Fri., Jan. 27 notes

Friday, Jan. 27, 2012
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Music from, Calexico, one of my favorite groups. They're a local group and usually appear somewhere in Tucson at least once a year (they were on the UA Mall for the January 8 memorial event). They often appear together with another local group Mariachi Luz de Luna (I'll play some of their music also at some point during the semester). Today you heard Alone Again Or and Ballad of Cable Hogue.

On my way back to my office after class on Wednesday I got to wondering what the pressure was underneath the pile of bricks that I had in class.

It's less than 1 psi. You'd need 94 bricks, 470 pounds of bricks to produce 14.7 psi.

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 1000s of pounds of weight (force).

A real potpourri of topics today.

The first topic is a short explanation of 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 messier version of what follows on p. 29 in the photocopied Class Notes.

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 P_L and P_R?

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 above at right) or a teeter totter (seesaw). Because the two pans are in balance, the two columns of air have the same weight. P_L and P_R are equal (but note that you don't really know what either pressure is, just that they are equal).

Now the situation is a little different, the liquid levels are no longer equal. You probably realize that the air pressure on the left, P_L, is a little higher than the air pressure on the right, P_R. P_L is now being balanced by P_R + 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 P_L and P_R.

Next we will just go and close off the right hand side of the manometer.

Air pressure can't get into the right tube any more. Now at the level of the dotted line the balance is between P_air and P (pressure by the extra liquid on the right). If P_air 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.

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 (there's some gas, it doesn't produce much pressure, but it would poison 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 is sealed to keep poisonous mercury vapor from filling a room.

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.

Most of the record low pressure values have all been set by intense hurricanes (the extreme low pressure is the reason these storms are so intense). 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. 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 (Tx) 925 mb

Note that a new all time record low sea level pressure was 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 potentially dangerous thing) 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.

What about density. How does air density change with increasing altitude? You get out of breathe more easily at high altitude than at sea level. Air gets thinner (less dense) at higher altitude.

Because air is compressible, a stack of mattresses might be a more realistic representation of layers of air than a pile of bricks.

Four mattresses are stacked on top of each other. Mattresses are reasonably heavy, the mattress at the bottom of the pile is compressed by the weight of the three mattresses above. This is shown at right. The mattresses higher up aren't squished as much because their 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 lot of information in this figure and 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. You should be able to explain why this happens.

2. Each layer of air contain the same amount (mass) of air. This is a fairly subtle point. You can tell because the pressure drops by 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.

4. Finally pressure is decreasing most rapidly with increasing altitude in the densest air in the bottom layer. This is something we covered on Wednesday.

Pressure at any level in the atmosphere depends on (is determined by) the weight of the air overhead. You might get the idea that pressure just pushes downward.

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.

Another helpful 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 pushing upward with enough pressure to support the weight of the air above.

The air pressure in the four tires on your automobile pushes pushes upward with enough force to keep this 1000 or 2000 pound vehicle (my own personal vehicle) off the ground. The air pressure also pushes downward, you'd feel it if the car ran over your foot.

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 that the upward force is fairly strong. The demonstration is summarized on p. 35 a in the ClassNotes.

Don't worry too much about the details above because there's a more detailed explanation is below. At this point you should wonder why is it that the water in a balloon will fall while the water in the wine glass does not.

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 pressure difference force (1 unit of upward force shown at the top of the right figure).

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. 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. 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, they're included on the right figure ). Gravity still pulls downward on the water but 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 net upward force is strong enough to keep the water in the glass.

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).

What difference does it make if pressure decreases with increasing altitude or if pressure pushes upward, downward, and sideways?
Here's one answer to that question.

Hot air balloons can go up and come back down. I'm pretty sure you know what would cause the balloon to sink. I suspect you don't know what causes it to float upward.

Gravity pulls downward on the balloon. The strength of this force will depend on whether the air is hot low density air (light weight) or cold higher density air (heavier air).

Pressure from the air surrounding the balloon is pushing against the top, bottom, and sides of the balloon (the blue arrows shown above at right). Pressure decreases with increasing altitude. The pressure at the bottom pushing up is a little higher than at the top pushing down (the pressures at the sides cancel each other out). Decreasing pressure with increasing altitude creates an upward pointing pressure difference force that opposes gravity.