Mon., Jan. 29 notes

Gravity exerts a downward force on the balloon. I just made up a number, 10, to give you some idea of its strength.
But the picture above isn't quite complete.

The water balloon is surrounded by air that is pushing upward, downward, and sideways on the balloon. These pressure forces are strong but mostly cancel each other out. The sideways forces do cancel out exactly.

The up and down forces aren't quite equal because pressure decreases with increasing altitude. The upward pointing force at the bottom is stronger (15 units) than the downward force at the top (14 units). They don't cancel and there is a weak upward pressure difference force (1 unit strong). I'm pretty sure that most people don't know about this pressure difference force.

This picture includes all the forces (gravity and pressure difference). The downward gravity force is stronger than the upward pressure difference force and the balloon falls.

It seems like we could change things a little bit and somehow keep the upward and downward pressure forces from working against each other. That's what we do in the demonstration.

In the demonstration a wine glass is filled with water (about the same amount of water that you might put in a small water balloon).

A small plastic lid is used to cover the wine glass (you'll need to look hard to see the lid in the photo above). 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. We'll split that into two parts - a water and lid part and an empty glass part.

The 14 units of pressure force is pushing on the glass now and not the water. I was holding onto the glass, I'm the one that balanced out this downward pressure force.

Gravity still pulls downward on the water with the same 10 units of force. But with 15 units, 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 Magdeburg hemispheres experiment (sideways pressure force)
Air pressure pushes downward with hundreds of pounds of force on someone lying on the beach.

The pressure of the air in tires pushes upward with enough force to keep a 1 ton automobile off the ground.

What about the sideways air pressure force?

Here's a description of a demonstration that really needs to be done in Arizona Stadium at half time during a football game. It involves Magdeburg hemispheres and two teams of horses (the following quote and the figure below are from an article in Wikipedia):

" ... Magdeburg hemispheres are a pair of large copper hemispheres with mating rims, used to demonstrate the power of atmospheric pressure. When the rims were sealed with grease and the air was pumped out, the sphere contained a vacuum and could not be pulled apart by teams of horses. The Magdeburg hemispheres were designed by a German scientist and mayor of Magdeburg, Otto von Guericke in 1656 to demonstrate the air pump which he had invented, and the concept of atmospheric pressure."

Gaspar Schott's sketch of Otto von Guericke's Magdeburg hemispheres experiment (from the Wikipedia article referenced above)

It is the pressure of the air pushing inward against the outside surfaces of the hemispheres that keeps them together. The hemispheres appear to have had pretty large surface area. There would be 15 pounds of force pressing against every square inch (at sea level) of the hemisphere which could easily have been several thousand pounds of total force.

Suction cups work the same way

The suction cup has been pressed against smooth surface. The cup is flexible and can be pulled away from the wall leaving a small volume between the wall and the cup where there isn't any air (a vacuum). There's no air pressure pushing outward, away from the wall, in the space between the wall and the suction cup. There's just pressure from the air surrounding the suction cup that is pushing and holding it against the wall. The name suction cup is a little misleading. There isn't any suction, rather just air outside the suction cup pushing and holding it against the wall.

I suspect that if I were to attach the suction cup I had in class to a white board mounted to a wall and were to ask a couple of strong people to come down and try to pull it off the white board they would end up pulling the white board off the wall. The Facilities Management people wouldn't appreciate that very much.

Changes in air density with altitude
(see p. 34 in the ClassNotes)

We've spent a lot of time (too much?) looking at air pressure and how it changes with altitude. Next we'll consider air density.

How does air density change with increasing altitude? You know the answer to that question. You get out of breath more easily at high altitude than at sea level. Air gets thinner (less dense) at higher altitude. A lungful of air at high altitude just doesn't contain as many oxygen molecules as it does at lower altitude or at sea level.

It would be nice to also understand why air density decreases with increasing altitude.

The people pyramid reminds you that there is more weight, more pressure, at the bottom of the atmosphere than there is higher up.

Layers of air are not solid and rigid like in a stack of bricks. Layers of air are more like mattresses stacked on top of each other. Mattresses are compressible, bricks (and people) aren't. Mattresses are also reasonably heavy, the mattress at the bottom of the pile would be squished by the weight of the three mattresses above. This is shown at right. The mattresses higher up aren't compressed as much because there 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 surprising amount of information in this figure, we(you) need to spend a minute or two looking for 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 contains the same amount (mass) of air. This is a fairly subtle point. You can tell because the pressure drops by the same amount, 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. That's the main point in this figure.

4. A final point. Pressure decreases 100 mb in a fairly short vertical distance in the bottom layer of the picture - a rapid rate of decrease with altitude. The same 100 mb drop takes place in about twice the vertical distance in the top layer in the picture - a smaller rate of decrease with altitude. Pressure is decreasing most rapidly with increasing altitude in the densest air in the bottom layer. We'll make use of this concept again at the end of the semester when we try to figure out why/how hurricanes intensify and get as strong as they do.