We discover for ourselves the Reynolds number

Those who are far from physics are consecrated. I can not begin this text otherwise, since the Reynolds number does not personally evoke any response in that part of the knowledge where information on physics should be stored. Let's try to fill this gap.

For the warm-up, let's clarify who Osborne Reynolds was in his time in his field. This scientist was the representative of English (in some sources - the Irish) scientific community in the field of physics, engineering and hydraulics. Born in 1842, after 28 years, he became a professor at the Department of Construction Mechanics in Cambridge. His studies led to the behavior of liquids in laminar (laminated) and turbulent (vortex) flow. It is he who owns the selection of a numerical criterion for the transition of one type of flow to another. This quantity is known to us as the Reynolds number.

What is the meaning of a number? This parameter is not a constant and represents a certain balance of inertial forces and internal friction in the fluid flow. As a designation for this criterion, Re is used. As for the units of measurement, then there are none, since the Reynolds number for water, gases and any other medium is a dimensionless quantity (a number per se).

Undoubted respect deserves the tenacity of the English scientist, who had to conduct more than one hundred experiments in order to reveal such a ratio. He succeeded in revealing the following regularity: at high rates (over 2 - 3 thousand) the flow of water will be completely turbulent, and at small - completely laminar.

Many relate the results of such calculations to indications that were obtained only experimentally, and with a change or an infinite repetition they can "fall out" of the current framework. However, many interpret them quite successfully from the standpoint of Newton's laws. In simple terms, the fluid in the stream has a certain inertia and is inclined to maintain its motion at the same speed.

The significance of this criterion, according to data from various sources, can not be overemphasized. It is this magnitude and the principle of its production that tell us that the impact of the environment (water, gas or other substance) is not so much dependent on speed, inertia or friction as on their interaction. It is this interaction that is reflected in the ratio, which is called the "Reynolds number". For water, the movement of which occurs through narrow channels (or pipes), the "borderline" transition index will be a value exceeding the value of 12,000 - 20,000. As it increases, the resistance of the medium will increase. For water in open space and air, the picture will be reversed: increasing the value of the Reynolds number will help reduce resistance.
This criterion was applied not only in hydromechanics, but also in aircraft and shipbuilding. For example, it is the Reynolds number that allows reliable tests of new aircraft models, fully reproducing the effect of real airflow in a reduced model.

PS I do not quote the formula of calculation with intent: if this topic interests the reader, it is not difficult to find out the order of calculation of such a value.