An ideal fluid, i.e. fluid moving without friction is an abstract concept. All real liquids and gases, to a greater or lesser extent, have viscosity or internal friction. Viscosity (internal friction), along with diffusion and thermal conductivity, refers to transfer phenomena and is observed only in moving liquids and gases. Viscosity is manifested in the fact that the movement that occurs in a liquid or gas after the cessation of the causes that caused it, gradually stops.

Viscosity(internal friction) - one of the phenomena of transfer, the property of fluid bodies (liquids and gases) to resist the movement of one of their parts relative to another. As a result, the energy expended on this movement is dissipated in the form of heat.

The mechanism of internal friction in liquids and gases is that randomly moving molecules carry 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.

In liquids, where the distances between molecules are much smaller than in gases, viscosity is primarily due to intermolecular interactions that limit the mobility of molecules. In a liquid, a molecule can penetrate into an adjacent layer only if a cavity is formed in it, sufficient for the molecule to jump there. The so-called activation energy of a viscous flow is spent on the formation of a cavity (on the "loosening" of the liquid). The activation energy decreases with increasing temperature and decreasing pressure. This is one of the reasons for the sharp decrease in the viscosity of liquids with increasing temperature and its growth at high pressures. With an increase in pressure to several thousand atmospheres, the viscosity increases by tens and hundreds of times. A rigorous theory of the viscosity of liquids, due to the insufficient development of the theory of the liquid state, has not yet been created.

The viscosity of individual classes of liquids and solutions depends on temperature, pressure and chemical composition.

The viscosity of liquids depends on the chemical structure of their molecules. In the series of similar chemical compounds (saturated hydrocarbons, alcohols, organic acids, etc.) Viscosity changes regularly - it increases with increasing molecular weight. The high viscosity of lubricating oils is due to the presence of cycles in their molecules. Two liquids of different viscosities that do not react with each other when mixed have an average viscosity in the mixture. If, however, a chemical compound is formed during mixing, then the viscosity of the mixture can be tens of times greater than the viscosity of the initial liquids.


The appearance in liquids (dispersed systems or polymer solutions) of spatial structures formed by the adhesion of particles or macromolecules causes a sharp increase in viscosity. When a “structured” fluid flows, the work of an external force is expended not only to overcome the viscosity, but also to destroy the structure.

In gases, the distances between molecules are much greater than the radius of action of molecular forces; therefore, the viscosity of gases is determined mainly by molecular motion. Between layers of gas moving relative to each other, there is a constant exchange of molecules due to their continuous chaotic (thermal) movement. The transition of molecules from one layer to the next, moving at a different speed, leads to the transfer from layer to layer of a certain momentum. As a result, slower layers speed up and faster layers slow down. The work of an external force F, which balances the viscous resistance and maintains a steady flow, completely transforms into heat. The viscosity of a gas does not depend on its density (pressure), since when the gas is compressed, the total number of molecules passing from layer to layer increases, but each molecule penetrates less deeply into the neighboring layer and transfers less momentum (Maxwell's law).

Viscosity is an important physical and chemical characteristic of substances. The value of viscosity has to be taken into account when pumping liquids and gases through pipes (oil pipelines, gas pipelines). The viscosity of molten slag is very significant in the blast-furnace and open-hearth processes. The viscosity of the molten glass determines how it is made. In many cases, viscosity is used to judge the readiness or quality of products or semi-products of production, since viscosity is closely related to the structure of a substance and reflects those physical and chemical changes in the material that occur during technological processes. The viscosity of oils is of great importance for calculating the lubrication of machines and mechanisms, etc.

The device for measuring viscosity is called viscometer.

Consider another coordinate system: υ from X(Fig. 3.5).

Let in a gas at rest upward, perpendicular to the axis X, the plate moves with a speed υ 0, and (υ T is the speed of thermal motion of molecules). The plate carries along the adjacent layer of gas, that layer - the neighboring one, and so on. The whole gas is divided, as it were, into the thinnest layers, sliding upwards the slower, the farther they are from the plate. Since the layers of gas move at different speeds, friction occurs. Find out the cause of friction in the gas.


Rice. 3.5

Each gas molecule in the layer takes part in two motions: thermal and directional.

Since the direction of thermal motion changes randomly, on average the thermal velocity vector is equal to zero. With directed motion, the entire set of molecules will drift at a constant speed υ. Thus, the average momentum of an individual molecule with a mass m in the layer is determined only by the drift velocity υ:

But since the molecules are involved in thermal motion, they will move from layer to layer. At the same time, they will carry with them an additional momentum, which will be determined by the molecules of the layer where the molecule has passed. Mixing of molecules of different layers leads to equalization of the drift velocities of different layers, which manifests itself macroscopically as the action of friction forces between the layers.

Let's return to fig. 3.5 and consider the elementary area d S perpendicular to the axis X. Through this site in time d t flows of molecules pass to the left and to the right:

But these flows carry different momentum: and .

When momentum is transferred from layer to layer, the momentum of these layers changes. This means that each of these layers is affected by a force equal to the change in momentum. This power is nothing but friction force between layers of gas moving at different speeds. Hence the name - internal friction .

Viscosity law was discovered by I. Newton in 1687

Carried in time d t momentum is:

From here we obtain the force acting on the unit area of ​​the surface separating two adjacent layers of gas:

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= µ / 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 medium 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).

Internal friction occurs in a liquid due to the interaction of molecules. Unlike external friction that occurs at the point of contact between two bodies, internal friction takes place inside a moving medium between layers with different speeds.

At speeds above the critical speed, the layers close to the walls noticeably lag behind the middle layers due to friction, significant speed differences arise, which entails the formation of vortices.

So, viscosity, or internal friction in liquids, causes not only energy losses due to friction, but also new formations - vortices.

Newton found that the force of viscosity, or internal friction, should be proportional to the velocity gradient (a value showing how quickly the speed changes when moving from layer to layer in the direction perpendicular to the direction of movement of the layers) and the area on which the action of this force is detected. Thus, we arrive at Newton's formula:

, (I.149)

Where - viscosity coefficient, or internal friction, a constant number that characterizes a given liquid or gas.

To find out the physical meaning of , let's put in the formula (I.149) sec –1, m 2 ; then numerically ; hence, the viscosity coefficient is equal to the friction force, which arises in a liquid between two sites in m 2, if the velocity gradient between them is equal to one.

SI unit of dynamic viscosity = pascal - second (Pa s).

(Pa s) is equal to the dynamic viscosity of the medium in which, with a laminar flow and a velocity gradient with a modulus equal to (m / s) per (m), an internal friction force arises in (N) per (m 2) of the contact surface of the layers ( Pa s = N s / m 2).

The unit allowed for use until 1980: poise (P), named after the French scientist Poiseuille, who was one of the first (1842) to start accurate studies of viscosity during the flow of liquids in thin tubes (the ratio between units of dynamic viscosity: 1 P \u003d 0.1 Pa s)

Poiseuille, observing the movement of liquids in capillary tubes, brought law , Whereby:

, (I.150)

where is the volume of fluid flowing through the tube in time;

Tube radius (with smooth walls);

Pressure difference at the ends of the tube;

The duration of the flow of liquid;

Tube length.

The greater the viscosity, the greater the forces of internal friction appear in it. Viscosity depends on temperature, and the nature of this dependence for liquids and gases is different:

q dynamic viscosity of liquids decreases sharply with increasing temperature;

q the dynamic viscosity of gases increases with increasing temperature.

In addition to the concept of dynamic viscosity, the concepts fluidity And kinematic viscosity.

fluidity is called the reciprocal of dynamic viscosity.

The SI unit of fluidity \u003d m 2 / (N s) \u003d 1 / (Pa s).

Kinematic viscosity is the ratio of dynamic viscosity to the density of the medium.

The SI unit of kinematic viscosity is m2/s.

Until 1980, a unit was allowed for use: stokes (St). Relationship between units of kinematic viscosity:

1 stokes (St) \u003d 10 -4 m 2 / s.

When a spherical body moves in a fluid, it has to overcome the force of friction:

. (I.153)

Formula (I.153) is Stokes' law .

The determination of the viscosity of a liquid with a Goeppler viscometer is based on the Stokes law. A ball is lowered into a pipe of a certain diameter, filled with a liquid whose viscosity must be determined, and the speed of its fall is measured, which is a measure of the viscosity of the liquid.

The English scientist O. Reynolds in 1883, as a result of his research, came to the conclusion that the criterion characterizing the movement of liquids and gases can be numbers determined by a dimensionless set of quantities related to a given fluid and its given movement. The composition of these abstract numbers, called numbers Reynolds, such.

Viscosity (internal friction) - it is the property of real liquids to resist the movement of one part of the liquid relative to another. When some layers of a real fluid move relative to others, internal friction forces arise, directed tangentially to the surface of the layers. The action of these forces is manifested in the fact that from the side of the layer moving faster, the layer moving more slowly is affected by an accelerating force. From the side of the layer moving more slowly, the layer moving faster is affected by a retarding force.

Force of internal friction F the greater, the larger the considered area of ​​the surface of the layer S (Fig. 52), and depends on how quickly the fluid flow velocity changes during the transition from layer to layer.

The figure shows two layers spaced from each other at a distance x and moving with speeds v 1 and v 2 At the same time v 1 -v 2 = v. The direction in which the distance between the layers is counted, perpendicular layer flow rates. The value v/x shows how quickly the speed changes when moving from layer to layer in the direction X, perpendicular to the direction of motion of the layers, and is called speed gradient. Thus, the modulus of the force of internal friction

where is the coefficient of proportionality  , depending on the nature of the liquid is called dynamic viscosity(or simply viscosity).

The unit of viscosity is pascal second (Pa s): 1 Pa s is equal to the dynamic viscosity of the medium in which, with a laminar flow and a velocity gradient with a module equal to 1 m / s per 1 m, an internal friction force of 1 N per 1 m 2 of surface arises touching the layers (1 Pa s \u003d 1 N s / m 2).

The greater the viscosity, the more the liquid differs from the ideal one, the greater the forces of internal friction appear in it. Viscosity depends on temperature, and the nature of this dependence for liquids and gases is different (for liquids, m] decreases with increasing temperature, for gases, on the contrary, it increases), which indicates a difference in them

mechanisms of internal friction. The viscosity of oils is especially dependent on temperature. For example, the viscosity of castor oil in the range of 18-40 ° WITH falls four times. The Soviet physicist P. L. Kapitsa (1894-1984; Nobel Prize 1978) discovered that at a temperature of 2.17 K, liquid helium passes into a superfluid state in which its viscosity is zero.

There are two modes of fluid flow. The current is called laminar (layered), if along the flow each selected thin layer slides relative to its neighbors without mixing with them, and turbulent (vortex), if intensive vortex formation and liquid (gas) mixing occur along the flow.

The laminar flow of a liquid is observed at low velocities of its movement. The outer layer of liquid adjacent to the surface of the pipe in which it flows, due to the forces of molecular cohesion, sticks to it and remains immobile. The velocities of subsequent layers are the greater, the greater their distance from the pipe surface, and the layer moving along the pipe axis has the highest speed.

In turbulent flow, fluid particles acquire velocity components perpendicular to the flow, so they can move from one layer to another. The velocity of liquid particles increases rapidly as they move away from the pipe surface, then changes quite slightly. Since the particles of the liquid pass from one layer to another, their velocities in different layers differ little. Due to the large gradient

velocities, vortices usually form near the pipe surface.

The average velocity profile for turbulent flow in pipes (Fig. 53) differs from the parabolic profile for laminar flow by a faster increase in velocity near the pipe walls and less curvature in the central part of the flow.

The English scientist O. Reynolds (1842-1912) in 1883 established that the nature of the flow depends on a dimensionless quantity called Reynolds number:

where v = / - kinematic viscosity;

 - liquid density; (v) is the fluid velocity averaged over the pipe section; d- characteristic linear dimension, such as pipe diameter.

At low values ​​of the Reynolds number (Re1000), a laminar flow is observed, the transition from laminar to turbulent flow occurs in the region of 1000: Re2000, and at Re = 2300 (for smooth pipes) the flow is turbulent. If the Reynolds number is the same, then the flow regime of various liquids (gases) in pipes of different sections is the same.