Viscosity coefficient. Dynamic viscosity coefficient. The physical meaning of the viscosity coefficient

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

What is viscosity?

The simplest empirical experience in determining viscosity: the same amount of water and oil is simultaneously poured onto a smooth inclined surface. Water flows faster than oil. It is more fluid. The moving oil is prevented from quickly draining by higher friction between its molecules (internal resistance - viscosity). Thus, the viscosity of a fluid is inversely proportional to its fluidity.

Viscosity Ratio: Formula

In a simplified form, the process of moving a viscous fluid 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 at different speeds (V and V + ΔV). Layer A having the highest velocity (V + ΔV) involves layer B moving at a lower speed (V). At the same time, layer B tends to slow down the speed of layer A. The physical meaning of the viscosity coefficient is that the friction of the molecules, which are the resistance of the layers of the flow, forms a force, which Isaac Newton described by the following formula:

F = µ × S × (ΔV / h)

Here:

• ΔV is the difference in the speeds 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) - a coefficient depending on the properties of the liquid is called absolute dynamic viscosity.

In SI units, the formula is as follows:

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

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

Viscosity value

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

ρ = m / V

Here:

• ρ is the fluid density;
• m is the mass of liquid;
• V is the volume of fluid.

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

ν = μ / ρ = [m ² / s]

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

• 1St = 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 coefficient of viscosity of water is determined by measuring the time of fluid flow 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 when the temperature changes. The viscosity coefficient is the ratio of the time in seconds that a fixed volume of distilled water needs to flow out of a calibrated hole to a similar value for the test fluid.

Viscometers

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

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

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

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

Value Translation

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

ν (cSt) = 7.6 × ° E × (1-1 / ° E3)

For instance:

• 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 dependence:

μ = ν × ρ

Example. Summing up the various formulas for converting Engler degrees (° E), centistokes (cSt) and centipoises (cP), we assume that a hydraulic oil with a density ρ = 910 kg / m ³ has a kinematic viscosity of 12 ° E, which in units of cSt is:

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

Since 1 cSt = 10 ^-6 m ² / s and 1 cP = 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.

Gas viscosity coefficient

It is determined by the composition (chemical, mechanical) of the gas, the temperature, pressure, and is used in gasdynamic calculations associated with the movement of gas. In practice, gas viscosity is taken into account when designing gas field developments, where the coefficient changes are calculated depending on changes in gas composition (especially relevant for gas condensate fields), temperature and pressure.

We calculate the coefficient of viscosity of air. The processes will be similar to the two streams of water discussed above. Suppose two gas flows U1 and U2 move in parallel, but with different speeds. Between the layers there will be convection (mutual penetration) of the molecules. As a result, the momentum of a faster moving air stream will decrease, and initially moving slower - 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 area of ​​influence of force;
• Coefficient h - dynamic viscosity.

Viscosity index

The viscosity index (VI) is a parameter that correlates the change in viscosity and temperature. The correlation dependence is a statistical relationship, in this case, two quantities at which a temperature change 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.

Oil viscosity

The foundations of modern oils have a viscosity index below 95-100 units. Therefore, in the hydraulic systems of machines and equipment, fairly stable working fluids can be used that limit a wide change in viscosity at critical temperatures.

A “favorable” viscosity coefficient can be maintained by introducing special additives (polymers) into the oil, obtained by distillation of oil. They increase the viscosity index of oils by limiting the variation of this characteristic in the allowable range. In practice, with the introduction of the required number of additives, the low viscosity index of the base oil can be increased to 100-105 units. However, the mixture thus obtained degrades its properties at 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 additives that increase the viscosity index are used in hydraulic circuits and other systems operating in the low / medium pressure range, in a limited temperature range, with small leaks and in periodic mode. With increasing pressure, the 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 coefficient of viscosity 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, the viscosity code should be indicated by a number at a temperature of 40 ° C in the oil brand code. In GOST, the viscosity value is given at 50 ° C. The grades 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 a temperature of 40 ° C have viscosity values ​​corresponding to their markings: 22, 32, 46, 68 and 100 cSt. The optimal kinematic viscosity of the working fluid in hydraulic systems lies in the range from 16 to 36 cSt.

The American Society of Automotive Engineers (SAE) has established ranges of viscosity at specific temperatures and assigned corresponding codes. The number 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 applies to all-season oils used in the automotive industry (transmission, motor, etc.).

Effect of viscosity on hydraulics

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

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

• Increased resistance to the flow of hydraulic fluid causes an excessive pressure drop in the hydraulic system.
• Slowing down control speed and mechanical movements of actuators.
• The development of cavitation in the pump.
• Zero or too low air discharge from the oil in the hydraulic tank.
• A noticeable loss of power (lower efficiency) of hydraulics due to the high energy costs of overcoming the internal friction of the fluid.
• The increased torque of the primary engine of the machine, caused by the increasing load on the pump.
• Hydraulic fluid temperature increase 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

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

• The drop in volumetric efficiency of pumps as a result of increasing internal leaks.
• The increase in internal leaks in the hydraulic components of the entire hydraulic system - pumps, valves, valves, hydraulic motors.
• Increased wear of the pumping units and jamming of the pumps due to insufficient viscosity of the working fluid necessary to ensure lubrication of the rubbing parts.

Compressibility

Any fluid is compressed by pressure. With regard to oils and coolants used in machine hydraulics, it is empirically established that the compression process is inversely proportional to the magnitude of the mass of fluid in its volume. The compression ratio is higher for mineral oils, significantly lower for water and much lower for synthetic fluids.

In simple low-pressure hydraulic systems, the compressibility of the liquid has negligible effect on the reduction of the initial volume. But in powerful machines with high-pressure hydraulic drives and large hydraulic cylinders, this process manifests itself noticeably. In 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 type of oil influence the change in the compression volume to a small extent.

Conclusion

Determination of the viscosity coefficient allows predicting the operation of equipment and mechanisms under various conditions, taking into account changes in the composition of a liquid or gas, pressure, temperature. Also, control of these indicators is relevant in the oil and gas sector, utilities, and other industries.