i am reserching airodynamic drag for a physics project and i keep finding references to reynolds number, the laws state that for reynolds number greater than 1000, use quadratic form and for reynolds number less than 1 use the liniar form. can anyone explane to me:

what is reynolds number?

how is it calculater?

what hapens for reynolds number between 1 and 1000?

The Reynolds number NR is proportional to the ratio of inertial forces (those required to accelerate the medium) to those of viscous drag.

The first goes as v^2, because the work done in accelerating the medium goes as (1/2)rho.v^2. The viscous drag is proportional to v.

At low speed and in high viscosity media, viscous forces are large and the flow is laminar. At high speed and in low viscosity, the medium is accelerated substantially.

At high values of NR, one gets turbulence. At low values, laminar flow. The value at which turbulence starts depends on the geometry and even with given geometry is uncertain, as it depends on history. It is typically at values of order 1000.

Individual molecules are often travelling faster than sound -- in fact the RMS speed is a bit greater than that of sound.

If molecules or electrons are going so much faster (say a dozen times the speed of sound) that they have enough energy to ionise atoms, then spectacular effects happen.