Thursday Sep. 7, 2017

Monsieur Perine (from Colombia): "Nuestra Cancion" (first song 3 set NPR Tiny Desk Concert) (6:30), "La Muerte" (3:30), "Llore" (6:32)

The first group of 1S1P reports were collected today (Assignment #1a).  These will take sometime to grade.  If things go really well you might get reports on the Origin and Evolution of the Earth's Atmosphere topic back on Tues., Sep. 19 together with your graded Practice Quiz.

A new In-class Optional Assignment was handed out in class today.  If you weren't in class and would like to download the assignment and turn it in at the start of class next Tuesday you can earn at least partial credit on the assignment.

The Practice Quiz Study Guide is now available.  I try to have these available before any scheduled quiz.  Reviews are scheduled for Tuesday and Wednesday afternoon next week.  See the Study Guide for times and locations.

There are three hurricanes (Irma, Jose, and Katia) at the present time in the Atlantic/Gulf of Mexico/Caribbean.  This is fairly unusual.  See the National Hurricane Center and TropicalTidbits.com for more information and the latest updates.  Here's a pretty good set of photos of damage from communities already affected by Hurricane Irma's passage.


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


Under normal conditions, at sea level, a 1" x 1" column of air stretching from sea level to the top of the atmosphere would weigh 14.7 pounds.  To determine the pressure you would need to divide the 14.7 pounds by the 1 sq. in. area at the bottom of the column. 

Pounds per square inch, psi, are perfectly good pressure units, but they aren't the ones that meteorologists normally use.
Principle of the mercury barometer
(pps 27 & 28 in the ClassNotes for a little longer version)


Easily the most impressive seesaw (teeter totter) that I've ever seen (source of this image).  If you understand how this works you'll be able to figure out how mercury barometers function.

 
A barometer is essentially a balance.
The weight of the atmosphere is balanced by a mercury column. 


















You can't use an ordinary pan balance to weight the atmosphere (because air is pushing down on both sides).  A U-shaped tube filled with some kind of liquid that can slosh back and forth would work.  Such an instrument is called a manometer and is often filled with mercury.





To turn the manometer into a true barometer, we'll extend the tube on the right and close the top so that air isn't pushing down on the mercury.  We'll also use somewhat larger cylindrical columns of air and mercury that completely fill the insides of the tube.

The weight of a very tall cylindrical column of air is balanced by a much shorter cylindrical column of mercury.  The height of the mercury column will change as air pressure varies.

Mercury is a liquid.  You need a liquid that can slosh back and forth in response to changes in air pressure.  Mercury is also very dense which means the barometer won't need to be as tall as if you used something like water.  A water barometer would need to be over 30 feet tall.  With mercury you will need only a 30 inch tall column to balance the weight of the atmosphere at sea level under normal conditions (remember the 30 inches of mercury pressure units mentioned earlier).  Mercury also has a low rate of evaporation so you don't have much mercury gas at the top of the right tube (there's some gas, it doesn't produce much pressure, but it would be hazardous you if you were to start to breath it).


Here is a more conventional barometer design.  The bowl of mercury is usually covered in such a way that it can sense changes in pressure but sealed to keep poisonous mercury vapor from filling a room.

Average and extreme sea level pressure values



Average sea level atmospheric pressure is about 1000 mb.  The figure above (p. 30 in the photocopied Class Notes) gives 1013.25 mb but 1000 mb is close enough in this class.  The actual pressure can be higher or lower than this average value and usually falls between 950 mb and 1050 mb. 

The figure also includes record high and low pressure values.  Record high sea level pressure values occur during cold weather.  The TV weather forecast will often associate hot weather with high pressure.  They are generally referring to upper level high pressure (high pressure at some level above the ground) rather than surface pressure.  You'll sometimes here this upper level high pressure referred to as a ridge, we'll learn more about this later in the semester.

There is some question about the accuracy of the 1085.7 mb value above.  The problem is that the pressure was measured at over 5000 feet altitude and a calculation was needed to figure out what the pressure would have been if the location were at sea level.  That calculation can introduce uncertainty.  But you don't really need to be concerned with all that, I just wanted to give you an idea of how high sea level pressure can get.

Most of the record low pressure values have all been set by intense hurricanes.  

Hurricane Wilma in 2005 set a new record low sea level pressure reading for the Atlantic, 882 mb.  Hurricane Katrina had a pressure of 902 mb.  The following table lists some of the information on hurricane strength from p. 146a in the photocopied ClassNotes.  2005 was a very unusual year, 3 of the 10 strongest N. Atlantic hurricanes ever occurred in 2005.

You may remember Hurricane Patricia off the west coast of Mexico in fall 2015.  Patricia set a new surface low pressure record for the Western Hemisphere - 879 mb.  Sustained winds of 200 MPH were observed.
Most Intense North Atlantic Hurricanes
 Most Intense Hurricanes
to hit the US Mainland
Wilma (2005) 882 mb
Gilbert (1988) 888 mb
1935 Labor Day 892 mb
Rita (2005) 895 mb
Allen (1980) 899
Katrina (2005) 902
 1935 Labor Day 892 mb
Camille (1969) 909 mb
Katrina (2005) 920 mb
Andrew (1992) 922 mb
1886 Indianola (Tx) 925 mb


What makes hurricanes so intense is the pressure gradient, i.e. how quickly pressure changes with distance (horizontal distance).  Pressure can drop from near average values (1000 mb) at the edges of the storm to the low values shown above at the center of the storm.  This large pressure gradient is what causes the strong winds found in a hurricane.

The 850 mb pressure value measured in 2003 inside a strong tornado in Manchester, South Dakota (F4 refers to the Fujita scale rating, F5 is the highest level on the scale).  This is very difficult (and very dangerous) thing to try to do.  Not only must the instruments be built to survive a tornado but they must also be placed on the ground ahead of an approaching tornado and the tornado must then pass over the instruments (also the person placing the instrument needs to get out of the way of the approaching tornado).

You can experience much lower pressure values than shown above (roughly 700 mb) by just driving up to Mt. Lemmon.  Very strong vertical changes in pressure are usually almost balanced exactly by gravity.   


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 wheel.

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 p. 35a 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 (see below - I broken the figure on p. 35b into pieces for clarity).



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 p. 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 p. 34 in the photocopied ClassNotes.  I've redrawn the figure found at the bottom of p. 34 below.


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 (see the questions on the back of the in class assignment).    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.