The proverb is that burnt in milk blows on water. The meaning of burnt on milk - blowing on water in a reference book on phraseology

Having been burned by milk, or “What we have, we don’t keep; when we lose it, we cry”? O memory of the heart, you are stronger than the mind of the sad memory K. Batyushkov So what to do when you want happiness, big and bright, and, if possible, here and now? After all, no one is immune from failure and

And, apparently, for good reason. But how can this be explained? Many people are probably familiar with the involuntary experiment: quickly removing your finger from boiling water, you want to blow on it or wave your hand (it’s better not to try to repeat this experiment). It is clear that here we are talking about enhancing heat transfer from the finger into the air. Physicists have long learned to describe this process. It is believed that the thermal energy flux density j t, measured in J/(m 2 s), in the direction of a certain coordinate r is proportional to the rate of change (more precisely, the rate of change) of temperature in the opposite direction:

Here Δ r- the distance between two points of the medium whose temperatures differ by Δ T. And the minus sign indicates that heat flows from hot to cold areas.

The ratio is called the temperature gradient along r, and dependence (1) itself is Fourier’s law - named after the French physicist and mathematician Jean Baptiste Fourier (1768–1830).

But it turns out that such proportionality occurs not only in the theory of thermal conductivity. For example, electric current density j e, measured in A/m 2 = C/(m 2 s), is proportional to the electric potential gradient φ, which directly determines the electric field strength:

(2)

This law is called (generalized) Ohm's law, after the German physicist Georg Simon Ohm (1787–1854). Comparing expressions (1) and (2), it is possible to determine the temperature T called potential - the difference in the values ​​of this potential causes a flow of heat.

Further, if in any solution, for example, sugar in water or perfume in the air, the concentration of the substance is not the same at different points, then diffusion occurs, and the flux density of the molecules of this substance j n turns out to be proportional to the concentration gradient n, i.e. the rate of its change in space:

(3)

This relationship is Fick's law, after the German physiologist Adolf Fick (1829–1901). Now we can call the concentration of a substance a potential, the difference in values ​​of which causes a diffusion flow of mass.

But that's not all. When we blow on a finger, the speed of air flow at its surface is close to zero, and with distance from the surface it increases. In other words, there is a change in the tangential component of the velocity in the direction of the normal Δ u/Δ r. As a result, shear stress occurs j u, measured in N/m 2, i.e. friction of air layers against each other and, ultimately, against the very surface of the streamlined body. And it turns out

(4)

But this voltage can be called the impulse flux density: N/m 2 = (kg m/s)/(m 2 s)! Comparing expression (4) with the previous ones, how can one not call speed potential? Fluids that obey this law are called Newtonian. Can you guess why? That's right: it was established by the great Newton back in 1687.

Now you can be surprised and admired: physical processes that are different in nature, the description of which was proposed by remarkable scientists from different countries more than 100–300 years ago, reflect a certain general fact: the flux density of any physical entity - thermal energy, electric charge, soluble matter, momentum. .. proportional to the rate of spatial change of the corresponding potential - temperature, electrical voltage, concentration, speed...

All mentioned processes are called transfer phenomena. The proportionality sign in the given relationships can be replaced with an equal sign if for each gradient we write the corresponding coefficient: thermal conductivity, electrical conductivity, diffusion, viscosity... - this is well known to first-year university students.

However, let's return to the scalded finger. Who transfers heat from a finger and why do you want to blow on it? Of course, molecules do this, and, of course, blowing speeds up heat removal.

Consider a sphere (or hemisphere) with radius R with surface temperature T p, modeling the fingertip. If the surrounding air is calm, "hot" molecules whose thermal speed corresponds to T n, are pushed in the direction from the surface (Fig. 1, A), and cold molecules from “infinity” are also pushed towards them, where the temperature is T∞. A certain temperature distribution is established, which is qualitatively represented by the curve A in Figure 2. It can be shown that the temperature drops in the radial direction quite smoothly, according to the hyperbolic law, changing significantly over a distance of the order of R. (These arguments do not take into account the Archimedes force, which causes warm gas to float in the atmosphere of cold gas and, of course, helps remove heat.) As a result, the density of the thermal energy flux from the surface can be written as a function of the finite temperature difference and the distance at which it occurs its significant change:

Now let's slowly start blowing on our finger. It is clear that the molecules carrying away heat are “blown away” by the air flow (Fig. 1, b). Finally, let’s assume that there are forces, then all the molecules “starting” from the surface will fit in a thin layer of characteristic thickness δ (Fig. 1, V), significantly smaller than the radius of the sphere R (δ << R). (Соответствующие этим случаям графики распределения температуры качественно представлены кривыми b And V in Figure 2.) As a result, the heat flow will increase:

This thin layer is called the boundary layer. It was first introduced by the famous German aerodynamicist Ludwig Prandtl (1875–1953) - of course, not as applied to a finger, but when solving problems of resistance of bodies in a flow of liquid or gas. There is an opinion that Prandtl should have been awarded the Nobel Prize alone for introducing this fruitful concept.

But let's continue our reasoning. We know that it is the molecules that carry heat away from the finger (and bring in “cold” from the environment). This means that to estimate the thickness of the thermal boundary layer, the characteristics of molecular chaos should be used. Which ones exactly? Of course, first of all, this is the average speed of thermal movement - the faster the molecules move, the more intense the heat exchange. Next, this is the mean free path of the molecule l- the larger it is, the further the molecule will carry the energy, transferring it to the next molecule upon collision. The product of these two quantities has the dimension m 2 /s, and if it is multiplied by the time it takes the air to travel a characteristic distance of the order of the radius R, then we obtain an estimate for the squared thickness of the boundary layer:

(5)

(By the way, it was Fourier who first began to use the method of dimensions.)

Relation (5) is typical for all wandering processes. It goes back to the first attempts to describe the Brownian motion of particles. And its figurative analogue is the problem of a drunken sailor in an unfamiliar city. Finding himself at any crossroads, the sailor randomly chooses one of four directions. The question is: how far will the sailor go from the starting point after passing N blocks? Answer: The average expected square of this removal is proportional N. It is clear that the distance δ will depend on both the speed of movement and the length of the blocks l, i.e. will be described by expression (5). It remains to substitute it into the formula for the heat flux density from the surface of the finger:

From this we can see that only the speed of air flow depends on us u. It is this that transforms the slow diffusion of molecules at the bottom of the boundary layer into fast convective transport at its outer boundary. So blow harder. But don't overdo it. For if you reach supersonic speed, then, on the contrary, the large kinetic energy of the air flow will turn into heat at the deceleration point and give a high surface temperature. Indeed, from the law of conservation of energy

recorded for one mole of air, at a blowing speed, for example, u∞ = 1000 m/s we get

However, it is unlikely that our lips and lungs will allow supersonic air flow around the finger.

It is interesting to note that when forging the famous sabers from Damascus steel, the blacksmith handed the horseman a red-hot blade, and the horseman immediately galloped at full speed, vigorously waving it. Apparently, this cooling mode was optimal for the innovative technology of that time.

But have we taken everything into account? No, not all of them: your finger is wet after boiling water! And here the process of evaporation of water molecules comes into force, followed by their diffusion in the boundary layer and entrainment by air. To describe this process, you need to use relation (3). This is not new to us - after all, the thermal conductivity discussed earlier is nothing more than the diffusion of thermal energy. And now, in addition to the heat removal by air molecules, the heat removal of the phase transition will be added L together with the evaporating mass of water:

Here j m = j n m (m- molecular mass) is the flow density of the mass carried away from the body being blown, n n and n∞ are the corresponding values ​​of the concentration of water molecules. This heat loss is greatest if the surrounding air is dry ( n∞ → 0). And this is a significant addition - after all, the specific heat of vaporization for water is quite high: L≈ 2 MJ/kg.

That is why, to cool aircraft entering the atmosphere at high speed, they use liquid forced from the inside through the porous surface of the body: when it evaporates, it carries away heat and saves the vehicle from combustion. It’s also not in vain that in hot deserts, to cool Pepsi, they put a bottle wrapped in a wet rag on the roof of a car and drive it as fast as possible. They are already working here u, And L, And...

This is how useful it is to know gas thermodynamics!

The proverb allegorically says that a person exposed to danger always begins to expect it and therefore plays it safe.

What am I talking about?
Preparing for the new school year, I look through the latest information on pedagogical sites, looking for something interesting. And then I came across an article about a teacher who found himself in an unpleasant situation. I try not to participate in such discussions, because... I consider this a shock of air. Teachers, parents, officials, children - everyone has their own truth and no one intends to give up ground in this battle. No one is ready to compromise, but lessons must be learned from such moments.

A teacher at one of the schools in the Central District of St. Petersburg was fined 10 thousand rubles because children ran around during recess and bumped heads, reports “Petersburg Diary”. Students collided during recess in May of this year in the presence of a teacher. As a result, one student suffered a traumatic brain injury and concussion. A case was initiated against the teacher for an administrative violation under Part 2 of Article 5.57 of the Code of Administrative Offenses of the Russian Federation (violation of the right to education). By decision of the magistrate, she was brought to justice and sentenced to a fine of 10 thousand rubles.
Tell me, where is the violation of the right to education?
If the teacher is responsible for the life and health of children, then what article is this?
Why are parents not fined when their children collide and fall in front of them?

In May, a teacher from Zlatoust was accused of child abuse due to difficult assignments. The prosecutor's investigation showed that the primary school teacher assigned homework to first-graders in the form of written work, as well as in the form of daily memorization of complex poems. “On her own initiative, she extended the duration of classes, shortened the duration of breaks, leaving the children after classes to continue studying the material covered. The assigned homework was not of a recommendatory nature; points were assigned based on the results of their completion, which is prohibited by order of the Russian Ministry of Education and Science,” the prosecutor’s office noted. As a result of the teacher’s actions, some students were deprived of proper rest, as well as the opportunity to study in additional clubs and attend sections. “From September 2015 to April 2016, in her teaching activities, the teacher used unacceptable methods of education against 1st grade students: rude, dismissive, degrading treatment,” the department added.

And no one will understand that before there were grades and assignments and no one was judged, but now it’s like this, because the Ministry of Education decided so. And my opinion and yours are of no interest to anyone. Moreover, it may not coincide with us, but how will we agree? And besides, the school and parents are being pitted against each other from all sides. If you don't like what's happening at school, write a complaint! A bruise is a complaint, a sideways glance (as it seemed to the child) is a complaint, the food is tasteless (and everyone has different tastes) - a complaint! No, I don’t want to live in anticipation of trouble.

Why did I write all this? Not to look for who is right and who is wrong. It's true it's a slippery thing. Truth is what we believe in, and everyone has their own faith. I wrote to remind you:
- to you, colleagues, that, most likely, teaching is our calling and it’s too late for us to get into business.
Those who are not suitable leave at the very beginning of their professional path. That we must try to maintain a balance between dedication at work and self-care.
- you, parents, should not blame the school for all your child’s troubles. We are not enemies, a successful student and well-mannered child is our goal. We need it even more!
- to you, officials, that the teacher’s task is not to “babysit” papers, but to teach children.
- I want to remind you guys that school and lessons are not punishment, not torture. Find your interest in studying, love her and she will reciprocate you too.
Good luck to everyone in the next school year!

People's About excessive caution, reinsurance. BMS 1998, 385; ZS 1996, 104.

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“Having been burned (burnt) on milk, he blows on the water” in books

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