How to derive air drag formula?

[Marek]

Hello, I have very interesting physics problem. But i really have no idea how to solve it... Maybe somebody can give me some useful hints?

Here we go:

"Air drag (air resistance, drag) is a resisitvie force which is the result of a moving object colliding with air molecules. Dervie the drag formula for a thin disc of area A moving with velocity v throught the air. Treat the air as a dense crowd of tiny particles, of concentration n0 per m^3 and with each having a mass u. Treat the collision as elastic ones. You should obtain the expression of the form Fd = 0.5 C q v^2 A, where C is a dimensionless drag coefficient, and q is air density"

 

[Physics Monkey]

You should probably start by getting the basic kinematics of the collision process down, for example, how many air molecules does the disk collide with in a time dt? Once you have this, you should probably then apply momentum and energy conservation to the collision. See where these suggestions take you.

 

[Marek]

so:
0|\
0 \ \ <--- A area
00 \ \
000 \ \
00000\|
<-->
x
0000 - molecules
Sorry for poor graph. So i can assume that: my area what is "pushing" by disc is Ax, in this area is Axn0 molecules, and mass of this area is Axn0u. I think that the molecules are not moving (so is false in reality, but there is written "dense crowd")
Probably i have now the solution, bu tell me please, what mean "dimensionless"? Because in my formula is no C, can I assume because of this "dimensionless" that C is so small so i can have this formula without C?