Lifting Air

Factual Questions
1

I was re-reading the Belgariad and Polgara just collapsed after causing a storm to come in because of the effort of moving all the air and it started my mind thinking in a weird direction.

Air is pressing down on us all the time, so when I raise my cupped hand, I am “lifting air”. How much air is actually lifted, and how much just moves out of the way, because, well air is so fluid?

Am I lifting any air at all?
Am I only lifting the air cupped in my hand?
Am I lifting a tiny column of air and is there a way of measuring it?

I did try google, but I must not be getting the right terms in because I’m either getting lists of items lighter than air, or advertisements for lifting equipment.

2

Your hand is acting as a fan blade.
You aren’t lifting air, in the same way you might lift a block of wood. What you are doing is imparting some momentum on a small volume of air. You can detect this by making a candle flame move. The momentum you impart will dissipate into negligibility after a few feet.

3

Air like any gas has no structure to it. Air molecules are bouncing off your hand all the time. When you lift your hand, the top side of it will happen to run into a few* more molecules than the bottom side of it. Because these are bounced away, they will happen to run into a few more above them, but you’re not really lifting anything.

Note also. To the extent you compress the air above your hand a tiny bit, the air below your hand will be expanded a tiny bit. This will cause more air molecules to wander into this space which will tend to leave fewer molecules above your hand to deal with.

  • a tremendously big few, but each is so small
4

You are lifting some air, but not very much. The difficulty is that most of the air above your hand isn’t moving up; it’s moving out of the way to the side, down around your hand, and filling in the space below your hand. How much air you’re moving will depend both on how big your hand is and on how fast it’s moving, as both will affect how easy it is for the air to get out of the way. Roughly speaking, I’d expect the height of the air column you’re actually lifting to be about the diameter of your hand times the ratio of your speed to the speed of sound. To an order of magnitude, that works out to about a millimeter thickness.

5

It’s easy to demonstrate what Chronos has posted with a bucket of water and some food coloring … the swirl patterns in the water will be roughly the same as with air …

6

Or in a steam room. Watch the steam as you lift your cupped hand, and you’ll see almost all of it move out of the way.

7

Yes, you’re lifting air, but it’s also immediately spilling off of your hand and filling in the space underneath it; the net effect is that you don’t really get a sense of the weight of the air above your hand.

You can get a better sense of that weight if you can prevent air from quickly filling in the space underneath your hand as you lift it. This is pretty much impossible, since your hand is so lumpy.

Instead, get a standard sheet of plywood, 4 feet by 8 feet. Set it on a couple of sawhorses (i.e. get it at least a couple of feet off of the ground). With you and a partner standing on opposite ends of the sheet, suddenly raise the plywood. The biggest resistance you’ll feel is simply from the mass/inertia of the plywood.

Now repeat the same experiment - except start with the plywood sheet flat on the floor. Make sure it’s a flat (unwarped) sheet and a smooth floor, so that there’s as little space as possible between plywood and floor. When you and your partner suddenly try to raise the plywood this time, you’ll feel a lot more resistance than you did before, because the air has a much harder time getting in below the plywood (at least until it’s a few inches off of the floor). Now you’re starting to get a sense of how heavy the atmosphere is above that sheet of plywood.

If you really want to eliminate the air rushing in behind that object as you move it, you’ll need to seal the edges. Instead of a sheet of plywood, you could use a syringe: plug the hole on the end of the syringe to prevent air from getting in, and pull the plunger back. The resistance you feel is because the atmosphere is trying to push that plunger back in, and air can’t get to the underside of the piston to push up on it. If you started with the plunger all the way at the bottom so that there’s no air under it, then the resistance you feel will be proportional to the area of the plunger and local atmospheric pressure. If your plunger area is 1 square inch and you’re at sea level, then it’ll be about 14.7 pounds of force.

If your plunger is really tall (like 20 or 30 miles tall), then as you raise the plunger upward, the amount of air above it gets smaller and smaller, so the pressure trying to cram it back into the cylinder gets less and less. If you made your syringe a couple hundred miles tall, the top end of it would so high that there would be no air above it to push down on it. When you got the plunger up to this height, there won’t be any force pushing the plunger back in (except for its own weight). In fact, you could lift the plunger entirely out of the cylinder at this point, and the cylinder would remain completely devoid of air.

8

Thanks y’all, and I really love the plunger comparison Machine Elf. That really helps put into perspective why Polgara passed out.

9

Here’s a smaller scale experiment to the plywood sheet. Break a wooden ruler in half with a sheet (or two) of newspaper:

10

Note that even if we disregard lifting against gravity, simply getting a stagnant, storm-sized mass of air moving from a standstill requires a colossal amount of energy. Consider a smallish storm cloud occupying a cube five kilometers on a side and moving across the countryside at a modest 20 km/h (5.56 m/s):

mass = (1.2 kg/m[sup]3[/sup]) x (5000 m)[sup]3[/sup]

= 150 billion kilograms

kinetic energy = 0.5 * (150B kg) * (5.56 m/s)[sup]2[/sup]

= 2.31 gigajoules

The Dodge Challenger Hellcat can make 527 kilowatts (707 hp); you’d have to run it at peak power output for over seven weeks (destroying it in the process) to put out that much energy. No wonder Polgara was dog-tired.

11

Isn’t lifting your hand (very slowly) actually lowering air? The volume the hand used to occupy is now filled by air while there is no longer air in the new spot of the hand, higher up. So, net effect is that one handsworth of air moved down.

Now, if the hand is moving quickly, it’s going to shove some air up, sure. Not sure what ‘fast’ and ‘slow’ mean in this context.

12

Sure, the net effect will be a downward movement of air. But some portion of the air will still be moving up.