Thu., Sep. 9 notes

Thursday Sept. 9, 2010
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3 songs ("White Winter Hymnal", "Tiger Mountain Peasant Song", and "Mykonos") from the Fleet Foxes before class today.

The 1st Optional (Extra Credit) Assignment of the semester is now available.

The 1st 1S1P Report Assignment is also online.

If today's quiz were a real quiz you'd have the entire period to work on it. But since this was just a Practice Quiz we did cover a little bit of new material today.

This first section 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.

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 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. (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).

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.

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.

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.

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.

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).