Thursday, Jan. 26, 2006

The Practice Quiz Study Guide (online version) is now available.

The first of this semester's Optional homework Assignments was distributed in class.  The assignment is due next Thursday, Feb. 2.

Don't forget, 1S1P Assignment #1 reports are due next Tuesday.
Mass, gravity, and weight are about all you need to know to start to understand atmospheric pressure.
atmospheric pressure at sea level, pressure units

Gravity pulls downward on the air surrounding the earth producing weight (people didn't really realize that air had mass and weight and didn't devise ways of measuring air pressure until the 1600s).

Air pressure is determined by and tells you something about the weight of the air overhead.  This is one way of trying to understand atmospheric pressure.  It is an important concept and will come up a lot in this course.  It is worth spending sometime to understand and remember it.

A one inch by one inch column of air extending from sea level to the top of the atmosphere would, under average conditions, weigh 14.7 pounds (the same as the 4 foot long iron bar that was passed around in class on Tuesday).  Pressure is defined as force divided by area, in this case weight divided by area.  So a typical sea level pressure would be 14.7 pounds per square inch or psi.  These are the same units used when filling an automobile tire with air.  You usually put around 30 psi into car tires.

We will use millibar (mb) units in our course.  Standard atmospheric pressure is about 1000 mb or 30 inches of mercury.  The second value refers to the reading from a mercury barometer.  1000 millibars is equal to 1 bar or 1 atmosphere.

pressure decreases (rapidly) with increasing altitude

As you move upward through the atmosphere there is less and less air left overhead.  Since the pressure at any level in the atmosphere is determined by the weight of the air remaining overhead, pressure decreases with increasing altitude.  Pressure changes much more quickly when you move in a vertical direction than it does when you move horizontally.  This will be important when we cover surface weather maps.  Meterologists attempt to map out small horizontal changes or differences in pressure on weather maps.  These small changes are what cause the wind to blow and produce weather.

Pressure increases rapidly as you descend into the ocean.  The pressure at some level in the ocean is determined by the atmospheric pressure plus the pressure produced by the weight of the water above you.  Water is much heavier than air; pressure already be 2000 mb when you are only about 30 feet deep in the ocean.

We took a short detour at this point and watched some more of the video tape about Auguste Piccard.  In this segment Auguste and his son Jacques descended to 10,000 feet depth in the ocean in a bathyscaph.  At that depth the pressure is 5000 psi. 

 Jacques would later descend to 35,000 feet with another person.  That is as deep as you can go in the ocean.

rate of pressure decrease with increasing altitude depends on air density

As you move upward from the ground pressure decreases by 100 mb in both figures.  Both layers contain the same amount of air (10% of the air in the atmosphere).  That air is found in a smaller volume in the figure at left (the layer is thinner).  This means the air at left is denser than the air at right.  The drop in air pressure in the layer at left occurs in a shorter vertical distance than in the air layer at right.

The rate of pressure decrease with altitude is higher in the dense air at left than in the lower density air at right.

This is a fairly subtle but important concept.  We will use it when we try to understand the intensification of hurricanes later in the semester.

You can use bricks and wooden blocks to to visualize and understand why pressure decreases with increasing altitude and why the rate of decrease depends on density.  You probably don't need to read this section if you already understand those concepts.
Piles of bricks and wood blocks that have the same total weight

A pile of 250 bricks each weighing 4 pounds will have the same total weight as a pile of 500 wooden blocks that weigh 2 pounds each.  The pressure at the bottoms of the two piles would be the same.  A relatively short column of high density material can produce the same surface pressure as a taller column of lower density material.

moving upward through the piles of bricks and blocks

Now imagine moving upward 5 bricks in the pile at left and the same distance, 5 blocks, in the pile at right.  At left the weight will decrease by 20 pounds, in the pile at right by 10 pounds.  To find the rate of decrease divide the decrease in weight by the distance over which it occurred (will use the number 5 and not worry about what the units might be).

So at left the rate of decrease is 20/5 = 4 and at right 10/5 = 2.  Weight (or pressure since it is determined by weight) is decreasing more rapidly in the high density pile of bricks than in the lower density pile of wooden blocks.

another way of showing that the rate of decrease in pressure with altitude depends on density

In this slightly different example you travel upward until there is an 8 pound drop in weight (up 2 bricks in the left pile, up 4 blocks in the right pile).  Again we will divide the amount of decrease by the distance over which it occurred.  For the brick pile this is 8/2  = 4.  For the pile of blocks it is 8/4 = 2.  We end up with the same conclusion again, that weight (pressure) decreases most rapidly when you move upward through high density material.
pressure is a force that pushes downward, upward, and sideways

Pressure is a force that pushes downward, upward, and sideways.  The bottom person in the "people pyramid" must push upward with enough force to support the other people.  A brick at the bottom of a pile of bricks must push upward with enough force to support the bricks above (otherwise the bottom brick will be crushed).  The air pressure in the four tires on your automobile push down on the road (you would feel that if the car ran over your foot) and push upward with enough force to keep the 1000 or 2000 pound vehicle off the road. 

demonstration of the upper air pressure force

I am going to redraw the two figures from p. 35 in the photocopied notes that described the class demonstration of upward air pressure force.  Hopefully this will make for a clearer explanation of the demonstration.
gravity and pressure forces acting on a water balloon
At left, gravity, the red arrow, pulls downward on the water balloon.  The 10 is the strength of the gravitational force (I just made this number up, don't worry about the units either).  Air pressure pushes upward on the bottom of the balloon with strength 15,  slighly weaker forces (14.5) push sideways, and at the top of the balloon air pressure pushes downward with strength 14.  Pressure decreases with increasing altitude, that is why the pressure forces get weaker as you move from the bottom to the top of the balloon. 

Notice the two sideways forces cancel each other out.  The upward pointing pressure force is slightly stronger than the downward pressure force.  They don't quite cancel each other out, you are left (as shown in the figure at right) with an upward pointing pressure difference force of strength 1.  Gravity (10) is stronger than the pressure difference force (1) and the water balloon falls.

Now we'll look at the situation for the water in an upside down wine glass

forces acting on water in an upside down wine glass
The figure at left shows the wine glass (the stem of the glass has been left off the drawing), the plastic cover, and the pressure and gravity forces. 

You can split this into two parts:  (1) gravity pulling downward and the pressure force pushing upward on the cover and water in the glass and (2) the pressure force pushing downward and sideways on the glass (which the instructor was holding in his hand).   Now notice that the 15 unit pressure force pushing up on the water is greater than the 10 units of gravity pulling downward.  The upward pressure force now can keep the water from falling out of the glass.

Here's another situation where pressure and gravity forces are battling each other for dominance, a balloon.

forces on a balloon
This is like a water balloon except that the balloon is now filled with a gas like air or helium.  This gas is much lighter than water.  The gravity force will be much weaker and the upward pressure difference force (the difference between the upward point force at the bottom of the balloon and the downward pointing force at the top of the balloon) will sometimes end up stronger than gravity.

air density decreases with increasing altitude

Three layers of air in the atmosphere are shown above (each layer contains the same amount of air, 10% of the air in the atmosphere).  The layer at the ground and at the bottom of the atmosphere is "squished" by the weight of the air above.  Squeezing all of this air into a thin layer or small volume increases the air's density.

 The next layer up is also squished but not as much as the bottom layer.  The density of the air in the second layer is lower than in the bottom layer.  The air in the 3rd layer has even lower density.  It is fairly easy to understand that air density decreases with increasing altitude. 

This figure also reminds you that air pressure decreases with increasing altitude.

If you look carefully you see again that the most rapid rate of pressure decrease with increasing altitude occurs in the thin layer of high density air next to the ground.