In this article we will consider the Reynolds number and give examples of its values. In addition, let's talk about the importance of discovering a scientist to prove self-organization in substances, and, as a consequence, to start a new, post-non-classical period of science.

## Imperceptible start

Science, like all aspects of human life, develops in stages. And the beginning of the next stage of evolution comes imperceptibly. As a rule, understanding in the next paradoxes (and there are always and everywhere abounding), some ordinary scientist, by virtue of curiosity or for simplicity, gives a definition, observes the regularity and derives the formula. Some time this discovery is used, not often paying attention to its universality or surprising utility. And then comes a genius (who most of the time does not consider himself to be such), expresses something revolutionary, and a well-known fact emerges that confirms new theories.

So it was with the Max Planck quanta: he introduced his formula for simplicity. Only Einstein realized the importance of his assumption. So it was with Mendel, who found the inheritance of the characteristics of hybrid plants interesting. His work was subjected to a lot of criticism, until Carl Correns proved her justice. So it was with Reynolds: studying the flow of water, he introduced the criterion by which the laminar flow was determined before us or turbulent. Its formula was used by scientists dealing with hydroturbines, without assuming how important this ratio is for the proof of the self-organization of matter.

## Biography of Osborne Reynolds

This scientist was born in the first half of the nineteenth century in the family of a priest, in England, in the city of Belfast. From a fairly early age, he was fond of machinery, moving parts of cars, worked in the workshop. He graduated from the prestigious University of Cambridge, and then taught in no less titled Manchester.

All his life he dedicated scrupulous study of various phenomena from the field of mechanics, heat exchange, electricity, magnetism, astrophysics and turbulence. With special care Reynolds was preparing an experiment: as a talented mechanic, he thought through all the processes to the smallest detail, trying to eliminate parasitic phenomena. Cleverly combined a master of all trades and a thoughtful scientist. He undertook any riddles of science, which could be solved by patient work and hours of observation.

As the reader sees, no outbursts, illuminations, cries: "Found!" Only the daily routine of a corrosive scientist. And as a result, there are many discoveries, among which the famous Reynolds number.

## What is called the Reynolds number

Water is the cradle of life on our planet. Even if the theory of panspermia is correct and complex organic molecules have arrived on comets, the one that its people see now, life has become in the first oceans.

The properties of water do not cease to amaze. And if scientists now study the structures that this liquid forms under extreme pressure and temperature, then in the nineteenth century they wondered how it flows. In particular, the difference between a laminar flow and a turbulent flow.

The Reynolds number is a dimensionless quantity that determines how much the viscosity of a liquid is capable of hindering the rectilinear motion of its particle at a given speed. In the stream, each particle tends to move forward, preferably the shortest path. However, all the molecules of the liquid are connected and can not exist in isolation from each other. The strength of this connection determines, in particular, the viscosity. The higher it is, the more complex the liquid takes on new forms and gives up its molecules. Water flows easily, honey - more difficult. Bitumen is the most viscous. Thomas Parnell of the University of Queensland poured his variety - peck - into the funnel. The first drop of it fell in eight years.

Thus, the viscosity prevents the movement of particles of liquid along the shortest path. Accordingly, depending on the flow velocity, the particles move more or less rectilinearly (laminarly) or, overcoming the resistance of the entire volume of the liquid, they begin to chaotically mix, creating mini whirlpools (this is called turbulence). The Reynolds number also has other definitions.

## Other definitions of the Reynolds number

In mathematical terms, it means the relation between the nonlinear and dissipative terms in the Navier-Stokes equation, which describes the propagation in a medium of a wave of finite amplitude.

Also, the Reynolds number determines the ratio between the kinetic energy of the fluid and the energy loss per unit length (due to internal friction). The formula for this indicator is:

Re = ρvD_{g} / η = vD_{g} / μ = QD_{g} / μA (Re - Reynolds number, ρ - liquid density, D_{g} - hydraulic diameter, v - characteristic velocity, η - dynamic viscosity of the liquid, μ - kinematic viscosity of the liquid, Q - volume flow rate, A - cross-sectional area of the pipe).

In acoustics, the formula is different:

Re_{a} = ρvC_{0} / ωb (C_{0} - speed of sound in a given fluid, ω - circular frequency, b - dissipation parameter).

For a Reynolds number, depending on the substance that forms the flow, the roughness and the shape of the pipe section, there is a certain critical exponent. Also, it depends on whether the flow occurs without obstacles or the fluid flows around something (for example, a metal ball).

In addition, the value of the Reynolds number indicates that the stream is still laminar or already turbulent. There is also an intermediate state of the current, when it can no longer be called uniform. But it still does not meet the requirements of turbulence. This Reynolds number for water in an ideal pipe is 2100.

## The importance for science of determining the Reynolds number

We have already mentioned above that new periods of science begin relatively imperceptibly. Also the reader, for certain, has already guessed that here is not simply described the magnitude associated with a very specific area - the flow of liquids. Let's start the story from afar.

Reynolds died in 1912. Five years later Ilya Romanovich Prigozhin was born in Moscow, and ten years later, in Germany - Herman Haken. In the middle of the twentieth century, these two men proclaimed a new period of science, called "post-nonclassical." It continues even now. In its foundation a relatively new discipline is laid - synergetics.

## Synergetics

This science does not share biology, chemistry, physics and geology. All these sections are of interest to synergetics because they investigate open nonequilibrium systems that are capable of self-organization. Nowhere to find a direct study of phenomena. Any science builds models, but most of them are static. Perfect vacuum, absolute zero occur in textbooks. But in reality such conditions are unattainable. Any two adjoining systems are exchanged by mass or energy, so that any processes occur in previously unequal conditions.

## Self-organization

And when some voluminous object (for example, water in a saucepan), which consists of a very large number of elements, receives energy from outside (heats up), then at some point its behavior changes.

We were always told at school that boiling is the process chaotic, the molecules cease to form a coherent system of fluid and begin to move in different directions inconsistently. However, it is not so. The presence of a very large number of elements, if one atom "ran" up, it is likely that several tens of neighboring atoms at the same time will move up. Thus, some time there will be a cluster of water in which the particles behave the same way.

This is the essence of self-organization: in a nonequilibrium system of many components this some of them begins to behave identically in small parts of time and space.

## Turbulence and self-organization

The idea of self-organization, as the reader sees, is very simple. The proof of coherent behavior is much more complicated. Remarkable Russian scientist Klimontovich, following the paradigm of synergetics, deduced: for the transition of any system from chaos to self-organization, there is one parameter. When it exceeds a certain critical value, the difficulty level rises. This same scientist for the first time in the world proved that for turbulent fluid motion such a criterion is the Reynolds number. Thus, the indicator, which has been used for almost fifty years, turned out to be the key to opening a new period in science.