About 12 years ago I took the AP Chemistry exam, and one of the essay questions was exactly this: “Why does a flag wave in the wind?”
It’s bugged me all this time. I can see answering this question on a physics exam, but chemistry? What’s the right answer?
I think Cecil covered it once. If not, there was definitely another thread on it. I seem to recall it got quite heated, oddly enough…
It’s an essay question, and deserves an essay answer. I can, however, tell you why it was in Chemistry and not Physics.
A good answer would require the gas laws, Bernoulli’s equation and principles of equilibria. While Bernoulli’s equation can also be covered in Physics, the other two are generally taught in the Chemistry curriculum. (A really good answer would require more math than I personally needed to get a science doctorate. A full answer would lead to a fistfight among eminent professors)
here is a high level mathematical discussion of flag waving (pdf)
enjoy
Man, those are fun.
Eight pages of detailed scientific explation is hard to decipher.
Probably this can be attributed to the Bernouli effect and/or wind flow instabilities.
Well, here’s a short answer.
Once there is any instability, a high pressure zone on one side of the flag moves the fabric, and the wind interacts with the fabric to translate the bumped out region in the downweb direction. Meanwhile the fabric interacts with the wind to increase the flow into the high pressure area and make the bumping out effect stronger. The displacement of the fabric travels toward the free end of the flag as a moving wave, and the free end flops back and forth, approximately following an arc around a point near the end of the flag. This travel in an arc creates a tension in the end of the flag (from the point of view of a coordinate system based on the flag, this would be centrifugal force). The coupling of wind energy into this traveling wave is what powers the fabric motion, much as it powers surf energy by coupling into ocean waves.
I’d consider this a problem from the field of mechanical engineering, more specifically an example of fluid-structure interaction (fsi). To model it effectively would require coupled models, one of them a computational fluid dynamics (CFD) model, and the other a mechanical model including the tension, mass, velocity, and possibly stiffness of the points in the flag. This is somewhat hard work.
Seems totally out of place in a chemistry exam, unless they want some sort of trick answer like solar energy driving the cycle of winds on Earth.