Force of viscous friction. Study of viscous friction forces Resistance force when moving in a viscous medium
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Objective: study of the phenomenon of viscous friction and one of the methods for determining the viscosity of liquids.
Instruments and accessories: balls of various diameters, micrometer, caliper, ruler.
Elements of the theory and method of experiment
All real liquids and gases have internal friction, also called viscosity. Viscosity is manifested, in particular, in the fact that the movement that has arisen in a liquid or gas after the cessation of the causes that caused it, gradually stops. From everyday experience, for example, it is known that in order to create and maintain a constant flow of fluid in a pipe, it is necessary to have a pressure difference between the ends of the pipe. Since, in a steady flow, the fluid moves without acceleration, the need for the action of pressure forces indicates that these forces are balanced by some forces that slow down the movement. These forces are internal friction forces.
Two main modes of liquid or gas flow can be distinguished:
1) laminar;
2) turbulent.
In a laminar flow regime, a liquid (gas) flow can be divided into thin layers, each of which moves in the general flow at its own speed and does not mix with other layers. The laminar flow is stationary.
In a turbulent regime, the flow becomes unsteady - the speed of particles at each point in space changes randomly all the time. In this case, intensive mixing of the liquid (gas) takes place in the flow.
Let us consider the laminar flow regime. Let us single out two layers in the flow with area S, located at a distance ∆ Z apart and moving at different speeds. V 1 and V 2 (Fig. 1). Then a viscous friction force arises between them, proportional to the velocity gradient D V/D Z in a direction perpendicular to the direction of flow:
Where the coefficient μ is by definition called the viscosity or coefficient of internal friction, D V=V 2-V 1.
From (1) it can be seen that the viscosity is measured in pascal seconds (Pa s).
It should be noted that the viscosity depends on the nature and state of the liquid (gas). In particular, the value of viscosity can significantly depend on temperature, which is observed, for example, in water (see Appendix 2). Failure to take this dependence into account in practice in some cases can lead to significant discrepancies between theoretical calculations and experimental data.
In gases, viscosity is due to the collision of molecules (see Appendix 1), in liquids, it is due to intermolecular interactions that limit the mobility of molecules.
Viscosity values for some liquid and gaseous substances are given in Annex 2.
As already noted, the flow of a liquid or gas can take place in one of two modes - laminar or turbulent. The English physicist Osborne Reynolds found that the nature of the flow is determined by the value of the dimensionless quantity
Where is a quantity called kinematic viscosity, V is the velocity of the fluid (or the body in the fluid), D is some characteristic size. In the case of fluid flow in a pipe under D understand the characteristic size of the cross section of this pipe (for example, diameter or radius). When a body moves in a fluid D understand the characteristic size of this body, for example, the diameter of a ball. For values Re< 1000 the flow is considered laminar, at Re> 1000 the flow becomes turbulent.
One of the methods for measuring the viscosity of substances (viscometry) is the falling ball method, or the Stokes method. Stokes showed that a ball moving at a speed V in a viscous medium, there is a viscous friction force equal to , where D is the diameter of the ball.
Consider the motion of the ball as it falls. According to Newton's second law (Fig. 2)
Where F— force of viscous friction, — force of Archimedes, — force of gravity, ρ AND And ρ are the densities of the liquid and the material of the balls, respectively. The solution to this differential equation will be the following dependence of the ball's speed on time:
Where V 0 is the initial speed of the ball, and
Is the speed of steady motion (at T>>τ). The quantity is the relaxation time. This value shows how quickly the stationary mode of motion is established. It is usually considered that T≈3τ the motion practically does not differ from the stationary one. Thus, by measuring the speed VAt, the viscosity of the liquid can be calculated. Note that the Stokes formula is applicable at Reynolds numbers less than 1000, that is, in the laminar regime of fluid flow around the ball.
A laboratory apparatus for measuring the viscosity of liquids using the Stokes method is a glass vessel filled with the liquid under study. Balls are thrown from above, along the axis of the cylinder. There are horizontal marks in the upper and lower parts of the vessel. By measuring the time of movement of the ball between the marks with a stopwatch and knowing the distance between them, the speed of the steady movement of the ball is found. If the cylinder is narrow, then the calculation formula must be corrected for the influence of the walls.
Taking into account these corrections, the formula for calculating the viscosity will take the form:
Where L - distance between marks, D is the diameter of the inside of the vessel.
Work order
1. Use a caliper to measure the inner diameter of the vessel, use a ruler to measure the distance between the horizontal marks on the vessel, and use a micrometer to measure the diameters of all the balls used in the experiment. The acceleration due to gravity is assumed to be 9.8 m/s2. The density of the liquid and the density of the substance of the balls are indicated on the laboratory setup.
2. Lowering the balls one by one into the liquid, measure the time it takes for each of them to travel between the marks. Record the results in a table. The table shows the number of the experiment, the diameter of the ball and the time of its passage, as well as the result of calculating the viscosity for each experiment.
DETERMINATION OF THE INTERNAL FRICTION COEFFICIENT
Low viscosity liquids
Viscosity determination
Examples of the manifestation of the viscosity of a liquid
An ideal fluid, i.e. fluid without friction, is an abstraction. All real liquids or gases have viscosity, or internal friction, to a greater or lesser extent. Viscosity is manifested in the fact that the movement that has arisen in a liquid or gas after the cessation of the causes that caused it, gradually stops.
Let us also consider the following examples, in which the viscosity of a liquid manifests itself. So, according to Bernoulli's law for an ideal fluid, the pressure in a pipe is constant if its cross section and height do not change. However, as is known, the pressure along such a pipe drops uniformly, as shown in Fig. one.
Rice. 1. Pressure drop in a pipe with a moving liquid.
This phenomenon is explained by the presence of internal friction in the liquid and is accompanied by the transfer of part of its mechanical energy into internal.
In the laminar flow of fluid through the pipe (Fig. 2), the velocity of the layers continuously changes from the maximum (along the axis of the pipe) to zero (near the walls).
From a mechanical point of view, any of the layers slows down the movement of the adjacent layer located closer to the axis of the pipe (moving faster), and has an accelerating effect on the layer located farther from the axis (moving more slowly).
Rice. 2. Velocity distribution in the cross section of the flow
liquids in a pipe of circular cross section (laminar flow).
Force of viscous friction
To clarify the patterns that the forces of internal friction obey, consider the following experiment. Two plates parallel to each other are immersed in a liquid (Fig. 3), the linear dimensions of which significantly exceed the distance between them d. The bottom plate is held in place, the top one is set in motion relative to the bottom one with some speed v 0 .
Rice. 3. Layered motion of a viscous fluid between the plates,
having different speeds.
The layer of liquid adjacent directly to the upper plate, due to the forces of molecular cohesion, sticks to it and moves along with the plate. The liquid layer adhering to the lower plate remains at rest with it. The intermediate layers move in such a way that each upper one has a speed greater than the one lying under it. That. each layer slides relative to adjacent layers. Therefore, from the side of the lower layer, the upper one is acted upon by a friction force, which slows down the movement of the second of them, and, conversely, from the side of the upper layer to the lower one, it accelerates the movement. The forces that arise between layers of fluid that experience relative displacement are called internal friction. The properties of a fluid associated with the presence of internal friction forces are called viscosity.
Experience shows that in order to move the upper plate at a constant speed v 0, it is necessary to act on it with a well-defined force F. The action of an external force F is balanced by an oppositely directed friction force equal to it in magnitude.
The force of internal friction between two layers of fluid can be calculated using Newton's formula:
, (1)
where h is the dynamic viscosity, coefficient of internal friction, s is the area of contact (in this case, the area of the plate), Dv/D z is the speed gradient.
The viscosity coefficient is numerically equal to the force acting per unit area of the layer, when per unit length, taken perpendicular to the layer, the velocity changes by one (Dv/D z= 1)
Viscosity(internal friction) ( English. viscosity) - one of the transfer phenomena, the property of fluid bodies (liquids and gases) to resist the movement of one of their parts relative to another. The mechanism of internal friction in liquids and gases is that randomly moving molecules transfer momentum from one layer to another, which leads to equalization of velocities - this is described by the introduction of a friction force. The viscosity of solids has a number of specific features and is usually considered separately. The basic law of viscous flow was established by I. Newton (1687): As applied to liquids, viscosity is distinguished:
- Dynamic (absolute) viscosity µ - the force acting on a unit area of a flat surface, which moves at a unit speed relative to another flat surface located at a unit distance from the first. In the SI system, dynamic viscosity is expressed as Pa×s(pascal second), off-system unit P (poise).
- Kinematic viscosity ν is the ratio of dynamic viscosity µ to the density of the liquid ρ .
- ν , m 2 /s - kinematic viscosity;
- μ , Pa×s – dynamic viscosity;
- ρ , kg / m 3 - the density of the liquid.
Force of viscous friction
This is the phenomenon of the occurrence of tangential forces that prevent the movement of parts of a liquid or gas in relation to each other. Lubrication between two solids replaces dry sliding friction with sliding friction of liquid or gas layers against each other. The speed of the particles of the medium smoothly changes from the speed of one body to the speed of another body.
The force of viscous friction is proportional to the speed of relative motion V bodies, proportional to the area S and inversely proportional to the distance between the planes h.
F=-V S / h ,The coefficient of proportionality, depending on the type of liquid or gas, is called dynamic viscosity coefficient. The most important thing in the nature of viscous friction forces is that in the presence of any arbitrarily small force, the bodies will begin to move, that is, there is no static friction. Qualitatively significant difference of forces viscous friction from dry friction
If a moving body is completely immersed in a viscous medium and the distances from the body to the boundaries of the medium are much greater than the dimensions of the body itself, then in this case we speak of friction or environment resistance. In this case, the sections of the medium (liquid or gas) immediately adjacent to the moving body move at the same speed as the body itself, and as you move away from the body, the speed of the corresponding sections of the medium decreases, turning to zero at infinity.
The resistance force of the medium depends on:
- its viscosity
- from body shape
- on the speed of the body relative to the medium.
For example, when a ball moves slowly in a viscous fluid, the friction force can be found using the Stokes formula:
F=-6 R V,A qualitatively significant difference between the forces of viscous friction and dry friction, among other things, the fact that the body in the presence of only viscous friction and an arbitrarily small external force will necessarily begin to move, that is, for viscous friction there is no static friction, and vice versa - under the influence of only viscous friction, the body, which initially moved, never (in macroscopic approximation that neglects Brownian motion) will not stop completely, although the motion will slow down indefinitely.
Viscosity of gases
The viscosity of gases (the phenomenon of internal friction) is the appearance of friction forces between gas layers moving relative to each other in parallel and at different speeds. The viscosity of gases increases with increasing temperature
The interaction of two layers of gas is considered as a process during which momentum is transferred from one layer to another. The force of friction per unit area between two layers of gas, equal to the momentum transferred per second from layer to layer through unit area, is determined by Newton's law:
τ=-η dv / dz
where:
dv / dz- velocity gradient in the direction perpendicular to the direction of motion of the gas layers.
The minus sign indicates that momentum is carried in the direction of decreasing velocity.
η
- dynamic viscosity.
η= 1 / 3 ρ(ν) λ, where:
ρ
is the density of the gas,
(ν)
- arithmetic mean speed of molecules
λ
is the mean free path of the molecules.
Viscosity of some gases (at 0°C)
Fluid Viscosity
Fluid Viscosity- this is a property that manifests itself only when the fluid is in motion, and does not affect fluids at rest. Viscous friction in liquids obeys the law of friction, which is fundamentally different from the law of friction of solids, because depends on the area of friction and the velocity of the fluid.
Viscosity- the property of a liquid to resist the relative shear of its layers. Viscosity is manifested in the fact that with the relative movement of fluid layers on the surfaces of their contact, shear resistance forces arise, called internal friction forces, or viscosity forces. If we consider how the velocities of different layers of the liquid are distributed over the cross section of the flow, then we can easily see that the farther from the walls of the flow, the greater the speed of the particles. At the walls of the flow, the fluid velocity is zero. An illustration of this is the drawing of the so-called jet flow model.
A slowly moving fluid layer "slows down" the adjacent fluid layer moving faster, and vice versa, a layer moving at a higher speed drags (pulls) a layer moving at a lower speed along with it. Forces of internal friction appear due to the presence of intermolecular bonds between the moving layers. If a certain area is allocated between adjacent layers of the liquid S, then according to Newton's hypothesis:
F=μ S (du / dy),- μ - coefficient of viscous friction;
- S is the area of friction;
- du/dy- speed gradient
Value μ in this expression is dynamic viscosity coefficient, equal to:
μ= F / S 1 / du / dy , μ= τ 1/du/dy,- τ - shear stress in the liquid (depends on the type of liquid).
The physical meaning of the coefficient of viscous friction- a number equal to the friction force developing on a unit surface with a unit velocity gradient.
In practice, it is more often used kinematic viscosity coefficient, so named because its dimension lacks a force notation. This coefficient is the ratio of the dynamic coefficient of viscosity of the liquid to its density:
ν= μ / ρ ,Units of measurement of the coefficient of viscous friction:
- N·s/m 2 ;
- kgf s / m 2
- Pz (Poiseuille) 1 (Pz) \u003d 0.1 (N s / m 2).
Analysis of the Viscosity Property of a Fluid
For dropping liquids, the viscosity depends on the temperature t and pressure R, however, the latter dependence manifests itself only at large pressure changes, on the order of several tens of MPa.
The dependence of the dynamic viscosity coefficient on temperature is expressed by a formula of the form:
μ t \u003d μ 0 e -k t (T-T 0),- µt - coefficient of dynamic viscosity at a given temperature;
- μ 0 - coefficient of dynamic viscosity at a known temperature;
- T - set temperature;
- T 0 - temperature at which the value is measured μ 0 ;
- e
The dependence of the relative coefficient of dynamic viscosity on pressure is described by the formula:
μ p \u003d μ 0 e -k p (P-P 0),- μ R - coefficient of dynamic viscosity at a given pressure,
- μ 0 - coefficient of dynamic viscosity at a known pressure (most often under normal conditions),
- R - set pressure,;
- P 0 - pressure at which the value is measured μ 0 ;
- e - the base of the natural logarithm is 2.718282.
The influence of pressure on the viscosity of a liquid appears only at high pressures.
Newtonian and non-Newtonian fluids
Newtonian liquids are liquids for which the viscosity does not depend on the strain rate. In the Navier - Stokes equation for a Newtonian fluid, there is a viscosity law similar to the above (in fact, a generalization of Newton's law, or Navier's law).
The difference between viscous friction and dry friction is that it can vanish simultaneously with speed. Even with a small external force, a relative velocity can be imparted to the layers of a viscous medium.
Resistance force when moving in a viscous medium
Remark 1In addition to friction forces, when moving in liquid and gaseous media, resistance forces of the medium arise, which are much more significant than friction forces.
The behavior of liquid and gas in relation to the manifestations of friction forces do not differ. Therefore, the following characteristics apply to both states.
Definition 1
The action of the resistance force arising when a body moves in a viscous medium is due to its properties:
- lack of static friction, that is, the movement of a floating multi-ton ship with a rope;
- the dependence of the resistance force on the shape of the moving body, in other words, on its streamlining to reduce the resistance forces;
- dependence of the absolute value of the resistance force on the speed.
There are certain regularities to which the forces of friction and resistance of the medium are subject, with the symbolic designation of the total force as the force of friction. Its value depends on:
- body shape and size;
- the state of its surface;
- speed relative to the medium and its properties, called viscosity.
To depict the dependence of the friction force on the speed of the body with respect to the medium, use the graph of Figure 1.
Picture 1 . Graph of the dependence of the friction force on the speed in relation to the medium
If the value of the speed is small, then the drag force is directly proportional with respect to υ, and the friction force increases linearly with speed:
F t p \u003d - k 1 υ (1) .
The presence of a minus means the direction of the friction force in the opposite direction relative to the direction of speed.
At a large value of the speed, the transition from a linear law to a quadratic one occurs, that is, an increase in the friction force is proportional to the square of the speed:
F t p \u003d - k 2 υ 2 (2) .
If in the air the dependence of the resistance force on the square of the speed decreases, one speaks of speeds with values of several meters per second.
The value of friction coefficients k 1 and k 2 depends on the shape, size and condition of the body surface and the viscous properties of the medium.
Example 1
If we consider a protracted paratrooper jump, then its speed cannot constantly increase, at a certain moment its decline will begin, at which the resistance force will be equal to the force of gravity.
The value of the speed at which the law (1) makes the transition to (2) depends on the same reasons.
Example 2
There is a fall of two metal balls of different masses from the same height with the missing initial velocity. Which ball will fall faster?
Given: m 1 , m 2 , m 1 > m 2
Solution
During the fall, both bodies pick up speed. At a certain moment, the downward movement is carried out with a steady speed, at which the value of the resistance force (2) is equal to the force of gravity:
F t p \u003d k 2 υ 2 \u003d m g.
We get the steady speed by the formula:
υ 2 = m g k 2 .
Therefore, a heavy ball has a greater steady-state falling velocity than a light one. Therefore, reaching the earth's surface will happen faster.
Answer: a heavy ball will reach the ground faster.
Example 3
A skydiver flies at a speed of 35 m/s until the parachute opens, and after that - at a speed of 8 m/s. Determine the tension in the lines when the parachute opens. Paratrooper weight 65 kg, free fall acceleration 10 m/s 2 . Designate the proportionality of F tr relative to υ.
Given: m 1 \u003d 65 kg, υ 1 \u003d 35 m / s, υ 2 \u003d 8 m / s.
Find: T-?
Solution
Picture 2
Before opening, the parachutist had a speed υ 1 = 35 m / s, that is, his acceleration was zero.
According to Newton's second law, we get:
0 = m g - k υ 1 .
It's obvious that
After the parachute has opened, its υ changes and becomes equal to υ 2 = 8 m / s. From here, Newton's second law takes the form:
0 - m g - k υ 2 - T .
To find the tension force of the lines, it is necessary to convert the formula and substitute the values:
T \u003d m g 1 - υ 2 υ 1 ≈ 500 N.
Answer: T = 500 N.
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Interestingly, absolutely dry bodies are practically never found in nature. Under any conditions of maintenance of equipment, thin films of atmospheric precipitation, fats, etc. are formed on the surface of a solid substance. The friction between a solid body and a liquid or gas is called viscous or fluid friction.
Where does viscous friction occur?
Viscous friction occurs when solid bodies move in a liquid or gaseous medium, or when the liquid or gas itself flows past stationary solid bodies.
What is the cause of viscous friction?
The cause of viscous friction is internal friction.
If a solid body moves in a stationary medium, a layer of water or air adhering to it moves with it. At the same time, it slides along the adjacent layer. There is a friction force that entrains this layer.
It sets in motion and, in turn, drags the next layer, and so on. The farther from the surface of the body, the slower the layers of liquid or gas move. The force of friction between the layers slows down the faster layers and, therefore, the solid body itself. It is braked directly by viscous friction. The same thing happens when a stream of liquid or gas flows past a stationary body.
Interesting features of viscous friction!
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Pour some water into a bowl and dip a piece of wood into it. Blow on a chip - it will float on the water. And even if you blew weakly, the chip will still move from its place. The main difference between viscous friction and dry friction is that there is no viscous static friction!
No matter how small the traction force acting on the body, it immediately causes the body to move in the fluid. The smaller this force, the slower the body will swim.
What determines the force of friction in a liquid or gas?
The friction force experienced by a moving body, for example, in a liquid, depends on the speed of movement, on the shape and size of the body, and on the properties of the liquid.
At low speeds of movement, the resistance force is directly proportional to the speed of movement and the linear size of the body. Bodies experience the greater the force of resistance, the thicker (viscous) the medium will be. And liquids can be not viscous, like water, or very viscous, like honey. Water has a lower viscosity than glue, and glue has a lower viscosity than resin.
Viscosity depends on the temperature of the liquid.
For example, in winter, the engine of a car standing in the cold has to be warmed up.
This is done in order to warm the frozen oil poured into the engine.
The viscosity of the frozen oil is greater than that of the heated one, and the motor cannot rotate quickly.
Conversely, the viscosity of gases decreases with decreasing temperature.
As the speed of the body increases, the resistance of the medium changes. It depends on the nature of the flow around the body moving in it. At high speeds, a complex turbulent flow arises behind a moving body, bizarre figures, rings and vortices are formed.
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Turbulent resistance to motion already depends on the density of the medium, the square of the speed of the body and the size (squared) of the body. Turbulent drag decreases many times after giving a streamlined shape to a moving body. The best shape for a body moving in a liquid or gas column is blunt in front and sharp in back (for example, in dolphins and whales).
A long time ago...
Some ancient drawings found in the pyramids show Egyptians pouring milk under the runners of a sleigh on which they are dragging blocks of stone.
Traces of olive oil, which helped to reduce friction, were found in the piers of the well gates from the Bronze Age (5th century BC) that have come down to us.
What is a "lube"?
So they say about lubrication: "it goes like clockwork."
Where you have to deal with the sliding of dry surfaces, they try to make them wet, lubricate. Wheel hubs are smeared with tar or grease; oil is poured into the bearings, grease is stuffed. At power plants, there is even a special position of an oiler, pouring lubricant from the oiler into the rubbing parts. There are oilers on the railroad too. Thanks to lubrication, friction is reduced by 8–10 times.
What natural fluids are best for lubrication?
These are vegetable fats, butter, beef or lard, tar. But with the development of technology, other, cheaper lubricants were found - mineral oils obtained from oil refining.
As modern lubricants, one can name machine, aviation, diesel oils, grease, grease, technical vaseline, autol, nigrol, spindle oil, gun oil.
It turned out that the more massive a rotating part, for example, the thicker the lubricant should be. The heavy shafts of hydraulic turbines are lubricated with thick grease, and the running parts of pocket watches are lubricated with liquid and transparent bone oil. A good lubricant should be "oily". Then, when the machine stops, the thinnest layer of lubricant remains in the gap between the rubbing parts, and when the machine is started, it is not necessary to overcome static friction between completely dry surfaces. This reduces friction and wear of rubbing parts. During the operation of the machine, the lubricant heats up and partially loses its properties, therefore, special devices are used to cool the lubricant. And such lubricant mixtures have been created that work well even in very cold weather.
But the most common liquid in nature - water is rarely used as a lubricant. It has a low viscosity and, in addition, causes corrosion of many metals.
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Carelessness with fire is the main cause of fire for all structures.
But for windmills, which have now practically disappeared, one of the main causes of the fire was a strong wind, since with a strong wind their axis often caught fire from friction !!!
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If high pressure water is applied to a canvas fire hose, it may rupture. And if you take a tarpaulin stronger? American firefighters conducted such an experiment. The hose did not break, but when the water flow rate reached 100 liters per second, the hose caught fire from the friction of water against the canvas walls!
Interesting!
There is a fluid that increases friction. This is a goon!
When lubricating rubbing surfaces with a lubricant, dry friction is replaced by viscous friction and decreases.
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Liquids are a friction lubricant, but when pulling nails out of a wooden product that has been in the rain for a long time or in a damp place, you need to apply much more effort than when pulling out of a dry one! The fact is that the gaps between the particles of wood swollen with moisture increase, and the nail is more strongly compressed by the wood fibers, while the friction force increases.
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When a tidal wave moves along the ocean floor, frictional forces cause the Earth's rotation to slow down and the day to lengthen.
Viscous friction leads to the loss of mechanical energy of the moving body, because slows him down. But this does not mean that, for example, an airplane will be better to fly in a medium devoid of viscous friction. An airplane in such air will not be able to take off at all, because. the lift of its wing and the thrust of its propeller will be zero!
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The linear speed of a satellite moving in rarefied layers of the atmosphere increases due to air resistance! The paradox is explained by the fact that the radius of the orbit decreases and part of the potential energy of the satellite is converted into kinetic energy.
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For a ship with a displacement of about 35,000 tons and a length of about 180 m, the loss of friction against water at a stroke of 14 knots is approximately 75% of the total power, and the remaining 25% is spent on overcoming wave resistance. Interestingly, this last type of loss is significantly reduced when the body moves in a submerged position.
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Our atmosphere near the earth's surface is about 800 times less dense than water, but it can also create a huge counteract to movement. Thus, an ordinary train at a speed of 200 km/h spends about 70% of its total power on overcoming air resistance. Even with a well-streamlined shape, this figure does not drop below half of the total power.
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Already the first aircraft clearly felt the gigantic force of air resistance. And from that moment on, the reduction of drag due to better streamlining has become one of the main problems in the development of aviation. After all, friction against the air not only absorbs the energy of the engines, but also leads to dangerous overheating of the aircraft in dense layers of the atmosphere. But at the same time, the oncoming flow serves as one of the sources of aircraft lift.