Coefficient of viscosity. The coefficient of dynamic viscosity. The physical meaning of the viscosity coefficient

The viscosity coefficient is the key parameter of the working fluid or gas. In physical terms, viscosity can be defined as internal friction caused by the movement of particles constituting the mass of the liquid (gaseous) medium, or, more simply, the resistance to movement.

What is viscosity?

The simplest empirical experience of determining the viscosity: a smooth amount of water is simultaneously poured onto a smooth inclined surface with the same amount of water and oil. Water drains faster than oil. It is more fluid. Moving oil prevents rapid flow of higher friction between its molecules (internal resistance - viscosity). Thus, the viscosity of a liquid is inversely proportional to its fluidity.

Coefficient of viscosity: formula

In a simplified form, the process of motion of a viscous liquid in a pipeline can be considered in the form of plane parallel layers A and B with the same surface area S, the distance between which is h.

These two layers (A and B) move with different velocities (V and V + ΔV). The layer A, having the highest velocity (V + ΔV), involves a layer B moving at a lower velocity (V). At the same time, layer B tends to slow the speed of layer A. The physical meaning of the coefficient of viscosity is that the friction of molecules that represent the resistance of the flow layers forms a force that Isaac Newton described by the following formula:

F = μ × S × (ΔV / h)

Here:

• ΔV is the difference in the velocities of the motions of the fluid flow layers;
• H is the distance between the layers of the fluid flow;
• S is the surface area of the liquid flow layer;
• Μ (mu) is a coefficient that depends on the property of the fluid, called absolute dynamic viscosity.

In units of the SI system, the formula is as follows:

Μ = (F × h) / (S × ΔV) = [Pa × s] (Pascal × second)

Here F is the gravity (weight) of a unit volume of the working fluid.

The viscosity value

In most cases, the dynamic viscosity coefficient is measured in centipoises (cps) in accordance with the system of CGS units (centimeter, gram, second). In practice, the viscosity is related by the ratio of the mass of the liquid to its volume, that is, the density of the liquid:

Ρ = m / V

Here:

• Ρ is the density of the liquid;
• M is the mass of the liquid;
• V is the volume of the liquid.

The relation between the dynamic viscosity (μ) and the density (ρ) is called the kinematic viscosity ν (ν - in Greek):

Ν = μ / ρ = [m ² / s]

By the way, the methods for determining the viscosity coefficient are different. For example, the kinematic viscosity is still measured in accordance with the CGS system in centistokes (cSt) and in the stolks (St):

• 1Cm = 10 ^-4 m ² / s = 1 cm ² / s;
• 1 cSt = 10 ^-6 m ² / s = 1 mm ² / s.

Determination of water viscosity

The water viscosity coefficient is determined by measuring the flow time of the liquid through a calibrated capillary tube. This device is calibrated using a standard fluid of known viscosity. To determine the kinematic viscosity, measured in mm ² / s, the fluid flow time, measured in seconds, is multiplied by a constant value.

As a unit of comparison, the viscosity of distilled water is used, the value of which is almost constant even with a change in temperature. The viscosity coefficient is the ratio of the time in seconds that a fixed volume of distilled water is required to flow out of a calibrated hole, to a similar value for the test fluid.

Viscometers

Viscosity is measured in degrees Engler (° E), Saybolt universal seconds ("SUS") or degrees Redwood (° RJ), depending on the type of viscometer used. The three types of viscometers differ only in the amount of liquid flowing out.

The viscometer measuring the viscosity in the European unit is the Engler Degree (° E), calculated for 200 cm ^{3 of the} effluent liquid. The viscosimeter measuring the viscosity in universal Saybolt seconds ("SUS or" SSU ") used in the USA contains 60 cm ^{3 of the} test fluid. In England, where the degrees Redwood (° RJ) are used, the viscometer measures the viscosity of 50 cc ^of liquid. For example, if 200 cc ^{of a} certain oil flows ten times slower than a similar volume of water, then the Engler viscosity is 10 ° E.

Since temperature is a key factor that changes the coefficient of viscosity, measurements are usually carried out first at a constant temperature of 20 ° C, and then at higher temperatures. The result is thus expressed by adding an appropriate temperature, for example: 10 ° E / 50 ° C or 2.8 ° E / 90 ° C. The viscosity of the liquid at 20 ° C is higher than its viscosity at higher temperatures. Hydraulic oils have the following viscosity at the appropriate temperatures:

190 cSt at 20 ° C = 45.4 cSt at 50 ° C = 11.3 cSt at 100 ° C.

Translation of meanings

Determination of the viscosity coefficient occurs in different systems (American, English, GHS), and therefore it is often required to translate data from one dimensional system to another. To translate the fluid viscosity values expressed in Engler's degrees to centistokes (mm ² / s), use the following empirical formula:

Ν (cSt) = 7.6 × ° E × (1-1 / ° E3)

For example:

• 2 ° E = 7.6 × 2 × (1-1 / 23) = 15.2 × (0.875) = 13.3 cSt;
• 9 ° E = 7.6 × 9 × (1-1 / 93) = 68.4 × (0.9986) = 68.3 cSt.

In order to quickly determine the standard viscosity of hydraulic oil, the formula can be simplified as follows:

Ν (cSt) = 7.6 × ° E (mm ² / s)

Having a kinematic viscosity ν in mm ² / s or cSt, it can be converted into a dynamic viscosity coefficient μ using the following relationship:

Μ = ν × ρ

Example. Summarizing the different formulas for the translation of Engler's degrees (° E), centistokes (cSt) and centipoise (cp), we assume that a hydraulic oil with a density ρ = 910 kg / m3 has a kinematic viscosity of 12 ° E, which in cSt units is:

Ν = 7.6 × 12 × (1-1 / 123) = 91.2 × (0.99) = 90.3 mm ² / s.

Since 1сСт = 10 ^-6 m ² / s and 1сП = 10 ^-3 N s / m ² , the dynamic viscosity will be equal to:

Μ = ν × ρ = 90.3 × 10 ^-6 · 910 = 0.082 N × s / m ² = 82 cp.

Coefficient of viscosity of gas

It is determined by the composition (chemical, mechanical) of the gas, affecting the temperature, pressure, and is used in gas-dynamic calculations related to the motion of the gas. In practice, the viscosity of gases is taken into account when designing the development of gas fields, where the calculation of the coefficient changes is carried out depending on the changes in the gas composition (especially relevant for gas condensate fields), temperature and pressure.

Calculate the coefficient of viscosity of air. The processes will be similar to the two streams of water discussed above. Suppose that two gas flows U1 and U2 move in parallel, but at different speeds. Between the layers there will be convection (mutual penetration) of molecules. As a result, the impulse of the moving air flow will decrease faster, and initially moving slower will accelerate.

The coefficient of viscosity of air, according to Newton's law, is expressed by the following formula:

F = -h × (dU / dZ) × S

Here:

• DU / dZ is the velocity gradient;
• S is the force impact area;
• The coefficient h is the dynamic viscosity.

Viscosity index

The viscosity index (IV) is a parameter correlating the change in viscosity and temperature. The correlation dependence is a statistical relationship, in this case of two quantities, at which the change in temperature accompanies a systematic change in viscosity. The higher the viscosity index, the smaller the change between the two values, that is, the viscosity of the working fluid is more stable when the temperature changes.

Viscosity of oils

At the base of modern oils, the viscosity index is less than 95-100 units. Therefore, in the hydraulic systems of machines and equipment, sufficiently stable working fluids can be used, which limit the wide variation in viscosity at critical temperatures.

The "favorable" viscosity coefficient can be maintained by adding special additives (polymers) to the oil obtained in the distillation of oil. They increase the viscosity index of oils by limiting the variation of this characteristic within the allowable range. In practice, when the required amount of additives is introduced, a low viscosity index of the base oil can be increased to 100-105 units. At the same time, the mixture thus obtained deteriorates its properties under high pressure and heat load, thereby reducing the effectiveness of the additive.

In the power circuits of powerful hydraulic systems, working fluids with a viscosity index of 100 units should be used. Working fluids with viscosity index improvers are used in hydraulic control circuits and other systems operating in the low / medium pressure range in a limited range of temperature changes, with small leaks and in a batch mode. With increasing pressure, viscosity also increases, but this process occurs at pressures above 30.0 MPa (300 bar). In practice, this factor is often neglected.

Measurement and indexing

In accordance with international ISO standards, the viscosity coefficient of water (and other liquid media) is expressed in centistokes: cSt (mm ² / s). Viscosity measurements of process oils should be carried out at temperatures of 0 ° C, 40 ° C and 100 ° C. In any case, in the oil grade code the viscosity should be indicated by the figure at a temperature of 40 ° C. In GOST, the viscosity value is given at 50 ° C. The brands most commonly used in engineering hydraulics range from ISO VG 22 to ISO VG 68.

Hydraulic oils VG 22, VG 32, VG 46, VG 68, VG 100 at 40 ° C have viscosity values corresponding to their marking: 22, 32, 46, 68 and 100 cSt. The optimum kinematic viscosity of the hydraulic fluid in hydraulic systems lies in the range from 16 to 36 cSt.

The American Society of Automotive Engineers (SAE) established ranges of viscosity change at specific temperatures and assigned appropriate codes to them. The figure following the letter W is the absolute dynamic viscosity coefficient μ at 0 ° F (-17.7 ° C), and the kinematic viscosity ν was determined at 212 ° F (100 ° C). This indexation concerns all-season oils used in the automotive industry (transmission, motor, etc.).

Effect of viscosity on the operation of hydraulics

The determination of the viscosity coefficient of a liquid is not only of scientific and cognitive interest, but also carries an important practical significance. In hydraulic systems, working fluids not only transfer energy from the pump to the hydraulic motors, but also lubricate all the components of the components and divert the heat from the friction pairs. The viscosity of the working fluid that does not correspond to the operating mode can seriously affect the efficiency of the entire hydraulics.

High viscosity of the working fluid (very high density oil) leads to the following negative phenomena:

• Increased resistance to the flow of hydraulic fluid causes an excessive drop in pressure in the hydraulic system.
• Deceleration of control speed and mechanical movements of actuators.
• Development of cavitation in the pump.
• Zero or too low release of air from the oil in the tank.
• Noticeable loss of power (reduced efficiency) of hydraulics due to high energy costs to overcome internal friction of the fluid.
• The increased torque of the primary engine of the machine, caused by the increasing load on the pump.
• The rise in temperature of the hydraulic fluid caused by increased friction.

Thus, the physical meaning of the viscosity coefficient lies in its influence (positive or negative) on the nodes and mechanisms of vehicles, machines and equipment.

Hydraulic power loss

The low viscosity of the working fluid (low-density oil) leads to the following negative phenomena:

• The fall in the volumetric efficiency of pumps as a result of increasing internal leaks.
• Increase of internal leaks in hydraulic components of the whole hydraulic system - pumps, valves, hydraulic distributors, hydraulic motors.
• Increased wear of swinging assemblies and jamming of pumps due to insufficient viscosity of the working fluid necessary to provide lubrication of rubbing parts.

Compressibility

Any liquid under pressure is compressed. With respect to oils and coolants used in machine-building hydraulics, it is empirically established that the compression process is inversely proportional to the mass of the liquid per its volume. The amount of compression is higher for mineral oils, much lower for water and much lower for synthetic fluids.

In simple low-pressure hydraulic systems, the compressibility of the liquid negligibly affects the decrease in the initial volume. But in powerful machines with a high-pressure hydraulic drive and large hydraulic cylinders, this process manifests itself noticeably. At hydraulic mineral oils at a pressure of 10.0 MPa (100 bar) the volume decreases by 0.7%. At the same time, the kinematic viscosity and oil type influence the change in the volume of compression to a small extent.

Conclusion

Determination of the coefficient of viscosity makes it possible to predict the operation of equipment and mechanisms under different conditions, taking into account changes in the composition of the liquid or gas, pressure, temperature. Also, monitoring these indicators is relevant in the oil and gas sector, municipal services, other industries.