Friday, Jan. 25, 2019

Dour/Le Pottier Quarter "Avel Gorn" (4:48), Startijenn "Strak ha pak" (4:23), "Skeud" (7:46), "Rond de Loudeac" (4:37); Plantec "Tennder" (7:07)

We'll be using page 25, page 33, page 35, page 36, page 34, and maybe page 26 from the ClassNotes today.

Quick recap
atmospheric pressure at any level in the atmosphere
depends on (is determined by)
the weight of the air overhead

Pressure units (found on page 24a in the ClassNotes packet)



Inches of mercury refers to the reading on a mercury barometer.  This seems like unusual units for pressure.  But mercury (13.6 grams/cm3)  is denser than steel (about 7.9 grams/cm3).  If we could some how construct a solid 1" x 1" bar of mercury it would only need to be 30 inches long to equal the weight or the iron bar or the weight of a tall column of air.


Each of these columns would weigh 14.7 pounds.  The pressure at the base of each would be the same. 

A mercury barometer is really just a balance.  You balance the weight of a very tall column of air with the weight of a much shorter column of (liquid) mercury.  You'll find a more detailed explanation of how mercury barometers work in a separate Supplementary Reading section.


Short detour

You never know where something you learn in ATMO 170 will turn up.  Take pressure units for example.  I once lived and worked in France.  Here's a picture of a car I owned when I was there (the one below is in mint condition, the one I had was in far worse shape).


It's a Peugeot 404.  I was at the service station one day and decided to pump up the tires a little bit.  I wanted to put about 30 psi into the tires but the scale on the compressor only went up to 4.  Not knowing much French it took me 15 minutes, before I realized the air compressor was marked in "bars" not "psi".  Since 14.7 psi is about 1 bar, 30 psi would be about 2 bars (90 psi needed in my bicycle tires would be about 6 bars).

Changes in atmospheric pressure with altitude

If you remember and understand the statement

atmospheric pressure at any level in the atmosphere
depends on (is determined by)
the weight of the air overhead

You can quickly and easily figure out what happens to air pressure as you move upward in the atmosphere.  A pile of bricks is helpful too.  Here's a picture of 5 bricks stacked on top of each other. 



Each brick weighs 5 pounds, there's a total of 25 pounds of weight.  At the bottom of the pile you would measure a weight of 25 pounds.  If you moved up a brick you would measure a weight of 20 pounds, the weight of the four bricks that are still above.  The pressure would be less.  Weight and pressure will decrease as you move up the pile.

Layers of air in the atmosphere is not too much different from a pile of bricks.  Pressure at any level is determined by the weight of the air still overhead.  Pressure decreases with increasing altitude because there is less and less air remaining overhead.  The figure below is an older version of the figure on page 25 in the ClassNotes.





At sea level altitude the pressure is normally about 1000 mb.  That is determined by the weight of all (100%) of the air in the atmosphere.

Some parts of Tucson are 3000 feet above sea level (most of central Tucson is a little lower than that, around 2500 feet).  At 3000 ft. about 10% of the air is below, 90% is still overhead.  It is the weight of the 90% that is still above that determines the atmospheric pressure in Tucson.  If 100% of the atmosphere produces a pressure of 1000 mb, then 90% will produce a pressure of 900 mb. 

Pressure is typically about 700 mb at the summit of Mt. Lemmon (9000 ft. altitude) because 70% of the atmosphere is overhead..

Pressure decreases rapidly with increasing altitude.  We will find that pressure changes more slowly if you move horizontally.  Pressure changes about 1 mb for every 10 meters of elevation change.  Pressure changes much more slowly normally if you move horizontally: about 1 mb in 100 km.  Still the small horizontal changes are what cause the wind to blow and what cause storms to form.



Here's an example of a surface weather map from last Friday.  The yellow lines are pressure contours and are called isobars.  Note that the values are near the 1000 mb average  sea level pressure value that we would expect at sea level altitude. 

The sketch of pressure versus altitude shows a submarine at a depth of about 30 ft. or so.  The pressure there is determined by the weight of the air plus the weight of the water overhead.  Water is much denser and much heavier than air.  At 30 ft., the pressure is already twice what it would be at the surface of the ocean (2000 mb instead of 1000 mb). 

I learned about a relatively new sport called free diving a semester or two ago.  Basically divers see how deep they can go while holding their breath.  They must descend and return to the surface on just a single lungful of air.  It is a very hazardous sport.  Here is a link to an article about a diver that made it to a depth of 236 feet but died upon reaching the surface.     Death was caused by the high pressure deep under water forcing fluid into the diver's lungs.

The downward force of air pressure


I am concerned that you might be thinking that a sea level pressure value of 14.7 psi might not sound like much.  But when you start to multiply 14.7 by all the square inches on your body it turns into a lot of pounds of force. 

The yellow box on the person's chest in the picture is a brick size, 4" x 8" = 32 square inch, area.  If you multiply 14.7 psi by 32 sq. in. you get 470 pounds!  It would take a stack of 90 to 100 bricks to produce that much weight.  Imagine lying on the beach with 90 bricks stacked up on your chest.  That's what the atmosphere is doing.

Why isn't the person in the picture above crushed by the weight of the atmosphere above.  The answer is that the person's body pushes back with the same amount of force.  Air does the same thing. 

Air pressure pushes downward, upward and sideways


Air pressure is a force that pushes downward, upward, and sideways.  If you fill a balloon with air and then push downward on it, you can feel the air in the balloon pushing back (pushing upward).  You'd see the air in the balloon pushing sideways as well. 



We were able to see this by placing a brick on top of a balloon.  The balloon gets squished (pushed out sideways) but not flattened.  It eventually pushes upward with enough force to support the brick.  The squished balloon is what air at the bottom of the atmosphere looks like.  And it is supporting more than just one brick, it is supporting a pile 90 to 100 bricks tall.
Another helpful representation of air in the atmosphere might be a people pyramid.




The people in the figure are like layers of air in the atmosphere all stacked on top of each other. 

If the bottom person in the stack above were standing on a scale, the scale would measure the total weight of all the people in the pile.  That's analogous to sea level pressure being determined by the weight of the all the air above.
The bottom person in the picture above must be strong enough to support the weight of all the people above.  The bottom layer of the atmosphere pushes upward with enough pressure to support the weight of the air above.

Here's another pretty amazing example of air pressure pushing upward.



 
This is my present day car (a 1980 Toyota Celica).  It sits on 4 tires, which are really nothing more than balloons.  The air pressure in the four tires pushes upward with enough force to keep the 1000 or 2000 pound vehicle off the ground.  The air pressure also pushes downward, that's something you'd feel if the car ran over your foot.  The air also pushes sideways with a lot of force; tires need to be strong to keep from exploding or coming off the rim.

6. Upward Air Pressure force demonstration

This is a logical point to do a demonstration.  A demo that tries to prove that air pressure really does push upward as well as downward.  Not only that but that the upward force is fairly strong.  The demonstration is summarized on page 35 in the ClassNotes.





It's pretty obvious that if you fill a balloon with a little water and let go it will drop.  And most everyone in the class knows why.



Gravity exerts a downward force on the balloon.  I just made up a number, 10, to give you some idea of its strength. 
But the picture above isn't quite complete.


The water balloon is surrounded by air that is pushing upward, downward, and sideways on the balloon.  These pressure forces are strong but mostly cancel each other out.  The sideways forces do cancel out exactly.

The up and down forces aren't quite equal because pressure decreases with increasing altitude.  The upward pointing force at the bottom is stronger (15 units) than the downward force at the top (14 units).  They don't cancel and there is a weak upward pressure difference force (1 unit strong).  I'm pretty sure that most people don't know about this pressure difference force.


This picture includes all the forces (gravity and pressure difference).  The downward gravity force is stronger than the upward pressure difference force and the balloon falls.

It seems like we could change things a little bit and somehow keep the upward and downward pressure forces from working against each other.  That's what we do in the demonstration.

In the demonstration a wine glass is filled with water (about the same amount of water that you might put in a small water balloon).


A small plastic lid is used to cover the wine glass (you'll need to look hard to see the lid in the photo above).  The wine glass is then turned upside and the water does not fall out.






All the same forces are shown again in the left most figure.  We'll split that into two parts - a water and lid part and an empty glass part. 

The 14 units of pressure force is pushing on the glass now and not the water.  I was holding onto the glass, I'm the one that balanced out this downward pressure force.

Gravity still pulls downward on the water with the same 10 units of force.  But with 15 units, the upward pressure force is able to overcome the downward pull of gravity.  It can do this because all 15 units are used to overcome gravity and not to cancel out the downward pointing pressure force. 

The Magdeburg hemispheres experiment (sideways pressure force)
Air pressure pushes downward with hundreds of pounds of force on someone lying on the beach.
The pressure of the air in tires pushes upward with enough force to keep a 1 ton automobile off the ground.

What about the sideways air pressure force?

Here's a description of a demonstration that really needs to be done in Arizona Stadium at half time during a football game.  It involves Magdeburg hemispheres and two teams of horses (the following quote and the figure below are from an article in Wikipedia):

" ... Magdeburg hemispheres are a pair of large copper hemispheres with mating rims, used to demonstrate the power of atmospheric pressure. When the rims were sealed with grease and the air was pumped out, the sphere contained a vacuum and could not be pulled apart by teams of horses. The Magdeburg hemispheres were designed by a German scientist and mayor of Magdeburg, Otto von Guericke in 1656 to demonstrate the air pump which he had invented, and the concept of atmospheric pressure."





Gaspar Schott's sketch of Otto von Guericke's Magdeburg hemispheres experiment (from the Wikipedia article referenced above)

 It is the pressure of the air pushing inward against the outside surfaces of the hemispheres that keeps them together.  The hemispheres appear to have had pretty large surface area.  There would be 15 pounds of force pressing against every square inch (at sea level) of the hemisphere which could easily have been several thousand pounds of total force.

Suction cups work the same way
 

The suction cup has been pressed against smooth surface.  The cup is flexible and can be pulled away from the wall leaving a small volume between the wall and the cup where there isn't any air (a vacuum).  There's no air pressure pushing outward, away from the wall, in the space between the wall and the suction cup.  There's just pressure from the air surrounding the suction cup that is pushing and holding it against the wall.  The name suction cup is a little misleading.  There isn't any suction, rather just air outside the suction cup pushing and holding it against the wall.

I suspect that if I were to attach the suction cup I had in class to a white board mounted to a wall and were to ask a couple of strong people to come down and try to pull it off the white board they would end up pulling the white board off the wall.  The Facilities Management people wouldn't appreciate that very much.


Changes in air density with altitude
 (see page 34 in the ClassNotes)
We've spent a lot of time (too much?) looking at air pressure and how it changes with altitude.  Next we'll consider air density.

 How does air density change with increasing altitude?  You know the answer to that question.  You get out of breath more easily at high altitude than at sea level.  Air gets thinner (less dense) at higher altitude.  A lungful of air at high altitude just doesn't contain as many oxygen molecules as it does at lower altitude or at sea level. 

It would be nice to also understand why air density decreases with increasing altitude.















The people pyramid reminds you that there is more weight, more pressure, at the bottom of the atmosphere than there is higher up. 

Layers of air are not solid and rigid like in a stack of bricks.  Layers of air are more like mattresses stacked on top of each other.  Mattresses are compressible, bricks (and people) aren't.  Mattresses are also reasonably heavy, the mattress at the bottom of the pile would be squished by the weight of the three mattresses above.  This is shown at right.  The mattresses higher up aren't compressed as much because there is less weight remaining above.  The same is true with layers of air in the atmosphere.

The statement above is at the top of page 34 in the ClassNotes.


There's a surprising amount of information in this figure, we(you) need to spend a minute or two looking for it

1. You can first notice and remember that pressure decreases with increasing altitude.  1000 mb at the bottom decreases to 700 mb at the top of the picture.  You should be able to explain why this happens.

2.  Each layer of air contains the same amount (mass) of air.  This is a fairly subtle point.  You can tell because the pressure drops by the same amount, 100 mb, as you move upward through each layer.   Pressure depends on weight.  So if all the pressure changes are equal, the weights of each of the layers must be the same.  Each of the layers must contain the same amount (mass) of air (each layer contains 10% of the air in the atmosphere). 

3. The densest air is found at the bottom of the picture.  The bottom layer is compressed the most because it is supporting the weight of all of the rest of the atmosphere.  It is the thinnest layer in the picture and the layer with the smallest volume.  Since each layer has the same amount of air (same mass) and the bottom layer has the smallest volume it must have the highest density.  The top layer has the same amount of air but about twice the volume.  It therefore has a lower density (half the density of the air at sea level).  Density is decreasing with increasing altitude.  That's the main point in this figure.

4.  A final point.    Pressure decreases 100 mb in a fairly short vertical distance in the bottom layer of the picture - a rapid rate of decrease with altitude.  The same 100 mb drop takes place in about twice the vertical distance in the top layer in the picture - a smaller rate of decrease with altitude.  Pressure is decreasing most rapidly with increasing altitude in the densest air in the bottom layer.  We'll make use of this concept again at the end of the semester when we try to figure out why/how hurricanes intensify and get as strong as they do.