quote:Original post by Anonymous Poster
However the formula above is a _model_ of the behavour in a vicous fluid (=air). Another model is to use v^2 instead of v.
And probably something interesting happens around the speed of sound...
Actually, v2 is more appropriate for a missile, which can move quite fast. The "v" version is only a good approximation at very low speeds.
And....since you added "..." I assume you want some information on what happens around the speed of sound (Mach 1),
. Since I happen to know just a wee little bit about that subject....At something less than the speed of sound (say, Mach 0.8), shock waves begin to form on the surface of a body. The shock waves occur before the object reaches the speed of sound since the flow accelerates around the body. And when the object is around Mach 0.8 or so, the accelerated air around the body exceeds Mach 1. The air just in front of the shock wave is supersonic. The air just behind the shock is subsonic. There are associated massive changes in air properties such as air pressure across the thickness of the shock. (A strong shock is very thin, actually only a few mean-free-paths between molecules in thickness, almost a true physical discontinuity. But lets not talk about the shock waves that occur in nebulae and galactic systems!)
The emergence of these shock waves, and corresponding large changes in air properties across the shock thickness, leads to a phenomenon known as "drag rise," which is a large increase in drag. The drag rise occurs within the transonic flight regime, which begins at the Mach 0.8 and extends to something beyond Mach 1, say Mach 1.2. Within this transonic regime, the shock waves emanate from the object surface. As the speed increases to the high end of the transonic regime, the shocks move rearward until eventually they move as far back as they can. The shock waves are then emanating from the most rearward edges of the object, and this is the limit of the transonic regime. The flow over the surface at this limit, the transonic/supersonic boundary, is entirely supersonic (Mach > 1). But the flow immediately behind the object, immediately behind the shock, is subsonic (Mach < 1). For example, an airplane wing in transonic flight would have a shock wave on the top and bottom surfaces, starting somewhere between the leading and trailing edge and extend upward above and below the wing until the shock is dissipated by the viscous and turbulent air above and below the wing. (The shock kind of smears out away from the wing to become merely a strong pressure wave, and this is what causes sonic boom.) But, I digress. As the wing moves at higher and higher speeds, ultimately the shock will move backwards until it reaches the trailing edge of the wing. When this happens, but not before, the flow over the surface of the wing is entirely supersonic. When the flow over the surface is entirely supersonic, you''re out of the transonic regime. When the flow becomes entirely supersonic, the shocks no longer interact with the flow over the wing in the same way. And, though it may seem strange, drag will begin to decrease from the maximum drag seen during drag rise. But the drag will once again increase as the speed continues to increase beyond the transonic/supersonic boundary.
Cool, n''est ce pas?
Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.
. To be honest, I haven''t given this problem much thought afterwards. Since I don''t know the general approach to solving differential equations, I can only guess the solution, which is pretty tedious. And so far, my guesses haven''t worked very well. 
