on statistical mechanics that show that if there were no molecular collisions at all, the distribution of molecules with elevation would be unchanged.

You are more or less reiterating what I said in an earlier post. With low concentrations or 'ideal molecules', the whole motion is a simple trajectory under gravity. Even if there are collisions, the same thing would apply. You would expect a lowering of temperature with altitude, according to the 1/R law of gravitational potential. This, of course, neglects everything else.

I feel there is far to much emphasis on the fact that pressure is altered when air is flowing. Whilst this is true, you have to bear in mind what actually causes it to move in the first place - that is a pressure difference between two places. Also, at some point, this gas that has moved from A to B must be balanced by a masses of air leaving B and arriving at A. It's analogous to Kirchoffs Laws in electrical circuits and the flow rate limits the extent to which pressure can differ between locations. If you could, somehow, isolate the whole of one of these convection cycles, the mean pressure in that region would just have to correspond to the overall weight of the air overhead, after all the energies had been taken into account..

Your basic argument reminds me of the story of the man who was following a white van over a rickety bridge. Every few yards the van driver got out and hit the sides of the van with a stick. When they reached the other side, the car driver asked the van driver what he had been doing. "Well" said the van driver, "The weight limit on the bridge is for 5cwt max loads and I have 6cwt of budgies on board. So I have to make sure that they don't all settle on their perches at once."
Nothing, in the end, can be keeping the air molecules from falling to the ground but an overall, upwards force from the ground - they don't pull themselves up there by their own bootstraps.

 

[klimatos]

1) This would violate Newton's third law. The downwards force of gravity on the water is equal and opposite of the upwards force of the river bed. The pressure at the river bed corresponds to the force per unit area at the river bed, and that force corresponds to the weight of the water, regardless of the speed of the water. Unless there is a vertical component of acceleration of the water, the force on the river bed corresponds to the weight of the water in the river, and so does the pressure.

2) The Bernoulli relationship between speed and pressure only applies when acceleration of a gas or fluid is due to a pressure gradient within that gas or fluid.

3) Getting back on topic, water vapor, temperature, and vertical accelerations of the atmosphere can affect the pressure. Wiki articles:

http://en.wikipedia.org/wiki/Low-pressure_area

http://en.wikipedia.org/wiki/High-pressure_area

4) In the case of a closed container experiencing the force of gravity (acceleration at 1 g would cause the same effect), there will be a pressure differential within the container, such that the net downwards force on the container by the gas inside the container will exactly equal the weight of the gas inside the container (if there is no vertical component of acceleration of the gas within the container).

1) Simply not true. Check any textbook on hydraulics. I seem to remember from a book on hydraulic geomorphology that even moderately moving rivers can use the pressure differential to lift boulders weighing many tons from river beds. I believe the lifting power was proportional to the fourth power of the velocity.

2) Not true, It applies whenever and wherever there is fluid motion. Again, check a hydraulics textbook.

3) Gee. Haven't I been saying all along that net atmospheric motions (winds) affect surface pressures?

4) I have no interest in closed containers. The atmosphere is not a closed system.

 

[klimatos]

I'm argunig that Bernoulli is best applied to relatively simple systems if you want reliable numbers. I don't think it is enough to lead to such sweeping conclusions about what the atmospheric pressure might be at ground level under 100 miles of air. I think there's far too much chaos involved.

I'm not saying I plan to demonstrate this, I'm saying that it's klimatos' initial assertion that it does apply, and the onus is on him to demonstrate that Bernoulli has much to say to about 100 miles of atmo.

Come on, Dave!

What's with this 100 mile nonsense? Virtually all of the winds that matter take place in the lowest 20 km.

Of course the onus is on me. Haven't you seen me scrambling about like a one-armed juggler with the hives?

You know as well as I do that Bernoulli had nothing at all to say about upper atmospheric air. He was primarily interested in liquids. Newton had nothing to say about gravity on Mars, but his principles still apply there.

 

[DaveC426913]

Come on, Dave!

What's with this 100 mile nonsense? Virtually all of the winds that matter take place in the lowest 20 km.

So what? That changes nothing. If you claim a thickness of atmo is accurately modeled by Bernoulli, then what diff can it make if we look at 20 or 100? OK, so 80% of it will be easy to calc...

You know as well as I do that Bernoulli had nothing at all to say about upper atmospheric air. He was primarily interested in liquids. Newton had nothing to say about gravity on Mars, but his principles still apply there.

So, you agree? It is a big stretch to say we're underestimating the weight of the atmo by not factoring in Bernoulli's Principle?

 

[klimatos]

1) I feel there is far to much emphasis on the fact that pressure is altered when air is flowing.

2) Whilst this is true, you have to bear in mind what actually causes it to move in the first place - that is a pressure difference between two places.

3) Also, at some point, this gas that has moved from A to B must be balanced by a masses of air leaving B and arriving at A. It's analogous to Kirchoffs Laws in electrical circuits and the flow rate limits the extent to which pressure can differ between locations.

4) If you could, somehow, isolate the whole of one of these convection cycles, the mean pressure in that region would just have to correspond to the overall weight of the air overhead, after all the energies had been taken into account..

5)Nothing, in the end, can be keeping the air molecules from falling to the ground but an overall, upwards force from the ground - they don't pull themselves up there by their own bootstraps.

1) My positions is that there is not enough appreciation of how moving air changes surface pressures.

2) Pressure differences are just one of many conditions that generate wind flow. How else do you explain the world-wide occurrences of air flowing from areas of low pressure toward areas of high pressure. Differences in density, differences in humidity, vaporization and condensation, volcanic outgassing, and anthropogenic outgassing (chimneys, etc.) all play a role.

3 Not true. You are ignoring atmospheric sources and sinks.

4. This just isn't true. You are assuming the hydrostatic equation is valid. I am denying that it is.

Let's skip the disagreement for a moment and follow your suggestion. Let's take a Hadley cell. It has four flows: up, across, down, across. Even if the two vertical flows balanced out (my experience is that they rarely ever do--because of evaporation, condensation, and entrainment), the two parallel flows would still drop the surface pressure.

5) Actually they do pull themselves up by their own activities. It is the thermal energies of translation that force gas expansion. The force does not come from the ground, since most of them never come into contact with the ground. The force comes almost entirely from the absorption of photons (95%), and very slightly from the conduction of heat energy from the surface (4%). The remaining 1% comes from the hydrologic heat pump.

 

[sophiecentaur]

1) My positions is that there is not enough appreciation of how moving air changes surface pressures.

2) Pressure differences are just one of many conditions that generate wind flow. How else do you explain the world-wide occurrences of air flowing from areas of low pressure toward areas of high pressure. Differences in density, differences in humidity, vaporization and condensation, volcanic outgassing, and anthropogenic outgassing (chimneys, etc.) all play a role.

3 Not true. You are ignoring atmospheric sources and sinks.

4. This just isn't true. You are assuming the hydrostatic equation is valid. I am denying that it is.

Let's skip the disagreement for a moment and follow your suggestion. Let's take a Hadley cell. It has four flows: up, across, down, across. Even if the two vertical flows balanced out (my experience is that they rarely ever do--because of evaporation, condensation, and entrainment), the two parallel flows would still drop the surface pressure.

5) Actually they do pull themselves up by their own activities. It is the thermal energies of translation that force gas expansion. The force does not come from the ground, since most of them never come into contact with the ground. The force comes almost entirely from the absorption of photons (95%), and very slightly from the conduction of heat energy from the surface (4%). The remaining 1% comes from the hydrologic heat pump.

Of course you can expect a change in pressure with moving air. But where does the force / pressure come from to get the air moving in the first place? Wind doesn't just start up on its own. You need a pressure difference between two places. Unless you can show, numerically, that the pressures on both sides of this 'manometer' (times, of course, the area involved) do not add up to more than they would without air flow then you cannot isolate the horizontally moving bits and prove anything about the overall mean pressure. You keep insisting that you are not interested in closed systems but the only system you are discussing is the 'wind' - which begins somewhere and ends somewhere due to a mechanism you just don't address.

It is also strange that you don't subscribe to the notion of closed systems when the basis of all the formula relies on starting with small, elemental, regions and then integrating. From the very start, the analysis discusses small, isolated regions with impermeable sides - yet you are constantly quoting it.
On two counts, you are being a bit too selective for a valid argument, I think.

I don't think your dismissal of my 'bootstraps' argument is valid - you just make an assertion that it's wrong. "pull themselves by their own ''''activities''' wtf?

What mechanism, other than pressure difference or gravity, can make a gas flow? It has a zero modulus under tension - so you can't pull it.

 

[rcgldr]

This would violate Newton's third law. The downwards force of gravity on the water is equal and opposite of the upwards force of the river bed.

Simply not true. I seem to remember from a book on hydraulic geomorphology that even moderately moving rivers can use the pressure differential to lift boulders weighing many tons from river beds. I believe the lifting power was proportional to the fourth power of the velocity.

In that case, as the water flows around a solid object, there is a pressure gradient due to the acceleration of the water as it slows and curves around the boulder. This is different than the case of a stream of water flowing at some near constant velocity and no pressure gradient other than the one created by gravity (rho g h).

The Bernoulli relationship between speed and pressure only applies when acceleration of a gas or fluid is due to a pressure gradient within that gas or fluid.

Not true, It applies whenever and wherever there is fluid motion.

Bernoulli is based on the premise that a pressure gradient co-exists with the acceleration of fluid and no external forces involved (other than gravity component (rho g h)). As an example of an external force, in the case of water flowing through a pipe of constant diameter with constant flow rate and velocity, friction force between pipe and water (the external force to the fluid) and viscosity result in pressure decreasing as the fluid flows through the pipe. If a powered propeller is accelerating water, there is a pressure jump in the imediate vicinity of the propeller, that violates Bernoulli because work is done by the propeller onto the water.

Getting back to my main point, if a section of a gutter holds 100 liters of water, then that water exerts 980 Newtons of downforce onto that section of the gutter (the weight of the water = 100 kg x 9.8 m / s ² = 980 N) regardless of the water's velocity (assuming sea level density of the water).

Note that a flush mounted static port on a civilian aircraft senses the ambient pressure of the air, regardless of the speed of the air (from zero to about mach .3) that flows perpendicularly across the static port. This is because the port is placed at a spot on the fuselage where no significant acceleration of air occurs.

 

[klimatos]

This is my last post on this thread.

I am beginning to repeat myself. I don’t like that in others and I won’t tolerate it in myself. For one last time:

1) I believe that the mean atmospheric pressure underestimates the total mass of the atmosphere. This is because the atmosphere is a dynamic fluid and fluids in motion drop the pressure on their underlying surfaces—indeed, on all adjacent surfaces.

2) I believe that barometers simply measure ambient air pressure. They are incapable of distinguishing between dynamic pressures and static pressure, between impulses that originated within an overlying column and impulses that originated outside of. I consider the hypothesis that barometers measure the weight of an overlying column of air to be patently ridiculous.

Thank you Graeme M for asking a question that you might have had reason to think might be ridiculed. It was a good question and it generated some good thinking.

Thank you all ladies and gentlemen for several days of excellent intellectual stimulation.

I look forward to seeing you on other threads. Go in peace.

 

[rcgldr]

The atmosphere is not a closed system.

Ignoring the small gravitational forces from the moon and the sun, the Earth and it's atmosphere are a closed system. Other than some tiny amount of centripetal reaction to air moving at high speed, the entire weight of the atmosphere (and any objects supported by the atmosphere such as balloons or aircraft) is supported by the surface of the earth. There is no Bernoulli like principle reducing the total force that the atmosphere applies to the Earth's surface. Weather and wind effects will affect local pressures, but the average pressure at any altitude is directly related to the average weight of the atmoshpere above that altitude.

conic section

Conic sections can't be used to fill up a spherical volume. You need extended polygon like structures such as a spherical triangles, rectangles, hexagons, ... to accomplish this.

 

[DaveC426913]

I am beginning to repeat myself.

The reason you're repeating yourself is because you're not backing up your claims when challenged; you're just - well - reiterating them.

Simply "believing" your claims isn't enough.