# Fluid viscosity

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Viscosity, internal friction - the property of liquids and gases to resist the movement of one layer relative to another. The viscosity of liquids is most easily detected by transfusion or stirring.

Quantitatively, viscosity is characterized by a value called dynamic viscosity or internal friction coefficient and denoted by n or u. A characteristic feature of this type of friction is that it is observed not at the boundary of a solid and a liquid, but in the entire volume of the liquid.

The unit of dynamic viscosity in the International System of Units (SI) is pascal second (Pa * s). Pascal second is equal to the dynamic viscosity of the medium, in which the shear stress for a laminar (ordered) flow and for a difference in the velocities of the layers at a distance of 1 m normal to the velocity direction equal to 1 m / s is 1 Pa.

Kinematic viscosity is equal to the ratio of the dynamic viscosity of the medium to its density at the same temperature:

SI unit of kinematic viscosity is square meter per second (m2 / s). At a kinematic viscosity of 1 m2 / s, the dynamic viscosity of a medium with a density of 1 kg / m3 is 1 Pa * s.

Often, they also use the value of relative, or conditional, viscosity (VU) - the ratio of the viscosity of a given liquid to the viscosity of water at the same temperature (see below).

A wide range of viscosity values, as well as the need to measure viscosity at low or high temperatures and pressures, leads to a wide variety of methods for determining the viscosity and design of viscometers.

## Types of Viscometers

Depending on the measurement method, viscometers are divided into capillary (expiration viscometers), ball, rotational, vibration and ultrasound.

When using capillary viscometers, the time of the expiration of a known amount (volume) of liquid through capillary tubes of a certain diameter is measured. Glass capillary viscometers are most often used in the practice of chemical laboratories.

When using ball viscometers, the speed of the ball falling in the test liquid is measured - it is the smaller, the higher the viscosity of the liquid.

Rotational viscometers measure the torque or angular velocity of rotation of one of the two coaxial bodies, in the gap between which is the test fluid. The viscosity measurement range is 0.5-1000000 Pa * s. They are widely used to determine the viscosity of high molecular weight liquids and solutions of polymer compounds.

Measurement of viscosity by vibrating viscometers is based on the dependence of the amplitude of body vibrations in the test fluid on its viscosity.

Ultrasonic viscometers measure the attenuation rate of the oscillations of the magnetostrictive material placed in the test fluid.

Regardless of the design of the viscometer, the determination of viscosity should be carried out under strict temperature control.

## Glass Capillary Viscometers

Viscometers VPZh-1, VPZh-2, such as Pinkevich, VPZhM, and for opaque liquids, are used to measure the viscosity of transparent liquids.

The kinematic viscosity of the liquid v is equal to the product of the time t flowing out through the capillary of a certain volume thereof and the constant of the viscometer C. The constant C is independent of temperature and is determined only by the geometric dimensions of the viscometer.

Reference liquids with known kinematic viscosity are used to determine the viscometer constant. By measuring the expiration time of a certain volume of the reference liquid, the constant of the viscometer is determined:

Viscometers are available with different capillaries, and the diameter of the capillary dramatically affects the constant of the viscometer. Each set contains nine viscometers, the diameters of the internal capillaries of which vary from 0.34-5.5 mm, which corresponds to C = 0.003-30 cSt / s. The set of viscometers of the Pinkiewicz type consists of 11 viscometers with capillary diameters from 0.4 to 4.0 mm.

Freshly distilled distilled water, the kinematic viscosity of which is assumed to be 1.0067 cSt / s at 20 ° C and 0.89748 cSt / s at 25 ° C, can serve as a reference liquid for calibrating viscometers for low-viscosity liquids.

According to the existing situation, each factory-made capillary viscometer should be equipped with a passport in which its constant is indicated. So, viscometers VPZh-1, VPZh-2, VNZh are available with a constant value of C: 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10 and 30 cSt / s. The constant of viscometer type VPMZh is 0.01, 0.03, 0.1, 0.3, 1 and 3 cSt / s.

### Viscometer Calibration

New viscometers, as well as viscometers that have been in operation for a long time, should be periodically subjected to verification calibration.

Calibration consists in determining the flow time through the viscometer of the reference fluid. Before performing work, the viscometer is washed sequentially with petroleum ether, a chromium mixture, tap and distilled water, alcohol and diethyl ether, and then purged with clean, dry air.

Let the VPZh-1 type viscometer be selected for calibration. A rubber hose connected to the bulb is put on the outlet pipe 3, and, holding the knee 2 with the finger, turn the viscometer over, lower the knee 1 hole into the vessel with the reference liquid, suck it into the viscometer using a rubber bulb or a water-jet pump to the M2 mark, making sure so that in the extensions 4 and 5 there are no liquid breaks. Then the elbow 1 is removed from the liquid and remove the hose from the outlet pipe 3.

A rubber tube is put on knee 1, the viscometer is immersed in a liquid thermostat so that the extension 4 is in the liquid, and strengthened strictly vertically with a clamp on a tripod. A thermometer is strengthened with another clamp, the ball of which should be at the same level with the middle of capillary 6. The temperature is set at 20 ± 0.2 ° C in the thermostat and the viscometer is kept at this temperature for 10-15 minutes.

Then, with a pear or pump attached to the rubber tube, the liquid is sucked into the elbow 1 to about 1/3 of its height, making sure that no breaks in the liquid or air bubbles form. Having stopped the suction, the liquid is allowed to drain into expansion 5 and the lowering of the liquid level is observed. As soon as the level of the escaping liquid touches the mark M1, the stopwatch is switched on, when the liquid level touches the mark M2, the stopwatch is stopped. Having recorded the time of fluid expiration, the determination is repeated at least four times. Then the viscometer is washed, dried, re-filled with a reference liquid and again made at least four determinations.

If the difference between the average time of two experiments does not exceed 0.3%, then find the arithmetic average of the time t of the reference fluid in both experiments and calculate the constant of the viscometer:

### Determination

The flow time through the viscometer of the test fluid is determined in the same way as when calibrated with the reference. It should only be kept in mind that the preliminary exposure time of the viscometer with the test substance in the thermostat should be increased with increasing temperature of the test (from 10 min at 20 ° C to 20 min at 100 ° C).

The arithmetic mean of the time of fluid outflow in a viscometer is determined with an accuracy of 0.1 s and the kinematic viscosity (in centistokes) is calculated by the formula:

where C is the constant of the viscometer, cSt / s, t is the arithmetic mean time of fluid flow, s, g is the acceleration of gravity at the point of viscosity measurement, cm / s2 (g / 980.7 = 1 can be taken if the additional error is 0.02 % does not matter), K is the coefficient taking into account the change in the hydrostatic pressure of the liquid as a result of its expansion when heated, for VPZh-1 K = 1, for VPZh-2 and VPZh-4 K = 1 ± 0.00004 dt, for residence permit K = 1 ± 0.000087 dt, for VPZHM K = 1 ± 0.000074 dt (dt - the difference between the temperature of the liquid when filling the viscometer and when determining the viscosity).

## Determination of the dynamic viscosity of dilute polymer solutions (according to GOST 18249-72)

The concentration of the polymer solution is chosen so that the ratio of the time of expiration of the solution t to the time of expiration of the solvent is 1.2-1.6. In accordance with this, a viscometer is selected.

The size of the polymer sample, the choice of solvent, its volume and dissolution conditions are indicated in the standards or specifications for the polymer.

When determining viscosity, viscosimeters of type VPZh-2 prepare solutions of four concentrations, and viscosimeters of VPZh-1 of one concentration; solutions of lower concentrations are obtained by dilution in the viscometer itself. To do this, 13-16 ml of the solution is poured into the viscometer, the expiration time is measured, after which the measured volume of solvent is successively added, and thoroughly mixed before each subsequent measurement of the expiration time. The concentration of the diluted solution A1 is calculated by the formula:

where A is the concentration of the polymer solution poured into the viscometer, g / ml, V is the volume of the solution in the viscometer, ml, V1 is the volume of the added solvent, ml.

The VPZh-2 type viscometer is filled with a pure solvent or solution in the same manner as described above. Deviations of temperature of temperature control should not exceed ± 0.05 ° С at room temperatures, at elevated ± 0.15 ° С. The thermostatic fluid level should be 3-4 cm below the upper end of the knee of the viscometer.

After a 15-minute temperature control of the viscometer with a solvent or polymer solution, the solvent expiration time m0 or solutions of various concentrations of m are determined. In this case, the arithmetic average is taken for at least three determinations, the difference between which should not exceed 0.4 s.

The dynamic viscosity of dilute solutions of n or solvent n0 (in centipoises) is calculated by the formulas:

where C is the constant of the viscometer, cSt / s, p, p0 is the density of the polymer or solvent solution at the test temperature, g / cm3, t, t0 is the expiration time of the solution or solvent, s.

## Determination of conditional viscosity

The method for determining the nominal viscosity is used for petroleum products, paints and varnishes and a number of other viscous liquids, the viscosity of which cannot be determined using glass capillary viscometers. For a number of petroleum products, viscosity is normalized in arbitrary units.

The conditional viscosity is the ratio of the time of the expiration of a VU type viscometer of 200 ml of the test product at the test temperature to the time of the expiration of 200 ml of distilled water at a temperature of 20 ° C, which is a constant (water number) of the device. The value of this ratio is expressed as the number of conditional degrees.

The water number of the viscometer should be controlled by the laboratory of the organization to which the device belongs.

Conventional viscosity at temperature t is indicated by ВУt.

A viscometer of the VU-4 type serves as a device for measuring conditional viscosity. It consists of a reservoir 1 with a tube 8 in its bottom. The tank is placed in a vessel 2 serving as a water or oil bath. The tank is closed with a lid with two holes. A wooden rod 6 is inserted into one of the openings, which closes the tube 8, and a thermometer 4 is placed in the other. Inside the tank 1, at an equal distance from the bottom, three pointed pin 5 are curved upward at a right angle. The level of the test liquid being poured into the tank , and, in addition, these pins are used to install the device in a horizontal position. A stirrer 7 and a thermometer with a scale from 10 to 110 ° C and a division value of 1 ° C are placed in an external tank.

The device is mounted on an iron tripod 10, on two legs of which there are set screws 9. To heat the thermostatic liquid in the vessel 2, a gas burner is attached to the tripod or the device is equipped with an electric heating device with a temperature regulator.

To measure the volume of liquid flowing out from the viscometer, a special volumetric flask calibrated at 20 ° C per 200 ml is attached to the device.

### Determination of the water number of the VU viscometer

The inner tank is washed sequentially with petroleum or diethyl ether, ethyl alcohol and distilled water and dried with air. Then the viscometer is inserted with legs into the slots of the tripod and secured with clamping screws. The outlet 3 is closed with a clean rod 6. Filtered distilled water is poured into the inner tank of the viscometer 1 to a level at which the tips of the three pins 5 barely protrude above the mirror surface of the water, the water temperature should be 20 ± 0.2 ° C.

The external vessel 2 is also filled with water of the same temperature. A measured flask is placed under the drain pipe 8 of the internal tank and, having raised the rod 6, they empty all the water from the tank into the flask without measuring the time of its expiration, and the whole pipe 8 is also filled with water on the lower the end of which is a drop of water. Having lowered the end of the rod 6 into the outlet 3, again carefully pour water from the flask into the reservoir using a glass rod, the emptied flask is kept 1-2 minutes above the reservoir in the overturned position and then again placed under the drain pipe.

The water in the inner tank and the outer vessel is thoroughly mixed: in the first - by rotating the lid around the rod 6, in the second - by the stirrer 7. After making sure that the water temperature in both tanks is 20 ° C and within 5 min the temperature deviation does not exceed ± 0.2 ° C, the rod 6 is lifted with a short movement, simultaneously starting the stopwatch, and water leakage from the reservoir is observed. At the moment when the lower edge of the meniscus reaches the annular mark on the flask, the stopwatch is stopped. Observation of the expiration time of 200 ml of distilled water is repeated at least 4 times. For a standard viscometer, the outflow time of 200 ml of water at 20 ° C should be 51 ± 1 s.

## The physical meaning of viscosity

For the concept of the physical nature of such a concept as the viscosity of a liquid, consider an example. Let there be two parallel plates A and B. A liquid is enclosed in the space between them: the lower plate is stationary, and the upper plate moves with a certain constant speed υ1

As experience shows, the fluid layers immediately adjacent to the plates (the so-called adherent layers) will have the same velocities with it, i.e. the layer adjacent to the lower plate A will be at rest, and the layer adjacent to the upper plate B will move at a speed υ1.

The intermediate layers of liquid will slide along each other, and their speeds will be proportional to the distances from the bottom plate.

Even Newton made an assumption, which was soon confirmed by experience, that the resistance forces arising from such sliding of the layers are proportional to the contact area of ​​the layers and the sliding speed. If we take the area of ​​contact equal to unity, this position can be written as

where τ is the drag force per unit area or the friction stress

μ is the coefficient of proportionality, depending on the type of liquid and called the coefficient of absolute viscosity or simply the absolute viscosity of the liquid.

The value of dυ / dy - a change in speed in the direction normal to the direction of the speed itself, is called the sliding speed.

Thus, fluid viscosity is a physical property of a fluid that characterizes their resistance to sliding or shear.

### Kinematic, dynamic and absolute viscosity

Now let's define various concepts of viscosity:

Dynamic viscosity. The unit of measurement for this viscosity is Pascal per second (Pa * s). The physical meaning is to reduce pressure per unit time. Dynamic viscosity characterizes the resistance of a liquid (or gas) to the displacement of one layer relative to another.

Dynamic viscosity is temperature dependent. It decreases with increasing temperature and increases with increasing pressure.

Kinematic viscosity. The unit of measure is Stokes. Kinematic viscosity is obtained as the ratio of dynamic viscosity to the density of a particular substance.

The kinematic viscosity is determined in the classical case by measuring the outflow time of a certain volume of liquid through a calibrated hole when exposed to gravity

Absolute viscosity is obtained by multiplying the kinematic viscosity by density. In the international system of units, absolute viscosity is measured in N * s / m2 - this unit is called Poiseuille.

#### Fluid viscosity coefficient

In hydraulics, the value obtained by dividing the absolute viscosity by density is often used. This value is called the kinematic viscosity coefficient of the liquid, or simply the kinematic viscosity, and is denoted by the letter ν. Thus the kinematic viscosity of the fluid

where ρ is the fluid density.

The unit of measurement of the kinematic viscosity of a fluid in the international and technical systems of units is m2 / s.

In the physical system of units, the kinematic viscosity has a unit of measure cm 2 / s and is called Stokes (St).

Viscosity of some liquids

 Liquid t, ° С ν, St Water 0 0,0178 Water 20 0,0101 Water 100 0,0028 Petrol 18 0,0065 Wine alcohol 18 0,0133 Kerosene 18 0,0250 Glycerol 20 8,7 Mercury 0 0,00125

The reciprocal of the absolute viscosity coefficient of a liquid is called fluidity

Как показывают многочисленные эксперименты и наблюдения, вязкость жидкости уменьшается с увеличением температуры. Для различных жидкостей зависимость вязкости от температуры получается различной.

Поэтому, при практических расчетах к выбору значения коэффициента вязкости следует подходить очень осторожно. In each case, it is advisable to take special laboratory tests as a basis.

The viscosity of liquids, as established from experiments, also depends on pressure. Viscosity increases with increasing pressure. An exception in this case is water, for which at temperatures up to 32 degrees Celsius with increasing pressure the viscosity decreases.

As for gases, the dependence of viscosity on pressure, as well as on temperature, is very significant. With increasing pressure, the kinematic viscosity of gases decreases, and with increasing temperature, on the contrary, it increases.

## Determination of kinematic viscosity of oil in capillary viscometers

Devices for determining viscosity are called viscometers. Most often, glass viscometers of the type are used to determine the kinematic viscosity according to GOST 33-82.

Pinkevich and VPZhT-2 with which they measure the kinematic viscosity of the products at positive and negative temperatures. The method is based on the well-known Poiseuille formula for dynamic viscosity:

• P is the pressure at which the outflow of fluid from the capillary
• r is the radius of the capillary
• L - capillary length
• V is the volume of fluid flowing through the capillary
• t is the fluid discharge time in volume V.

## Devices and materials

The following is used in the work: Viscometer of the type VPZhT-2 thermo-stating device that provides long-term maintenance of the set temperature with an accuracy of ± 0.03 ° C for accurate and ± 0.1 ° C for technical measurements. A glass mercury thermometer with a minimum scale division of 0.05 ° C for accurate and 0.2 ° C - for technical measurements, a stopwatch thermostatic liquid: distilled water, glycerin or a mixture of glycerin with water in a ratio of 1: 1

## Measurement Procedure

To determine the kinematic viscosity, the viscometer is selected so that the flow time of the oil product is at least 200 s. Then it is thoroughly washed and dried. A sample of the test product is filtered through a paper filter. Viscous products are heated to 50-100 ° C before filtering. If there is water in the product, it is dried with sodium sulfate or coarse crystalline salt, followed by filtration. In the thermostatic device set the desired temperature. The accuracy of maintaining the selected temperature is of great importance, therefore, the thermostat thermometer must be installed so that its tank is approximately at the level of the middle of the viscometer capillary while immersing the entire scale. Otherwise, a correction is made for the protruding column of mercury according to the formula:

• B - coefficient of thermal expansion of the working fluid of the thermometer:
• for mercury thermometer - 0.00016
• for alcohol - 0.001
• h is the height of the protruding column of the working fluid of the thermometer, expressed in divisions of the scale of the thermometer
• T1 - set temperature in the thermostat, ° C
• T2 - ambient temperature near the middle of the protruding column, ° C.

The determination of the expiration time is repeated several times. In accordance with GOST 33-82, the number of measurements is determined depending on the expiration time: five measurements - at the expiration time from 200 to 300 s, four - from 300 to 600 s and three - at the expiration time over 600 s. When conducting readings, it is necessary to monitor the constancy of temperature and the absence of air bubbles.
To calculate the viscosity, the arithmetic mean of the expiration time is determined. In this case, only those readings are taken into account that differ by no more than ± 0.3% for accurate and ± 0.5% for technical measurements from the arithmetic mean.

### Processing measurement results

The kinematic viscosity of the test oil at a temperature t is calculated by the formula:

• С - viscometer constant, mm2 / s2
• t is the arithmetic average of the considered samples of the time of fluid flow, s
• g - acceleration of gravity in the place of measuring viscosity, m / s2
• 9,807 - normal acceleration of gravity, m / s2
• K = 1 + 0.00004 ^ t - coefficient taking into account the change in the hydrostatic pressure of the liquid due to its expansion when heated
• ^ T is the difference between the temperature of the product when filling the viscometer and its temperature when determining the viscosity.

The kinematic viscosity of the oil is calculated to the fourth significant digit

##### Methods for measuring viscosity. Stokes Method

The area devoted to measuring fluid viscosity is called viscometry, and the instrument for measuring viscosity is called a viscometer.

Modern viscometers are made of durable materials, and in their production the most modern technologies are used to ensure operation with high temperature and pressure without harming the equipment.

The following methods are available for determining fluid viscosity.

Capillary method.

The essence of this method is the use of communicating vessels. Two vessels are connected by a glass tube of known diameter and length. The liquid is placed in a glass channel and for a certain period of time flows from one vessel to another. Further, knowing the pressure in the first vessel and using the Poiseuille formula for calculations, the viscosity coefficient is determined.

Hessian method.

This method is somewhat more complicated than the previous one. For its implementation it is necessary to have two identical capillary installations. In the first place the medium with a predetermined value of internal friction, and in the second - the test fluid. Then, time is measured according to the first method in each of the plants and, finding the proportion between the experiments, they find the viscosity of interest.

Rotational method.

To perform this method, it is necessary to have a construction of two cylinders, one of which must be located inside the other. The test fluid is placed between the vessels, and then the inner cylinder is accelerated.

The fluid rotates with the cylinder at its angular velocity. The difference in the force of the moment of the cylinder and the liquid allows you to determine the viscosity of the latter.

Stokes Method

To perform this experiment, a Geppler viscometer is required, which is a cylinder filled with liquid.

First, two notes are made along the height of the cylinder and the distance between them is measured. Then a ball of a certain radius is placed in the liquid. The ball begins to sink into the liquid and travels the distance from one mark to another. This time is fixed. Having determined the speed of the ball, the fluid viscosity is then calculated.

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