First, I'd like to say that I am no professional aerodynamicist, and the following text may contain errors. I'd be happy if someone points them out!

About Reynolds numbers:

Let's say you're a pioneer of flight, and you want to build an airplane that can fly. How big a wing do you need? To answer this, you could simply build a wing, put it in your pioneer-wind tunnel, and measure the forces on it at the speed you think your airplane will be able to attain with the pioneer-engine you have available. Let's say the wing wasn't big enough. Now, what do you do? You have to build another one! And another one... etc, until you get it right. You don't wan't a too big wing (weight!), and not a too small (can't fly!).

Anyway, this quickly grows old. Someone said: Why can't we predict how much lift a given wing will have without building the darned thing every time?

So someone set out to build lots of different wings, and tried to see if there was some kind of pattern to the amount of lift different wings gave. Let's see, this one over here is 1m wide, and gives 1N at this speed, but that one over there gave 2N at the same speed. Hmm, why.. oh, it's twice as wide, but identical otherwise! Okay, lift seems to increase linearly with wingspan! And people built lots of wings, and thought hard, and came up with a formula:

Lift = chord * span * CL * Velocity * Velocity * airdensity / 2

Whe
chord = Width of wing, from leading edge to trailing edge
span = Length of wing, from tip to tip
velocity = The relative forward speed of the wing in relation to the air
air density = The weight of air, per volume (1.2kg / cubic meter)
CL = Lift Coefficient, (varies with angle of attack, and reynolds number!)

Anyway, this worked pretty well.

The was just one problem! When you build a 30 cm (1') wing, and it gives 10N of lifting force, you'd expect the same kind of wing, but 3m (10'), to give 100N (if it has the same chord), at the same speed! But, this did not occur! Rather, it turned out, that when you take a small wing, and make it many times bigger, or run it many times faster through the air, the above formula doesn't work anymore.

When does it work? Does speed have to be the same? Does chord have to be the same? No! It works when the Reynolds number is the same!

So, if you build a small wing, and run it in a wind tunnel with a different medium (perhaps water), and this makes the reynolds number the same as it will be when your real aircraft flies its real mission, you can expect the lift equation above to 'work'.

So, the Lift Equations allows the lifting force from a wing to be predicted (very handy when constructing aircraft). But the lift equation only works when supplied with a CL measured at the same Reynolds number as you'll be flying at! So you need the Reynolds number in order to be able to use the lift equation!