There's a lot of information in
this figure. It is worth
spending a minute or two looking at it and thinking about 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.
Each layer of air contain the same amount (mass) of air. This is a fairly subtle point. You can tell because there is an equal 100 mb pressure drop 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. Since 100 mb is 10% of 1000 mb, each layer contains 10% of the air in the atmosphere.
2. The densest air is found in the bottom layer. The bottom layer is compressed the most and is the thinnest layer. 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 thickness and twice the volume. It therefore has a lower density.
3. The rate of pressure change with altitude depends on air density. The most rapid rate of pressure decrease with increasing altitude is in the densest air at the bottom of the picture. I've added an extra page from the photocopied notes at the end of today's notes that explains this further. This idea will be important when we study the intensification of hurricanes at the end of the semester.
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.
Each layer of air contain the same amount (mass) of air. This is a fairly subtle point. You can tell because there is an equal 100 mb pressure drop 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. Since 100 mb is 10% of 1000 mb, each layer contains 10% of the air in the atmosphere.
2. The densest air is found in the bottom layer. The bottom layer is compressed the most and is the thinnest layer. 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 thickness and twice the volume. It therefore has a lower density.
3. The rate of pressure change with altitude depends on air density. The most rapid rate of pressure decrease with increasing altitude is in the densest air at the bottom of the picture. I've added an extra page from the photocopied notes at the end of today's notes that explains this further. This idea will be important when we study the intensification of hurricanes at the end of the semester.
The next bunch of material tries to explain how a mercury barometer works. A mercury barometer is used to measure atmospheric pressure and is really just a balance that can be used to weigh the atmosphere. You'll find a somewhat messier version of of what follows on p. 29 in the photocopied Class Notes.
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The instrument in the left figure
above ( a u-shaped
glass
tube filled with a
liquid of some kind) is actually called a manometer and can be used to
measure pressure
difference. The
two ends of the tube are open so that air can get inside and air
pressure can press on the liquid. Given that the liquid levels on
the two sides of the manometer
are equal, what could you about PL and PR?
The liquid can slosh back and forth just like the pans on a balance can move up and down. A manometer really behaves just like a pan balance (pictured at right) or a teeter totter (seesaw). Because the two pans are in balance, the two columns of air have the same weight. PL and PR are equal (but note that you don't really know what either pressure is just that they are equal).
The liquid can slosh back and forth just like the pans on a balance can move up and down. A manometer really behaves just like a pan balance (pictured at right) or a teeter totter (seesaw). Because the two pans are in balance, the two columns of air have the same weight. PL and PR are equal (but note that you don't really know what either pressure is just that they are equal).
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Now
the
situation is a little
different,
the
liquid levels
are no
longer equal. You probably realize that the air pressure on the
left, PL, is a little higher than the air pressure on the
right,
PR. PL is now being balanced by PR
+ P acting together. P
is the pressure produced by the weight of the extra fluid on the right
hand side of
the manometer (the fluid that lies above the dotted line). The
height
of
the
column
of
extra
liquid
provides
a
measure
of
the difference between PL and PR.
Next we will just go and close off the right hand side of the manometer.
Next we will just go and close off the right hand side of the manometer.
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Air pressure can't get into the
right tube any
more. Now at the level of the dotted line the balance is between
Pair and P (pressure by the extra liquid on the
right). If
Pair
changes, the height of the right column, h, will
change. You now have a barometer, an instrument that can measure
and monitor the atmospheric pressure. (some of the writing
in the upper right portion of the left figure was cut off, it should
read "no air
pressure")
Barometers like this are usually filled with mercury. 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 (it is the mercury vapor that would make a mercury spill in the classroom dangerous).
Barometers like this are usually filled with mercury. 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 (it is the mercury vapor that would make a mercury spill in the classroom dangerous).
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 is sealed to keep poisonous mercury
vapor from filling a room.
In an earlier class we saw that a
52 inch long 1"x1" steel bar
weighs the same as a 1" x 1" column of air stretching from sea level to
the top of the atmosphere. Now we can add a 30 inch tall 1" x 1"
column of mercury (frozen so that it would be rigid) to the list.
All three columns above would weigh 14.7 pounds. They would all
be pushing against the ground with a pressure of 14.7 psi.
The figure above (p. 30 in the
photocopied Class Notes)
first
shows average sea level pressure values. 1000 mb or 30 inches of
mercury are close enough in this class.
Sea level pressures usually fall between 950 mb and 1050 mb.
Record high sea level pressure values occur during cold weather. The TV weather forecast will often associated 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.
Record low pressure values have all been set by intense hurricanes (the record setting low pressure is the reason these storms were so intense). Hurricane Wilma in 2005 set a new record low sea level pressure reading for the Atlantic. 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. 3 of the 10 strongest N. Atlantic hurricanes occurred in 2005.
Sea level pressures usually fall between 950 mb and 1050 mb.
Record high sea level pressure values occur during cold weather. The TV weather forecast will often associated 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.
Record low pressure values have all been set by intense hurricanes (the record setting low pressure is the reason these storms were so intense). Hurricane Wilma in 2005 set a new record low sea level pressure reading for the Atlantic. 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. 3 of the 10 strongest N. Atlantic hurricanes occurred in 2005.
| 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 (Texas) 925 mb |
Pressure
at
any
level in the
atmosphere depends on (is determined by) the weight of the air
overhead. We used a pile of bricks (each brick represents a layer
of air)
to help visualize and understand why pressure decreases with
increasing altitude. A pile of bricks and columns of air or
mercury on a pan balance can lead to the believe
that
air pressure exerts force in just a downward direction.
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.
The air pressure in the four tires on your automobile pushes pushes upward with enough force to keep the 1000 or 2000 pound vehicle off the road.
A better representation of air in the atmosphere might be a people pyramid.
The air pressure in the four tires on your automobile pushes pushes upward with enough force to keep the 1000 or 2000 pound vehicle off the road.
A better representation of air in the atmosphere might be a people pyramid.
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. That is equivalent to the bottom layer of the atmosphere having enough pressure, pressure that points up, down, and sideways, to support the weight of the air above.
The bottom person in the picture above must be strong enough to support the weight of all the people above. That is equivalent to the bottom layer of the atmosphere having enough pressure, pressure that points up, down, and sideways, to support the weight of the air above.
This was 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 the upward force is fairly
strong. The demonstration is summarized on p. 35 a in the
ClassNotes.
Here's a little bit more detailed
and more complete explanation of
what is going on. First the case of a water balloon.
The figure at left shows air
pressure (red
arrows)
pushing on all
the
sides of the balloon. Because pressure decreases with increasing
altitude, the pressure from the air at the top of the balloon pushing
downward (strength=14) is a
little weaker than the pressure from the air at the bottom of the
balloon that is pushing upward (strength=15). The two sideways
forces cancel each other
out. The
total effect of the pressure is a weak upward force (1 unit of upward
force shown at the top of the right
figure, you might have heard this called a bouyant force).
Gravity exerts a downward force on the water
balloon. In the figure at right you can see that the gravity
force (strength=10) is stronger than the upward pressure difference
force (strength=1). The
balloon falls as a result. This is what you know would happen if
you let go of a water balloon, it would fall.
In the demonstration a wine glass is filled with water. A small plastic lid is used to cover the wine glass. You can then turn the glass upside down without the water falling out.
In the demonstration a wine glass is filled with water. A small plastic lid is used to cover the wine glass. You can then turn the glass upside down without the water falling out.
All the same forces are shown again
in the left most
figure.
In
the right two figures we separate this into two parts. First
the water inside the glass isn't feeling the downward and sideways
pressure forces (because they're pushing on the glass, this is shown at
the right side of the figure above). Gravity
still pulls downward on the water but the upward pressure force is able
to overcome the downward pull of gravity. The upward pointing
pressure force is used to overcome gravity not to cancel out the
downward pointing pressure force.
The demonstration was repeated using a 4 Liter flash (more than a gallon of water, more than 8 pounds of water). The upward pressure force was still able to keep the water in the flask (much of the weight of the water is pushing against the sides of the flask which the instructor was supporting with his arms).
The demonstration was repeated using a 4 Liter flash (more than a gallon of water, more than 8 pounds of water). The upward pressure force was still able to keep the water in the flask (much of the weight of the water is pushing against the sides of the flask which the instructor was supporting with his arms).
In class Optional Assignment
Questions
This is the figure alluded to
earlier in the notes that explains why the rate of pressure change as
you move or down in
the atmosphere depends on air density. The figure
wasn't shown in class.
There is a lot going on here.
Point 1 - Notice there is a 100 mb drop in pressure in both air layers. In order for this to be true both layers must weigh the same. In order for both layers to have the same weight they must contain the same amount of air, they have the same mass.
Point 2a - The pressure decreases 100 mb in a relatively short distance. This produces a relatively rapid rate of pressure decrease with increasing altitude.
Point 2b - The pressure also decreases 100 mb but in a longer distance. Pressure is decreasing at a slower rate in this layer.
Point 3 - The air in the left layer is denser than the air in the right layer. The same amount (mass) of air is squeezed into a thinner layer, a smaller volume, in the left layer. This results in relatively high density air.
The fact that the rate of pressure decrease with increasing altitude depends on air density is a fairly subtle but important concept. This concept will come up 2 or 3 more times later in the semester. For example, we will use this concept to explain why hurricanes can intensify and get as strong as they do.
Try to reproduce this figure in your mind (together with the written discussion and explanation) the next time you are lying in bed at night trying to fall asleep. It'll put you right to sleep without any of the side effects that medications might have.
Point 1 - Notice there is a 100 mb drop in pressure in both air layers. In order for this to be true both layers must weigh the same. In order for both layers to have the same weight they must contain the same amount of air, they have the same mass.
Point 2a - The pressure decreases 100 mb in a relatively short distance. This produces a relatively rapid rate of pressure decrease with increasing altitude.
Point 2b - The pressure also decreases 100 mb but in a longer distance. Pressure is decreasing at a slower rate in this layer.
Point 3 - The air in the left layer is denser than the air in the right layer. The same amount (mass) of air is squeezed into a thinner layer, a smaller volume, in the left layer. This results in relatively high density air.
The fact that the rate of pressure decrease with increasing altitude depends on air density is a fairly subtle but important concept. This concept will come up 2 or 3 more times later in the semester. For example, we will use this concept to explain why hurricanes can intensify and get as strong as they do.
Try to reproduce this figure in your mind (together with the written discussion and explanation) the next time you are lying in bed at night trying to fall asleep. It'll put you right to sleep without any of the side effects that medications might have.