Friday Sep. 7, 2012

Marching into the weekend with "Rhapsody in Blue" by Pearl Kaufman.  I couldn't find Kaufman's version on YouTube but here's a good substitute.   You should listen to "Bumble Boogie" (Pearl Kaufman's version).

The first of the Optional Assignments is now online (copies of the assignment were handed out in class)  You don't have to do these assignments, but if you do you can earn extra credit.  The assignment is due next Friday (Sep. 14).  To earn full credit you need to make an sincere attempt at answering all the questions and you should have the assignment done before coming to class.

The Practice Quiz has been graded and was returned in class today.  The average was 66% which, as you can seen from the table below, is pretty typical.

 MWF class T Th class F12 66% ?? F11 65% 65% F10 60% 67% F09 66% 68% F08 64% 65%

If you weren't in class you can download a copy of the Practice Quiz.  I would suggest you do that so that you can become familiar with the quiz format.  Here are answers to the questions on the Practice Quiz.

Three mains topics were covered in class today.

1st some appreciation for how strong the force exerted by air pressure is.  Then we'll try to understand the basic principle of a mercury barometer used to measure atmospheric pressure.  Finally I'll try to convince you that air pressure just doesn't push downward but also upward and sideways.  We didn't have time for the 4th item on the list above.

Recent classes have featured a steel bar and 25 pounds of bricks.

All of the weight of the steel bar rested on 1 square inch of area.  Even though the pile of bricks was heavier, the weight was spread out over a greater area.  As a result the pressure at the bottom of bricks was less than 1 psi.  You'd need 94 bricks, 470 pounds of bricks, to produce 14.7 psi.

Sea level pressure, 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).  As the picture above shows, when you're lying on the beach there are 470 pounds of air pressing down on a 4" x 8" area of your chest.

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.  This is a topic that we will come back to at the end of the class today.

The next  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 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 above 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).

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.

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.

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 very hazardous) 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.

And now the last topic of the day.

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.

We were able to see this by placing a brick on top of a balloon.  The balloon gets squished but not flattened.  It eventually pushes back with enough force to support the brick.

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).

I've added one small piece of additional material that we didn't have time to cover in class.
What difference does it make if pressure decreases with increasing altitude or if pressure pushes upward, downward, and sideways?

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.  It is this upward pressure difference force that can cause a balloon to float upward.