Those who are far from physics are dedicated. I cannot start this text otherwise, since the Reynolds number personally does not cause me any response in that part of the knowledge where the information on physics should be stored. Let's try to fill this gap.
To warm up, we will clarify who Osborne Reynolds was at one time in his field. This scientist was a representative of the English (in some sources - Irish) scientific community in the fields of physics, engineering and hydraulics. Born in 1842, after 28 years, he became a professor at the Department of Structural Mechanics in Cambridge. He conducted his research regarding the behavior of liquids in laminar (layered) and turbulent (vortex) flows. He belongs to the allocation of the numerical criterion for the transition of one type of flow to another. It is this quantity that is known to us as the Reynolds number.
What is the meaning of the number? This parameter is not constant and represents a certain ratio of inertia forces and internal friction in the fluid flow. Re is used to denote this criterion. As for the units of measurement, these do not exist, since the Reynolds number for water, gases, and any other medium is a dimensionless quantity (the number as such).
The stubbornness of the English scientist deserves undoubted respect, who had to conduct more than one hundred experiments in order to reveal such a relationship. He managed to identify the following pattern: at high rates (over 2–3 thousand), the water flow will be completely turbulent, and at small - completely laminar.
Many attribute the results of such calculations to readings that were obtained only empirically, and when changing or endlessly repeating, they can “fall out” of the current framework. However, many quite successfully interpret them from the standpoint of Newton's laws. In simple terms, a fluid in a 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, cannot be overestimated. It is this quantity and the principle of its receipt that tell us that the effect of the medium (water, gas or other substance) does not so much depend on speed, inertia or friction, but 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 indicator will be a value exceeding that of 12,000–20,000. With its increase, the medium resistance will increase. For water in open space and air, the picture will be reversed: an increase in the Reynolds number will contribute to a decrease in resistance.
This criterion was applied not only in hydromechanics, but also in aircraft and shipbuilding. So, for example, it is the Reynolds number that allows for reliable testing of new aircraft models, fully reproducing the effect of real air flow in a reduced model.
PS I don’t bring the calculation formula with intent: if this topic is of interest to the reader, it will not be difficult to find out the procedure for calculating such a value.