Consider a 10 inch by 10 inch sheet of paper lying flat on the ground. If atmospheric pressure is 15 pounds per square inch (sea level), then there is 1500 pounds of force acting downwards on the papers surface. How am I able to lift the sheet of paper? If air gets underneath the sheet of paper, then atmospheric pressure on either side will cancel and I'd only have to lift against gravity. But for the most part, I'm assuming there is more pressure on top than below.
My guess is that the seal between the sheet of paper and the ground is not great, allowing air to flow underneath. However, consider the following demonstration: a ruler lies on a table with 5 inches hanging off the side. If I spread a sheet of newspaper over the part of the ruler on the table, I increase the surface area for air pressure to press down on the ruler (without the sheet of newspaper, the air pressure is just acting on the ruler which doesn't have a lot of surface area). Now I can karate chop the ruler and break it in half due to atmospheric pressure giving a counter torque. However, why is it that I can easily lift the ruler with the newspaper on it (meaning, instead of karate chopping, I grab the ruler and just lift)? My guess is that, even if there is 3000 lbs of force acting downwards on the newspaper, I can still lift the ruler newspaper ensemble with say 1 lb of force because air instantly rushes into the cracks. But why don't I feel 2999 lbs of resistive force pushing down on my hand? Air flows in too fast and neutralizes the air pressure instantaneously?
Best Answer
A few things happen. One, the paper would bend, but lets pretend it's rigid, what happens when you lift. Your assumption is correct, air moves very fast, reducing but not completely eliminating the difference in air pressure between above and below. Air (molecules) moves at about 1,000 miles per hour.
http://www.phy.mtu.edu/~suits/SpeedofSound.html
So, in theory, if you could lift rigid paper at 1,000 MPH, you might approach the air pressure on that paper of 1,500 lbs, perhaps even exceed it due to compressive forces above (and there's probably people here who could do that math - I'd prefer not to try), but you'd only get that kind of pressure if you are able to lift faster, or about as fast as the air can move in below the paper.
Another thing to keep in mind about air is that it's compressible, so, even in a sealed tube where air couldn't get past what you were lifting, the air could compress so movement would be possible even if Air couldn't get past what you were lifting.