Unit kinematic viscosity. What is liquid viscosity
The viscosity of a liquid can be measured in several ways using devices called viscometers. Such devices measure the time it takes a substance to move or the time it takes an object of a given size and density to pass through a liquid. The units for this parameter are Pascal squared.
Factors affecting viscosity
In general, liquids composed of larger molecules will have higher viscosity. This is especially true for long chain substances that are polymers or heavier hydrocarbon compounds. Such molecules tend to overlap each other, preventing movement through them.
Another important factor is how the molecules interact with each other. Polar compounds can form hydrogen bonds, which hold individual molecules together, increasing the overall resistance to flow or movement. Although the water molecule is polar, it has low viscosity due to the fact that its molecules are quite small. The most viscous liquids tend to be those that have stretched molecules or strong polarity. Examples include glycerin and propylene glycol.
Temperature has a great influence on viscosity. Measurements of liquid properties are always given as a function of temperature. In liquids, viscosity decreases with increasing temperature. This can be seen when heating syrup or honey. This happens because the molecules move faster and therefore spend less time in contact with each other. The viscosity of gases, on the contrary, increases with increasing temperature. This happens because the molecules move faster and there are more collisions between them. This increases the flux density.
Importance to industry
Crude oil often travels long distances between regions of different temperatures. Therefore, the flow rate and pressure changes over time. The oil that flows through Siberia is more viscous in the Persian Gulf pipelines. Due to differences in ambient temperature, the pressure in the pipes must also be different in order to force it to flow. To solve this problem, a special oil is first poured into the pipes, which has a practically zero coefficient of internal resistance. In this way, the contact of oil with the inner surface of the pipes is limited. Oil viscosity also changes with temperature changes. To improve its characteristics, polymers are added to the oil to prevent it from thickening and mixing.
Viscosity characterizes the ability of gases or liquids to create resistance between layers of fluid (not solid) bodies moving relative to each other. That is, this value corresponds to the force of internal friction (English term: viscosity) that occurs when a gas or liquid moves. It will be different for different bodies, as it depends on their nature. For example, water has a low viscosity compared to honey, which has a much higher viscosity. Internal friction or fluidity of solid (loose) substances is characterized by
The word viscosity comes from the Latin word Viscum, which means mistletoe. This is due to bird glue, which was made from mistletoe berries and used to catch birds. Tree branches were smeared with an adhesive substance, and birds, sitting on them, became easy prey for humans.
What is viscosity? The units of measurement of this characteristic will be given, as is customary, in, as well as in other non-system units.
Isaac Newton in 1687 established the basic law of flow of liquid and gaseous bodies: F = ƞ. ((v2 - v1) / (z2 - z1)) . S. In this case, F is the force (tangential) that causes a shift in the layers of the moving body. The ratio (v2 - v1) / (z2 - z1) shows the rate of change in the flow rate of a liquid or gas during the transition from one moving layer to another. Otherwise called flow velocity gradient or shear velocity. The value S is the area (in cross section) of the flow of the moving body. The proportionality coefficient ƞ is the dynamic of a given body. Its reciprocal quantity j = 1 / ƞ is fluidity. The force acting per unit area (cross section) of the flow can be calculated using the formula: µ = F / S. This is the absolute or dynamic viscosity. Its SI units are expressed as pascals per second.
Viscosity is the most important physicochemical characteristic of many substances. Its significance is taken into account when designing and operating pipelines and apparatus in which movement occurs (for example, if they are used for pumping) of a liquid or gaseous medium. This can be oil, gas or their products, molten slag or glass, etc. Viscosity in many cases is a qualitative characteristic of intermediates and finished products of various industries, since it directly depends on the structure of the substance and shows the physical and chemical state of the material and changes occurring in technology. Often, to estimate the value of resistance to deformation or flow, not dynamic, but kinematic viscosity is used, the units of measurement of which in the SI system are expressed in square meters per second. Kinematic viscosity (denoted by ν) is the ratio of dynamic viscosity (µ) to the density of the medium (ρ): v = µ / ρ.
Kinematic viscosity is a physical and chemical characteristic of a material, showing its ability to resist flow under the influence of gravity.
In the SI system, the units of kinematic viscosity are written as m 2 /s.
In the GHS system, viscosity is measured in Stokes (St) or centistokes (cSt).
The following relationship exists between these units of measurement: 1 St = 10 -4 m 2 /s, then 1 cSt = 10 -2 St = 10 -6 m 2 /s = 1 mm 2 /s. Often, another non-systemic unit of measurement is used for kinematic viscosity - these are Engler degrees, the conversion of which to Stokes can be carried out using the empirical formula: v = 0.073oE - 0.063 / oE or according to the table.
To convert system units of dynamic viscosity into non-system units, you can use the equation: 1 Pa. s = 10 poise. The short designation is written: P.
Typically, the units of measurement of liquid viscosity are regulated by regulatory documentation for the finished (commercial) product or for the intermediate product, along with the permissible range of variation of this qualitative characteristic, as well as the error of its measurement.
To determine viscosity in laboratory or production conditions, viscometers of various designs are used. They can be rotary, with a ball, capillary, ultrasonic. The principle of measuring viscosity in a glass capillary viscometer is based on determining the flow time of liquid through a calibrated capillary of a certain diameter and length, while the viscometer constant must be taken into account. Since the viscosity of a material depends on temperature (as it increases, it will decrease, which is explained by molecular kinetic theory as a result of the acceleration of chaotic movement and interaction of molecules), therefore, the test sample must be kept for some time at a certain temperature to average the latter over the entire volume of the sample. There are several standardized methods for testing viscosity, but the most common is the interstate standard GOST 33-2000, on the basis of which kinematic viscosity is determined, the units of measurement in this case are mm 2 / s (cSt), and dynamic viscosity is recalculated as the product of kinematic viscosity and density .
DEFINITION
Viscosity called one of the types of transfer phenomena. It is associated with the property of fluid substances (gases and liquids) to resist the movement of one layer relative to another. This phenomenon is caused by the movement of particles that make up matter.
There are dynamic viscosity and kinematic viscosity.
Let us consider the movement of a gas with viscosity as the movement of flat parallel layers. We will assume that the change in the speed of movement of the substance occurs in the direction of the X axis, which is perpendicular to the direction of the speed of gas movement (Fig. 1).
In the direction of the Y axis, the speed of movement at all points is the same. This means that speed is a function of . In this case, the modulus of the friction force between the gas layers (F), which acts per unit surface area that separates two adjacent layers, is described by the equation:
where is the velocity gradient () along the X axis. The X axis is perpendicular to the direction of movement of the layers of matter (Fig. 1).
Definition
The coefficient () included in equation (1) is called the coefficient of dynamic viscosity (coefficient of internal friction). It depends on the properties of the gas (liquid). is numerically equal to the amount of motion that is transferred per unit time through a platform of unit area with a velocity gradient equal to unity, in a direction perpendicular to the site. Or is numerically equal to the force that acts per unit area with a velocity gradient equal to unity.
Internal friction is the reason why a pressure difference is required for gas (liquid) to flow through a pipe. In this case, the higher the viscosity coefficient of the substance, the greater the pressure difference must be to impart a given flow speed.
The coefficient of kinematic viscosity is usually denoted by . It is equal to:
where is the gas (liquid) density.
Gas internal friction coefficient
In accordance with the kinetic theory of gases, the viscosity coefficient can be calculated using the formula:
where is the average speed of thermal motion of gas molecules, and is the average free path of a molecule. Expression (3) shows that at low pressure (rarefied gas) viscosity is almost independent of pressure, since 
But this conclusion is valid until the ratio of the free path of the molecule to the linear dimensions of the vessel becomes approximately equal to unity. With increasing temperature, the viscosity of gases usually increases, since
Liquid viscosity coefficient
Assuming that the viscosity coefficient is determined by the interaction forces between the molecules of a substance, which depend on the average distance between them, the viscosity coefficient is determined by the experimental Baczynski formula:
where is the molar volume of the liquid, A and B are constants.
The viscosity of liquids decreases with increasing temperature and increases with increasing pressure.
Poiseuille's formula
The viscosity coefficient is included in the formula that establishes the relationship between the volume (V) of gas that flows per unit time through the pipe section and the pressure difference required for this ():
where is the length of the pipe, is the radius of the pipe.
Reynolds number
The nature of gas (liquid) movement is determined by the dimensionless Reynolds number ():
Viscosity Coefficient Units
The basic unit of measurement for the coefficient of dynamic viscosity in the SI system is:
1Pa c=10 poise
The basic unit of measurement for the coefficient of kinematic viscosity in the SI system is:
Examples of problem solving
EXAMPLE 1
| Exercise | Dynamically, the viscosity of water is equal to Pa s. What is the maximum diameter of the pipe that will allow the water flow to remain laminar if in 1 s a volume of water flows out through the cross section equal to ? |
| Solution | The condition for laminarity of fluid flow has the form: Where we find the Reynolds number using the formula:
We find the speed of water flow as: In expression (1.3) is the height of a water cylinder having a volume: According to the condition = 1 s. Substituting speed (1.4) into the expression for the Reynolds number, we have: Density of water at no. kg/m3. Let's carry out the calculations and get: |
| Answer | m |
EXAMPLE 2
| Exercise | A ball of density and diameter d floats up in a liquid of density with a speed of . What is the kinematic viscosity of the fluid? |
| Solution | Let's make a drawing. |
Viscosity is the most important physical constant that characterizes the performance properties of boiler and diesel fuels, petroleum oils, and a number of other petroleum products. The viscosity value is used to judge the possibility of atomization and pumpability of oil and petroleum products.
There are dynamic, kinematic, conditional and effective (structural) viscosity.
Dynamic (absolute) viscosity [μ ], or internal friction, is the property of real fluids to resist shearing tangential forces.
Obviously, this property manifests itself when the fluid moves. Dynamic viscosity in the SI system is measured in [N·s/m2]. This is the resistance that a liquid exhibits during the relative movement of its two layers with a surface of 1 m2, located at a distance of 1 m from each other and moving under the influence of an external force of 1 N at a speed of 1 m/s. Given that 1 N/m 2 = 1 Pa, dynamic viscosity is often expressed in [Pa s] or [mPa s]. In the CGS system (CGS), the dimension of dynamic viscosity is [dyn s/m 2 ]. This unit is called poise (1 P = 0.1 Pa s). μ Conversion factors for calculating dynamic [
| ] viscosity. | Units | Micropoise (mcP) | Centipoise (sp) | Poise ([g/cm s]) | Pa s ([kg/m s]) | kg/(m h) |
| Units | 1 | 10 -4 | 10 -6 | 10 7 | kg s/m 2 | 3.6·10 -4 |
| Micropoise (mcP) | 10 4 | 1 | 10 -2 | 10 -3 | 3,6 | 1.02·10 -8 |
| Centipoise (sp) | 10 6 | 10 2 | 1 | 10 3 | 1.02·10 -4 | 3.6 10 2 |
| Poise ([g/cm s]) | 10 7 | 10 3 | 10 | 1 3 | 1.02·10 -2 | 3.6 10 3 |
| Pa s ([kg/m s]) | 1.02·10 -1 | 2.78 10 3 | 2.78·10 -1 | 2.78·10 -3 | 1 | 2.78·10 -4 |
| kg/(m h) | 2.84·10 -3 | 9.81 10 7 | 9.81 10 3 | 9.81 10 2 | 9.81 10 1 | 1 |
3.53 10 4 [ν Kinematic viscosity μ ] is a quantity equal to the ratio of the dynamic viscosity of the liquid [ ρ ] at the same temperature: ν = μ/ρ. The unit of kinematic viscosity is [m 2 /s] - the kinematic viscosity of such a liquid, the dynamic viscosity of which is 1 N s / m 2 and the density is 1 kg / m 3 (N = kg m / s 2). In the CGS system, kinematic viscosity is expressed in [cm 2 /s]. This unit is called Stokes (1 Stokes = 10 -4 m 2 /s; 1 cSt = 1 mm 2 /s).
Conversion factors for calculating kinematic [ ν Conversion factors for calculating dynamic [
| ] viscosity. | mm 2 /s (cSt) | cm 2 /s (St) | m 2 /s | m 2 /h |
| mm 2 /s (cSt) | 1 | 10 -2 | 10 -6 | 3.6·10 -3 |
| cm 2 /s (St) | 10 2 | 1 | 10 -4 | 0,36 |
| m 2 /s | 10 6 | 10 4 | 1 | 1.02·10 -2 |
| m 2 /h | 2.78 10 2 | 2,78 | 2.78 10 4 | 1 |
Oils and petroleum products are often characterized conditional viscosity, which is taken to be the ratio of the flow time of 200 ml of petroleum product through the calibrated hole of a standard viscometer at a certain temperature [ t] by the time 200 ml of distilled water has flowed at a temperature of 20°C. Conditional viscosity at temperature [ t] is indicated by the sign ВУ, and is expressed by the number of conventional degrees.
Conditional viscosity is measured in degrees VU (°VU) (if the test is carried out in a standard viscometer according to GOST 6258-85), Saybolt seconds and Redwood seconds (if the test is carried out on Saybolt and Redwood viscometers).
You can convert viscosity from one system to another using a nomogram.
In petroleum dispersed systems under certain conditions, unlike Newtonian liquids, viscosity is a variable value depending on the shear rate gradient. In these cases, oils and petroleum products are characterized by effective or structural viscosity:
For hydrocarbons, viscosity depends significantly on their chemical composition: it increases with increasing molecular weight and boiling point. The presence of side branches in the molecules of alkanes and naphthenes and an increase in the number of cycles also increase viscosity. For different groups of hydrocarbons, viscosity increases in the series alkanes - arenes - cyclanes.
To determine viscosity, special standard instruments are used - viscometers, which differ in their operating principle.
Kinematic viscosity is determined for relatively low-viscosity light petroleum products and oils using capillary viscometers, the action of which is based on the fluidity of the liquid through the capillary in accordance with GOST 33-2000 and GOST 1929-87 (viscometer type VPZh, Pinkevich, etc.).
For viscous petroleum products, the relative viscosity is measured in viscometers such as VU, Engler, etc. The liquid flows out of these viscometers through a calibrated hole in accordance with GOST 6258-85.
There is an empirical relationship between the values of conditional °VV and kinematic viscosity:
The viscosity of the most viscous, structured petroleum products is determined on a rotational viscometer according to GOST 1929-87. The method is based on measuring the force required to rotate the inner cylinder relative to the outer one when filling the space between them with the test liquid at a temperature t.
In addition to standard methods for determining viscosity, sometimes in research works non-standard methods are used, based on measuring viscosity by the time of falling of a calibration ball between marks or by the time of damping of vibrations of a solid body in the test liquid (Heppler, Gurvich viscometers, etc.).
In all the described standard methods, viscosity is determined at a strictly constant temperature, since with its change the viscosity changes significantly.
Dependence of viscosity on temperature
The dependence of the viscosity of petroleum products on temperature is a very important characteristic both in oil refining technology (pumping, heat exchange, sedimentation, etc.) and in the use of commercial petroleum products (draining, pumping, filtering, lubrication of rubbing surfaces, etc.).
As the temperature decreases, their viscosity increases. The figure shows curves of changes in viscosity depending on temperature for various lubricating oils.
Common to all oil samples is the presence of temperature regions in which a sharp increase in viscosity occurs.
There are many different formulas for calculating viscosity depending on temperature, but the most commonly used is Walther's empirical formula:
Taking the logarithm of this expression twice, we get:
Using this equation, E. G. Semenido compiled a nomogram on the abscissa axis of which, for ease of use, temperature is plotted, and viscosity is plotted on the ordinate axis.
Using the nomogram, you can find the viscosity of a petroleum product at any given temperature if its viscosity at two other temperatures is known. In this case, the value of the known viscosities is connected by a straight line and continued until it intersects with the temperature line. The point of intersection with it corresponds to the desired viscosity. The nomogram is suitable for determining the viscosity of all types of liquid petroleum products.
For petroleum lubricating oils, it is very important during operation that the viscosity depends as little as possible on temperature, since this ensures good lubricating properties of the oil over a wide temperature range, i.e., in accordance with the Walther formula, this means that for lubricating oils, the lower the coefficient B, the higher the quality of the oil. This property of oils is called viscosity index, which is a function of the chemical composition of the oil. For different hydrocarbons, viscosity changes differently with temperature. The steepest dependence (large value of B) is for aromatic hydrocarbons, and the smallest for alkanes. Naphthenic hydrocarbons in this respect are close to alkanes.
There are various methods for determining the viscosity index (VI).
In Russia, IV is determined by two values of kinematic viscosity at 50 and 100°C (or at 40 and 100°C - according to a special table of the State Committee of Standards).
When certifying oils, IV is calculated according to GOST 25371-97, which provides for determining this value by viscosity at 40 and 100°C. According to this method, according to GOST (for oils with VI less than 100), the viscosity index is determined by the formula:
For all oils with ν 100 ν, ν 1 And ν 3) are determined according to the GOST 25371-97 table based on ν 40 And ν 100 of this oil. If the oil is more viscous ( ν 100> 70 mm 2 /s), then the values included in the formula are determined using special formulas given in the standard.
It is much easier to determine the viscosity index using nomograms.
An even more convenient nomogram for finding the viscosity index was developed by G.V. Vinogradov. Determining IV is reduced to connecting known viscosity values at two temperatures with straight lines. The intersection point of these lines corresponds to the desired viscosity index.
Viscosity index is a generally accepted value included in oil standards in all countries of the world. The disadvantage of the viscosity index is that it characterizes the behavior of the oil only in the temperature range from 37.8 to 98.8 ° C.
Many researchers have noted that the density and viscosity of lubricating oils to some extent reflect their hydrocarbon composition. A corresponding indicator was proposed linking the density and viscosity of oils and called the viscosity-mass constant (VMC). The viscosity-mass constant can be calculated using the formula of Yu. A. Pinkevich:
Depending on the chemical composition of the VMC oil, it can be from 0.75 to 0.90, and the higher the VMC of the oil, the lower its viscosity index.
At low temperatures, lubricating oils acquire a structure that is characterized by the yield strength, plasticity, thixotropy or viscosity anomaly characteristic of dispersed systems.
The results of determining the viscosity of such oils depend on their preliminary mechanical mixing, as well as on the flow rate or both factors simultaneously. Structured oils, like other structured petroleum systems, do not obey the law of Newtonian fluid flow, according to which the change in viscosity should depend only on temperature. Oil with an intact structure has a significantly higher viscosity than after its destruction. If you reduce the viscosity of such an oil by destroying the structure, then in a calm state this structure will be restored and the viscosity will return to its original value. The ability of a system to spontaneously restore its structure is called thixotropy
. With an increase in the flow speed, or more precisely the speed gradient (section of curve 1), the structure is destroyed, and therefore the viscosity of the substance decreases and reaches a certain minimum. This minimum viscosity remains at the same level with a subsequent increase in the velocity gradient (section 2) until a turbulent flow appears, after which the viscosity increases again (section 3).
Dependence of viscosity on pressure
The viscosity of liquids, including petroleum products, depends on external pressure. The change in oil viscosity with increasing pressure is of great practical importance, since high pressures can arise in some friction units. The dependence of viscosity on pressure for some oils is illustrated by curves; the viscosity of oils changes parabolically with increasing pressure. Under pressure R
it can be expressed by the formula:
In petroleum oils, the viscosity of paraffin hydrocarbons changes least with increasing pressure, and naphthenic and aromatic hydrocarbons change slightly more. The viscosity of high-viscosity petroleum products increases with increasing pressure more than the viscosity of low-viscosity petroleum products. The higher the temperature, the less the viscosity changes with increasing pressure.
At pressures of the order of 500 - 1000 MPa, the viscosity of oils increases so much that they lose the properties of a liquid and turn into a plastic mass.
To determine the viscosity of petroleum products at high pressure, D.E. Mapston proposed the formula: ν 0 And The dependence of viscosity on pressure for some oils is illustrated by curves; the viscosity of oils changes parabolically with increasing pressure. Under pressure Based on this equation, D.E. Mapston developed a nomogram, using which known values, for example
Viscosity of mixtures
When compounding oils, it is often necessary to determine the viscosity of mixtures. As experiments have shown, additivity of properties manifests itself only in mixtures of two components that are very close in viscosity. When there is a large difference in the viscosities of the petroleum products being mixed, the viscosity is usually less than that calculated by the mixing rule. The viscosity of an oil mixture can be approximately calculated by replacing the viscosities of the components with their reciprocal values - mobility (fluidity) ψ cm:
To determine the viscosity of mixtures, you can also use various nomograms. The most widely used are the ASTM nomogram and the Molina-Gurvich viscosigram. The ASTM nomogram is based on the Walther formula. The Molina-Gurevich nomogram was compiled on the basis of the experimentally found viscosities of a mixture of oils A and B, of which A has a viscosity °ВУ 20 = 1.5, and B has a viscosity °ВУ 20 = 60. Both oils were mixed in different ratios from 0 to 100% (vol.), and the viscosity of the mixtures was established experimentally. The nomogram shows the viscosity values in el. units and in mm 2 /s.
Viscosity of gases and oil vapors
The viscosity of hydrocarbon gases and oil vapors is subject to different laws than for liquids. With increasing temperature, the viscosity of gases increases. This pattern is satisfactorily described by the Sutherland formula:
Viscosity forces are tangential forces, that is, they are directed along the contact surface of the liquid layers.
Physical meaning of the viscosity coefficient: the viscosity coefficient is numerically equal to the force of internal friction arising between two layers of fluid per unit area required to maintain a velocity gradient equal to one.
With S = 1 area unit, = 1, h = F
Viscosity coefficient units:
SI: 
(Pascal second)
1 Pas is the viscosity of a liquid in which, with a velocity gradient equal to unity, a force equal to 1 N acts on each square meter of contact area between the layers.
In medicine, viscosity is expressed in poises.
1 Pass = 10 P (poise) = 10 3 cP (centipoise)
The viscosity coefficient depends on:
1. by nature liquid,
2. on temperature: with increasing temperature, the viscosity of a liquid decreases, for gases it increases.
Liquids are distinguished:
1. Newtonian– these are liquids whose viscosity coefficient does not depend on the velocity gradient (shear rate). The viscosity coefficient of Newtonian liquids depends only on its nature and temperature. They obey Newton's linear law, that is, they are a continuous, homogeneous and isotropic medium. Thus, the viscosity of lymph and blood plasma is well described by Newton’s equation. This is normal viscosity.
2. Non-Newtonian- rheologically more complex liquids, in which the viscosity coefficient depends on the velocity gradient (on the shear rate), i.e. on fluid flow conditions. The viscosity coefficient in this case is not a constant of the substance. They have nonlinear properties. These include high-molecular compounds, such as solutions, polymers, suspensions, emulsions, systems of biological origin: blood, synovial fluid. The viscosity of non-Newtonian fluids depends on a number of kinematic and dynamic parameters. This is abnormal viscosity. Non-Newtonian rheological properties of blood change velocity profiles in the channels of extracorporeal devices.
2.POISEUILLE FORMULA expresses the volume of liquid flowing through a capillary, which depends on the capillary radius, viscosity coefficient, pressure gradient and flow time of the liquid:
- the formula is valid for laminar fluid flow, where r is the cross-sectional radius of the capillary
Capillary length
DP = P in – P out – pressure difference at the ends of the capillary
grad P = - pressure gradient
t – fluid flow time
To calculate the flow of liquid in a vessel, an important characteristic is the volumetric flow rate, in particular blood.
Volume velocity – this is a quantity numerically equal to the volume of liquid flowing per unit time through a given section of the pipe.
The volumetric velocity of a liquid is expressed by the formula Q =
Unit m³/s
For a stationary laminar flow of a real fluid in a cylindrical pipe of constant cross-section, Poiseuille’s formula takes the form:
According to this formula, the volumetric velocity of the liquid is proportional to the pressure drop per unit length of the pipe, the fourth power of the pipe radius, and inversely proportional to the viscosity coefficient.
For pipes of variable cross-section, Poiseuille’s formula has the form
Hydraulic resistance is expressed by the formula: 
Then the volumetric velocity of the liquid can be represented as:
The drop in fluid pressure (in particular blood) depends on the volumetric velocity and significantly on the radius of the vessel, expressed by the formula: DP = Q∙R hydr .
3. STOKES FORMULA expresses the resistance force when a body moves in a liquid, which slows down its movement and is directed in the direction opposite to the speed of the body relative to the medium.
The resistance force when moving bodies in a liquid depends on:
1) on body shape
2) on body size
3) on the viscosity coefficient
4) on the speed of movement of the body
The general pattern of Stokes' law is expressed by the formula:
where p and k are a numerical coefficient that determines the geometric shape of the body.
