Water viscosity WST at different temperatures. Water viscosity
Water viscosity at different temperatures
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η 10 6 kg / m · s | ||||||||||
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η · 10 6 kg / m · s |
Table 15.5.
Kinematic viscosity of some liquids at 20 °(Hadgman.C.d., 1965)
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Viscosity, PZ. |
Density, g / cm 3 |
Kinematic Viscosity, cm 2 / s |
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Water prevents the swimmer's promotion. In the hydrodynamics to calculate the flow of fluid, the number of Reynolds is used. The Reynolds number is a dimensionless value where the density and viscosity of the fluid, and- The speed of its movement relative to the body and A is some length.
The rule according to which the stream structure near the bodies of the same form is the same if the same number of Reynolds is not applicable in cases where it comes to the behavior of the fluid near its free surface.
Reynolds number is convenient to express how 
The value called kinematic viscosity.
In many cases, it is difficult to measure the forces that act on the body moving in the liquid. In this regard, aerodynamic and hydrodynamic pipes are used for experiments.
Drag. Forthe movement of some body in the liquid, the power delaying its movement. This force is called frontal resistance. Its value depends on the nature of the liquid and on the size, shape and speed of the moving body.
As shown experiments in aerodynamic pipes, the windshield resistance of the body or various bodies of the same form can be determined by the formula 
where d - windshield resistance, r - liquid density, and- The speed of the fluid movement relative to the body, and the characteristic area and C d - the value called the windshield coefficient, which depends on the body shape and on the Rainolds number.
Unfortunately, there is no single definition A, which would be comfortable with any body shape. The following areas are used:
1) The frontal area, i.e., the area of \u200b\u200bthe body projection on the plane perpendicular to the flow direction. In the case of a cylinder having a height h.and radius gthe frontal square will be equal π r. 2 , if the axis of the cylinder is parallel to the flow, and 2RH,if she is perpendicular to him;
2) the area of \u200b\u200bthe highest projection, i.e. projections by the direction where it will be the highest area; This amount is used when they deal with the flow around the wing profile; Compared to the frontal area, it has the advantage that does not change when the profile is tilted;
3) Total body surface. It should be remembered that in the case of a thin plate, it will be the total area of \u200b\u200bboth sides.
If there are doubts, then it is important to specify whatit was from these areas that was used when calculating the coefficient with
In fig. 15.34 The curves of the dependence of the windshield coefficient of the Reynolds number for the bodies of various shapes are shown.
All coefficients were calculated on the basis of the frontal square.
The Reynolds number for all bodies, except for the disk, was determined in the usual way in length measured in the flow direction; For the disk, it was determined by a diameter, although it is located perpendicular to the stream.
Due to the lack of work on the frontal resistance of swimmers, we give data to T.O. Lang, k.s. Norris (1966), R. Alexander (1968) obtained when studying dolphins. It was found that with short "throws" dolphin can develop a speed of up to 830 cm / s (about 16 nodes), and at a rate of 610 cm / s (about 12 knots) is capable of sailing for about 1 min. Dolphin (Turbiopsgilli) had a length of 191 cm, so that the Ranolds number at the first of these velocities was 830 · 191 / 0.01 \u003d 1.6 · 10 7. Dolphin profile is well encouraged. The skin is very smooth and devoid of hair. Everything points to a small amount of windshield.
Fig. 15.34.The dependence of the windshield coefficient on the Reynolds number for a disk located perpendicular to the direction of its movement; For an extended cylinder moving perpendicular to its axis; For a ball and for the body of a streamlined form moving along its axis (according to R. Alexander, 1970)
Let us try to estimate the magnitude of the windshield for a dolphin floating at a speed of 830 cm / s and the power developed by its muscles. The frontal area of \u200b\u200bthe dolphin is 191 cm long, it is likely to be about 1100 cm 2. The windscreen coefficients for the streamlined bodies with the number of Reynolds about 1.6-10 7 are close to 0.055. Substituting these values \u200b\u200binto the equation
We will find that the windshield resistance in our dolphin is approximately 1/2 (830) 2 × 1100 · 0.055 \u003d 2.0-10 7 DIN. Power is equal to the resistance multiplied by the speed, i.e., in this case, 830 · 2.0 · 10 7 ERG / s, or 1660 W. However, the muscles require high power, since the Dolphin efficiency when swimming cannot reach 100%; Therefore, she could hardly be less than 2000 W. Dolphin weighs 89 kg, of which muscle participating in swimming are probably about 15 kg. Thus, the power of the muscles should be approximately 130 W / kg. It is 3 times the maximum power that human muscles can develop when working on a cyergometer.
The windshield is not the only hydrodynamic force acting on the bodies that move in the liquid or are in the stream. By definition, it has the same direction as the speed of fluid movement relative to the body. When a symmetric body moves along its axis of symmetry, the hydrodynamic force acting on it is directed directly and is a windshield resistance. But when a symmetric body moves at some angle to the axis of symmetry, the hydrodynamic force acts at an angle to its path. It can be decomposed into two components, one of which is directed back and is a windshield resistance, and the other acts at right angles to the first.
Energy swimmer.When a person is swimming, he informs some amount of energy to move (sailing) in it. This creates a wave, which ultimately will lose all the energy reported to it in the form of heat, and the surface of the water will again become calm. Estimated in this way when swimming, energy is a perfect operation plus heat lost by the body of a swimmer.
skiing
On the ski racing there is a combination of free sliding, repulsion by skis and sticks from snow, handlets of hands and legs and throwing (moving) ahead-up (Fig. 15.35).
Fig. 15.35.Phases of alternate skiing (by H.H. Gross)
Free slide(Phase I) occurs when the effect of friction in the snow and insignificant air resistance. To lose less speed, you can not make sharp movements (hand or leg) aimed up-forward. Free slide ends with a stick on the snow.
Begins the sliding phase with straightening of the support leg(Phase II). By increasing the slope of the body and push the skier stick seeks to increase (increase) ski slip speed.
Halfingit starts even (already) when skiing (phase III), which, with an energetic extension of the support leg in the knee and hip joints, quickly loses (extinguishes) speed and stops. The rating started in Phase III continues and ends in phase IV, accompanied by a drop-down movement of the portable leg. With the end of the country begins straightening of the push legsin the knee joint (phase V), accompanied by the completed deposition.
It should be noted that with an increase in the speed of movement changes the rhythm of the sliding step (the time of the repulsion of the ski is reduced; the hurdhes and straightening of the push legs are faster).
The basis of the ski equipment is an alternate step with sticking sticks at every step. It corresponds to a normal run, which, with a skis, goes into a rhythmic glide. The push to slip is given to a powerful repulsion of the corresponding leg from a snow base and push sticks. Repulsion always starts when both legs are approximately nearby. However, it is effective if skiing at this point has sufficient friction with a snow base due to the correct lubricant. While the left foot is repelled, the right becomes sliding. In this case, the mass of the body moves from the repulsive leg to the sliding. The skier-racer slides mainly on one ski. Only during a short period of repulsion to foot both ski simultaneously concern snow.
Cycling
The cyclist should overcome three strengths of resistance (Fig. 15.36):
the power of the resistance of the oncoming air flow;
Fig. 15.36.
Planting cyclist
Fig. 15.37.Muscles involved in the cyclist ride:
BUT- respiratory muscles, b - muscles involved in moving pedal down, IN -muscles involved in moving pedal up
Strength of rolling friction (see Fig. 6.5, Table 6.2);
Starting power when lifting mountain.
The external forces of resistance athlete opposes the power of its muscles, the right landing, etc.
In fig. 15.37, showing muscles working in the process of puming to pedals.
The main obstacle to overcome the distance is a counter-stream of air. The higher the speed, the more the resistance force of the oncoming air flow. Air resistance can be reduced in several ways.
Air flow resistance force f. b.
A - the size of the resistance surface that can be changed by landing;
To C - the coefficient of resistance, which depends on the streamlining of the figure of the cyclist and from the size of the surface of the clothing;
- air density, which is approximately constant on the plain, and in mountainous areas are slightly lower;
V 2 - Speed \u200b\u200bSquare. The air resistance grows, therefore, is not proportional to the speed of the cyclist, but much stronger.
With the oncoming wind, this force increases, with passing - decreases, which gives a decrease or increase in speed. To reduce the resistance force of the oncoming air flow, it is necessary to sit so that the surface (A) you take is relatively small. In the sprint - it is preferable to perform (taking) a horizontal landing. To reduce air resistance, special helmets and streamlined suits (overalls) are used (apply).
At the speed of moving the cyclist affects the rolling friction force (rubbing tires on the highway coating). The harder cyclist, the more friction rolling, as well as the thickness of the tire and less they are pumped up - the more rolling friction. Affect the speed of the cyclist is also the quality of the highway coating, the size of the wheels.
Rolling friction force F. m. r depends on the following factors:
- F. n. - Normal force corresponds to the weight of an athlete with a bike, if it is directed perpendicular to the surface at which movement occurs;
- r. - wheel radius;
- f. - The distance between the theoretical point of the tire support and the actual point of meeting the tire with the surface at which moves. From here we have the formula:
Planting a cyclist on time of the highway should be the most streamlined and at the same time do not interfere with the operation of the internal organs (Fig. 15.38). Planting a cyclist on a lift may be like this: 1) hand brushes on brake levers; 2) brushes in the steering center, clasp it below; 3) The situation in which the center of gravity of the body is transferred.
During the rise, the speed is small, the decisive role acquires the collaborating force, and the resistance of the oncoming air flow can be neglected.
Fig. 15.38. Planting a cyclist with highway races
For colliding power (F.), the following factors are decisive:
G.- the total weight of the athlete with a bike;
l. - Length of the path;
h.- Lifting height by 100 m
The greater the weight of the athlete with the bicycle and the residency of the lifting (for example, when the heights of 6 m per 100 m of the rise - 6%), the greater the stalking force.
When performing turning arises centrifugal force, the value of which depends on the three factors: 1) than more speed and the weight of the athlete with the machine and the less radius of the rounding, the more centrifugal force; 2) To counter the centrifugal force should be leaning along with the bike towards the roundabout. In fig. 15.39 shows the centrifugal force and the direction of the interaction of other forces arising from the passage of the virage; 3) Depending on the shape of the magnifier and the speed, it is necessary to be leaning so that the angle between the bike and the surface of the track ranged from 70 ° to 110 °. In the perfect version, it must be 90 °.
But in some situations, the racer must go along the track slowly, for example, in the sprint, a pair group race, etc. In these cases, with too little speed, you can fall, since the wheel will slip down. With a slow ride or an attempt to fully stop centrifugal forces are insignificant or even equal to zero, which means to be tilted on the brightener it is impossible.
Fig. 15.39.Forces acting on a cyclist when passing the virage: F-centrifugal force, F. H. - normal strength, R. - resulting, α - the angle of the tracks of the track, F. C - Stipping force, β - angle of inclination
The advantage of riding from above is the ability to use colliding power (F c) for a significant increase in speed. Stipping force is directly proportional to the height of the curve (h)and the weight of the cyclist with the machine (G).
The harder athlete and the higher it is on the priese, the greater the stalking force. The advantage will be on the side of the rider, if, when leaving the finish turn, it will be in its upper part on the same level with the opponent.
Jumping
When jumping both legs after flexing in the main joints (hip, knee, ankle), they straighten with a rapid and strong abbreviation of extensors and fell off from the ground to the impetus, which is transmitted to the body. At the same time, the jump or accomplished on the spot - the body rises in the vertical direction, or the body is reported forward and upwards (Fig. 15.40).
Fig. 15.40. Long jumps from running
Long jumps from running.The faster the person runs, the farther he can jump. The kinetic energy of the run may also be used for jumping in height. In this principle, pole jumps are based on (G.h. Dyson, 1962).
Before the jump, the center of gravity is already at an altitude of about 90 cm above the ground, and during the jump it turns out only slightly above the plank. For example, when using the Western Roll method, the center of gravity (CT) of the body may rise above the strip on a height of about 15 cm (G.H. Dyson, 1962).
When a person jumps "from the spot", each of the muscles participating in this act is reduced only once. The maximum force developed by the muscle is proportional to the area of \u200b\u200bits cross-section. Possible shortening of the muscle is proportional to its length. Consequently, the work that it can perform during a single reduction is proportional to the product of its length on the cross-sectional area, i.e. its volume. Muscles of the same volume (or weight) are capable of making the same work. Imagine now an animal, the mass of which t,and the muscles involved in the jump - mass t "Let these muscles at a single reduction capable of doing work Km ".This work is equal to the kinetic energy that the body of the animal acquires when the earth is separated:
where and - Speed \u200b\u200bat the time of separation. If the animal jumped vertically, it would rise to height. In the case of a jump at an angle of 45 ° it would be sank at a distance 
from the initial point. Therefore, it can be expected that different animals in which the mass ratios used when jumping muscles to the total weight of the body are equal (that is equal to the values), are able to jump to the same height and the same distance independently of the sizes of the body.
Let's try to proceed from other assumptions about muscles. We assume that the ability to perform jumps is limited to the maximum power that muscles can develop, and that the unit of mass of muscle tissue can develop power Ki.Let during the start of the muscles to reduce until the bottom of the legs from the ground, the center of gravity (CT) of the animal moves to the distance l.. For most animals l. It will be a little less leg length. We already know that by the time of separation from the Earth, work should be performed. To find the necessary power, we need to divide this job for a while t,for which it is produced. Passing the way / during T, the animal increases its speed from 0 to U.Suppose that acceleration is constantly and use the equation. Then we get
(15.8)
The power required to perform the operation is the time, and the power that can develop the muscles used when jumping is equal to KM. 1 . From here
If the animal is removed at this speed from the ground vertically up, it reaches a height.
If it takes off at an angle of 45 °, it will jump over the distance 
.
For animals of different values, but with the same relative mass of the muscles used when jumping, the greatest height and length of jumping should be proportional to the acceleration path (i.e. the path on which the speed is evenly increasing from 0 to and)by degree 2/3. The athlete can jump in length from running up to 8 m. With the help of the formulas discussed above, we can approximately determine the initial speed with which the athlete should break away from the Earth (separation rate). In the case of an optimal angle of separation from the Earth at 45 °, the required speed is determined
from the equation 
\u003d 800, from here
and = (15.10)
Consequently, the speed of separation from the Earth is 885.8 cm / s without taking into account air resistance.
If the separation angle is 55 °, and the jump distance is the same, then the athlete must break away from the ground at the rate that can be found from the equation
If at the same time the acceleration was constant, it could be calculated by the formula:
(913) 2 \u003d 2a · 4, (15.13)
but\u003d 104196 cm / sec 2.
If the body's mass of the athlete is equal to m grams, then in order to give it such an acceleration, it would be necessary to force 104 196 m Dean. One dina is the force required in order to inform the mass in 1 g acceleration, equal to 1 cm / c 2 (i.e., increase its speed by 1 cm / s per second).
Fig. 15.41. Diving.
and - from the front rack, bent a bent forward bent; - from the front rack of one and a half turn of the "summer" bent; in -half turn back with two and a half screws
Diving
Jumping in water belongs to technical and composite sports and include jumps from a springboard and from the tower. Jumping are performed from the front or rear rack, with rotational movements, screws, jumps from the rack at the brushes, etc. (Fig. 15.41).
The main element of the equipment jumping from springboard and tower is running, push, the phase of the flight and the entrance to the water.
Performing the entire jump depends on the push. At the same time, the subsequent path of the flight is determined by the subsequent trajectory of the athlete will not be able to change during the flight phase. The flight phase begins at the time of emanating legs from the board or from the site and ends with a touch of the surface of the water. The flight phase is introduced by an impetus, which determines the optimal flight path and movement. The main requirement for the entrance to the water is the vertical position of the immersible part of the body relative to the surface of the water in order to enter the water almost without splashes.
Shot put
The sequence of movements by pushing the kernel can be described by dividing the exercise into three phases: jump, turning the body and straightening the hand (Fig. 15.42). The nuclear flight range depends on the kernel path, from the starting point until the core is released, the jump rate (i.e. in the first phase of the exercise), the velocity of the nucleus of the nucleus is straightened, the height of the nuclear release, the mass of the athlete, etc.
Fig. 15.42.
Shot put
pushing kernel)
S. Francis (1948) revealed that the average height of the nucleus was 152 mm above the average growth of the surveyed athletes (183 cm).
Weightlifting
Weightlifting- sport, requiring high accuracy of reproduction of exercise as systems of movements. Suites for lifting (raising) of weights (rods) are related to such sports in which a decisive role is played in the same extent physical strength and technique.
Exercises for the development of force are quite diverse, they can be performed using a rod, girome, dumbbells, traction shells (simulators), etc. These exercises have proven themselves in many sports and serve athletes for the development of force and endurance (high-speed-security qualities ). Large weight exercises are used mainly to develop maximum strength, and with the help of exercises at a high pace, high-speed power develops, i.e. high-speed-force qualities.
The purpose of the rod is the rise of the rod while maintaining the body equilibrium on a small support area during the recovery movements. At the same time, motion differ from the lifting phase to the support phase. At a certain time, a relatively small force is required for the impact on the bar, in order to make the necessary changes in the stability of the legs during the hold of the rod. The force is used in the vertical direction, but since the rod describes the curve in the form of the letter S at the body level of the body, horizontal forces can also come into effect. The acceleration of the rod depends on the amount of force that affects it, as well as from the mass of the projectile. The less the mass of the projectile, the greater the speed with an equal use of force and vice versa. The achieved maximum speed is decisive for the so-called traction height of the bar.
The forces acting on the system "rod - hull" should be used in the main period of the traction phase only for the necessary rearrangements of parts of the body body from the lifting phase to the undermination. The impact of muscle strength on the bar causes the elastic deformation of the rod. There are so-called elastic forces in the projectile. They contribute to the acceleration of the rod and reliable movement of it. The rod must, to use the elastic action of the bar, develop a certain sense of rhythm during training.
When moving the rod, the athlete reaches and overcomes different forces: a) the weight of the rod (gravity strength); b) the power of the rod inertia, which depends on the mass and from the speed of the rod; c) the strength of gravity and the power of inertia of their own body.
These factors are decisive criteria for assessing the technique and forces of the athlete. The development of exercise techniques contributes to the development of the right posture.
The most important exercises include squats and tilts with a barbell on the shoulders (Fig. 15.43). In fig. 15.44 Education is shown the right (normal) posture when performing exercises with burdens.
Coordination of weightlifting movements is hampered as a result of some factors:
1. Difficulties when lifting the limit weight rod - this is a complex factor: a) athlete all the time is forced to change the weight of the rod raised, which causes to change the coordination of muscle stresses; b) The athlete does not have the ability to repeat the jerk and the impetus with the competitive weights of the rod weight due to the limit nature of the load.
Fig. 15.43.The load on the spine when picked up the rod: a - incorrectly; b.- right
Fig. 15.44.Exercise with burden: A - right; B - wrong
2. Significant shifts in the forceatic preparedness of weightlifters in the process of training are caused accordingly to change the technique of lifting the rod due to large changes in the domestic forces in the Athlete - Rod system.
3. Briefness of the entire exercise or individual parts limits the possibility of current movement correction based on the functioning of feedback.
For the development (training), the strength of those or other muscles is important is the initial position of an athlete. In fig. 15.45 shows the squatting of an athlete with a barbell weighing 50 kg on the shoulders in one of the poses and the moment of force acting in individual joints will be bottled (Table 15.6), although the strength of the rod is everywhere and the same - 50 kg.
Table 15.6.
In a state of equilibrium, different phases of the substance are at rest relative to each other. With their relative movement, braking (viscosity) will appear, which seek to reduce the relative speed. The viscosity mechanism can be reduced to the exchange of an ordered movement of molecules between different layers in gases and liquids. The emergence of viscous friction forces in gases and liquids belong to the transfer processes. Viscosity solid tel It has a number of essential features and is considered separately.
Definition
Kinematic viscosity Determine as the ratio of dynamic viscosity () to the density of the substance. It is usually the letter (NU). Then mathematically determining the kinematic viscosity coefficient we write as:
where is the gas density (liquid).
Since in the expression (1) the density of the substance is in the denominator, then, for example, the fired air at a pressure of 7.6 mm Hg. Art. And the temperature of 0 o C has a kinematic viscosity of two times greater than glycerin.
The kinematic viscosity of the air under normal conditions is often considered to be equal, so when moving in the atmosphere, the Stokesa law apply when the product of the body radius (cm) at its speed () does not exceed 0.01.
The kinematic viscosity of water under normal conditions is often considered to be about, so when moving in water use the Stokes law when the product of the body radius (cm) at its speed () does not exceed 0.001.
Kinematic viscosity and Reynolds numbers
Reynolds (Re) numbers are expressed using kinematic viscosity:
where - linear dimensions of the body moving in the substance - the speed of the body.
In accordance with the expression (2) for the body, moving with a constant speed, the number decreases if the kinematic viscosity grows. If the number Re is small, then in the front impedance of the forces of viscous friction dominate the forces of inertia. Conversely, large numbers of Reynolds, which are observed with small kinematic viscosities, indicate the priority of the inertia forces over friction.
The Ranolds number is not enough for a given kinematic viscosity value, when small body sizes and the speed of its movement.
Units of measuring the kinematic viscosity coefficient
The main unit of measuring kinematic viscosity in the SI system is:
Examples of solving problems
Example 1.
| The task | The metal ball (its density is equal) evenly falls in the liquid (the density of the liquid is kinematic viscosity). With what the maximum possible diameter of the ball will remain laminar? Consider that the transition to turbulent flow occurs at Re \u003d 0.5. For the characteristic size to take the diameter of the ball. |
| Decision | Let's make a drawing Using Newton's second law, we get expression: where - the power of Archimedes, is the power of viscous friction. In the projection on the axis y, equation (1.1) will take the form: At the same time we have: Wherein:
Substitute results (1.3) - (1.5) in (1.2), we have: Reynolds number is defined in our case as:
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The viscosity coefficient is the key parameter of the working fluid or gas. IN physical terms Viscosity can be defined as inner friction caused by the movement of particles constituting a mass of liquid (gaseous) medium, or, more simply, resistance to movement.
What is viscosity
The simplest viscosity definition: the same amount of water and oil is simultaneously poured into a smooth inclined surface. Water flows faster than oil. She is more fluid. Moving oil interferes quickly quickly drain higher friction between its molecules (internal resistance - viscosity). Thus, the viscosity of the liquid is inversely proportional to its fluidity.
Viscosity coefficient: Formula
In a simplified form, the process of movement of a viscous fluid in the pipeline can be considered in the form of flat parallel layers A and B with the same surface area S, the distance between which is H.
These two layers (A and B) are moved at different speeds (V and V + ΔV). Layer a having the greatest speed (V + ΔV), involves a layer B, moving at a lower rate (V). At the same time, the layer B strives to slow down the speed of the layer A. The physical meaning of the viscosity coefficient is that the friction of molecules representing the resistance of the layer of the flow forms the force that the following formula described:
F \u003d μ × s × (Δv / h)
- ΔV is the difference in the speed of movement of fluid flow layers;
- h is the distance between the layers of fluid flow;
- S is the surface area of \u200b\u200bthe fluid flow layer;
- μ (MJ) is a coefficient depending on is called an absolute dynamic viscosity.
In units of measurement of the system of the formula, it looks like this:
μ \u003d (F × H) / (S × ΔV) \u003d [PA × C] (Pascal × second)
Here F is the gravity of the volume of the working fluid.
Viscosity value
In most cases, the coefficient is measured in centipuamas (SP) in accordance with the system of SGS units (centimeter, gram, second). In practice, the viscosity is associated with the ratio of mass fluid to its volume, that is, with a liquid density:
- ρ - liquid density;
- m - mass of liquid;
- V is the volume of fluid.
The ratio between the dynamic viscosity (μ) and the density (ρ) is called the kinematic viscosity ν (ν - in Greek - NU):
ν \u003d μ / ρ \u003d [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 SGS system in Sortistoxes (CST) and in the dolly values \u200b\u200b- Stokes (ST):
- 1st \u003d 10 -4 m 2 / s \u003d 1 cm 2 / s;
- 1Sst \u003d 10 -6 m 2 / s \u003d 1 mm 2 / s.
Determination of water viscosity
The water viscosity coefficient is determined by measuring the flow time of the fluid through the calibrated capillary tube. This device is calibrated using standard liquid known viscosity. To determine the kinematic viscosity measured in mm 2 / s, the flow time of the fluid, measured in seconds, is multiplied by a constant value.
The viscosity of distilled water is used as a comparison unit, the value of which is almost constant even when the temperature changes. The viscosity coefficient is the ratio of time in seconds, which is necessary for the fixed volume of distilled water for the expiration of the calibrated hole, to the similar value for the test liquid.
Viscometers
The viscosity is measured in degrees of Englera (° E), universal seconds of the Saus ("Sus) or degrees of the Redwood (° Rj) depending on the type of viscometer used. Three types of viscimeters differ only in the resulting liquid medium.
The viscometer, measuring the viscosity in the European unit of the degree of Englera (° E), is calculated for 200 cm 3 arising from the liquid medium. The viscometer, measuring viscosity in universal seconds of the SSU ("SUS or SSU), used in the US, contains 60 cm 3 of the test liquid. In England, where the deduct degrees (° Rj) are used, the viscometer performs a viscosity measurement of 50 cm 3 of liquid. For example, if 200 cm 3 of a certain oil flows ten times more slower than a similar amount of water, the Engeru viscosity is 10 ° E.
Since the temperature is a key factor changing the viscosity coefficient, the measurements are usually carried out first at a constant temperature of 20 ° C, and then at higher values. 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 fluid at 20 ° C is higher than its viscosity at higher temperatures. Hydraulic oils have the following viscosity at the corresponding temperatures:
190 CST at 20 ° C \u003d 45.4 CST at 50 ° C \u003d 11.3 CST at 100 ° C.
Translation of values
The definition of viscosity coefficient occurs in different systems (American, English, SGS), and therefore it is often necessary to translate data from one dimensional system to another. To transfer the values \u200b\u200bof the viscosity of the fluid, expressed in the degrees of Englera, in centistoks (mm 2 / s) use the following empirical formula:
ν (CST) \u003d 7.6 × ° E × (1-1 / ° E3)
For example:
- 2 ° E \u003d 7.6 × 2 × (1-1 / 23) \u003d 15.2 × (0.875) \u003d 13.3 CST;
- 9 ° E \u003d 7.6 × 9 × (1-1 / 93) \u003d 68.4 × (0.9986) \u003d 68.3 CST.
In order to quickly determine the standard viscosity of the hydraulic oil, the formula can be simplified as follows:
ν (USC) \u003d 7.6 × ° E (mm 2 / s)
Having a kinematic viscosity ν in mm 2 / C or CST, it can be translated into a dynamic viscosity coefficient μ using the following dependence:
Example. Summing up various formulas for the translation of the degrees of Englera (° E), Sortistoks (CST) and Santipoise (SP), suppose that hydraulic oil with a density ρ \u003d 910 kg / m 3 has a kinematic viscosity of 12 ° E, which in units of CST is:
ν \u003d 7.6 × 12 × (1-1 / 123) \u003d 91.2 × (0.99) \u003d 90.3 mm 2 / s.
Since 1cst \u003d 10 -6 m 2 / s and 1sp \u003d 10 -3 N × C / m 2, then dynamic viscosity will be equal to:
μ \u003d ν × ρ \u003d 90.3 × 10 -6 · 910 \u003d 0.082 N × C / m 2 \u003d 82 SP.
Gas viscosity coefficient
It is determined by the composition (chemical, mechanical) gas acting in temperature, pressure and is used in gas-dynamic calculations associated with gas movement. In practice, the viscosity of gases is taken into account when designing the development of gas deposits, where the calculation of the coefficient changes depending on changes in the gas composition (especially relevant for gas condensate deposits), temperature and pressure.
Calculate the air viscosity coefficient. Processes will be similar to those discussed above two water flows. Suppose, in parallel, two gas flux U1 and U2 are moving, but at different speeds. Convection (mutual penetration) of molecules will occur between the layers. As a result, the pulse of a moving faster air flow will decrease, and initially moving slower - to accelerate.
The coefficient of air viscosity, according to Newton's law, is expressed by the following formula:
F \u003d -H × (du / dz) × s
- dU / DZ is a speed gradient;
- S - the exposure area;
- The coefficient h is a dynamic viscosity.
Viscosity index
The viscosity index (IV) is a parameter that correlates the change in viscosity and temperature. The correlation dependence is a statistical relationship, in this case two values \u200b\u200bat which the temperature change is accompanied by 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 basics of modern oils, the viscosity index is below 95-100 units. Therefore, in hydraulic systems of machinery and equipment, sufficiently stable working fluids can be used, which limit the wide viscosity change in critical temperatures.
The "favorable" viscosity coefficient can be maintained by introducing special additives (polymers) to oil, obtained when they increase the viscosity index of oils by limiting the change in this characteristic in the allowable interval. In practice, with the introduction of the required number of additives, the low base oil viscosity index can be increased to 100-105 units. At the same time, the mixture thus obtained worsens its properties at high pressure and thermal load, thereby reducing the efficiency of the additive.
In power circuits of powerful hydraulic systems, working fluids with a viscosity index of 100 units should be applied. Working fluids with additives that increase the viscosity index are used in the circuits of hydraulic control and other systems operating in the low / medium pressure range, in a limited temperature change interval, with small leaks and in periodic mode. With increasing pressure, viscosity increases, but this process occurs at pressures over 30.0 MPa (300 bar). In practice, this factor is often neglected.
Measurement and indexation
In accordance with international ISO standards, the water viscosity coefficient (and other liquid media) is expressed in centistoxes: CST (mm 2 / s). Measuring the viscosity of technological oils should be carried out at temperatures of 0 ° C, 40 ° C and 100 ° C. In any case, the viscosity should be specified in the oil brand code at 40 ° C. In GOST, the viscosity value is given at 50 ° C. The brands most often used in engineering hydraulics range from ISO VG 22 to ISO VG 68.
Hydraulic oils VG 22, VG \u200b\u200b32, VG \u200b\u200b46, VG 68, VG 100 at a temperature of 40 ° C have viscosity values \u200b\u200bcorresponding to their marking: 22, 32, 46, 68 and 100 CST. The optimal kinematic viscosity of the working fluid in the hydraulic systems lies in the range from 16 to 36 CST.
The American Society of Automotive Engineers (SAE) installed viscosity change ranges at specific temperatures and assigned to them the appropriate codes. The figure following the letter W is an 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 to work hydraulics
The determination of the viscosity coefficient of the fluid is not only scientific and cognitive interest, but also carries an important practical value. In hydraulic systems, working fluids not only transmit energy from the pump to hydrodinators, but also lubricate all component parts and disassembled heat from pairs of friction. Not appropriate working fluid viscosity can seriously disrupt the efficiency of the entire hydraulics.
The 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 pressure drop in the hydraulic system.
- Slow down the control rate and mechanical movements of the executive mechanisms.
- Development of cavitation in the pump.
- Zero or too low isolation of air from oil in a hydraulician.
- A noticeable loss of power (reduction in efficiency) hydraulics due to high energy costs to overcome the internal friction of the fluid.
- Increased torque of the primary engine engine caused by the increasing load on the pump.
- The increase in the temperature of the hydraulic fluid generated by increased friction.
Thus, the physical meaning of the viscosity coefficient is its influence (positive or negative) on the components and mechanisms of vehicles, machine tools and equipment.
Power loss hydraulic system
Low viscosity of the working fluid (low density oil) leads to the following negative phenomena:
- The fall in the volume efficiency of pumps as a result of increasing internal leaks.
- Increasing inland leaks in the hydrocomponents of the entire hydraulic system - pumps, valves, hydraulic distributors, hydromotors.
- Increased wear of pumping nodes and jamming of pumps due to insufficient viscosity of the working fluid necessary to ensure lubrication of rubbing parts.
Compressibility
Any liquid under pressure is compressed. With regard to oils and coolant used in the engineering hydraulics, it is empirically established that the compression process is inversely proportional to the magnitude of the mass of the fluid on its volume. The magnitude of compression is higher for mineral oils, significantly lower for water and is much lower for synthetic liquids.
In simple low pressure hydraulic systems, the compressibility of the fluid is negatively little effect on the decrease in the initial volume. But in powerful machines with high-pressure hydraulics and large hydraulic cylinders, this process manifests itself noticeable. Hydraulic at a pressure of 10.0 MPa (100 bar) volume decreases by 0.7%. At the same time, kinematic viscosity and oil type are affected by the change in the compression volume.
Output
The definition of the viscosity coefficient allows predicting the operation of equipment and mechanisms under various conditions, taking into account the change in the composition of the liquid or gas, pressure, temperature. Also, the control of these indicators is relevant in the oil and gas sphere, utilities, other industries.
Viscosity of liquids | Viscosity of water, milk, gasoline, oil, alcohol
Date:2008-12-10
Viscosity - The property of fluid to resist with relative movement (shift) of liquid particles. This property is due to the occurrence of internal friction in the moving fluid, for they are manifested only when it is moved due to the presence of clutch forces between its molecules. Viscosity characteristics are: dynamic viscosity coefficient μ and kinematic viscosity coefficient ν .
The unit of dynamic viscosity coefficient in the SGS system is PUAZ (P): 1 n \u003d 1 dina · C / cm 2 \u003d 1 g / (cm · s). A hundreds of Pouase share is called Sortipuaise (SP): 1 SP \u003d 0,01P. In the ICGSS system, the unit of dynamic viscosity coefficient is kgf · C / m 2; In the SI system - Pa · s. Communication between units is as follows: 1 n \u003d 0.010193 kgf · C / m 2 \u003d 0.1 Pa · s; 1 kgf · C / m 2 \u003d 98.1 n \u003d 9.81 Pa · s.
Kinematic viscosity coefficient
ν = μ /ρ,
The unity of the kinematic viscosity coefficient in the SGS system is Stockc (Article), or 1 cm 2 / s, as well as centistox (CST): 1 CST \u003d 0.01 tbsp. In the ICGSS and SI systems, the units of the kinematic viscosity coefficient is m 2 / s: 1 m 2 / s \u003d 10 4 art.
The viscosity of the fluid with an increase in temperature decreases. The effect of temperature on the dynamic fluid viscosity coefficient is estimated by the formula μ = μ 0 · e. A (T-T 0), where μ = μ 0 - values \u200b\u200bof the dynamic viscosity coefficient, respectively at temperatures t and T 0degrees; but- indicator degree depending on the kind of fluid; For oils, for example, its values \u200b\u200bare changed in the range of 0.025-0.035.
For lubricating oils and liquids used in machines and hydraulic systems, a formula binding a kinematic viscosity coefficient and temperature is proposed:
ν T.= ν 50 · (50 / t 0) n,
where ν
T. - kinematic viscosity coefficient at temperatures t. 0 ;
ν
50
- kinematic viscosity coefficient at a temperature of 50 0 s;
t. -
the temperature in which you want to define viscosity, 0 C;
n. - An indicator of the degree varying from 1.3 to 3.5 or more depending on the value ν
50
.
With sufficient accuracy N. may be determined by expression n.\u003d LG. ν 50 +2.7. Values N. depending on the initial viscosity ν at 50 0 s are given later in the table
Values dynamic and kinematic viscosity coefficients of some fluids Led later in the table
| Liquid | t, 0 C | μ, P. | μ, n · C | ν, Art |
| Petrol | 15 | 0,0065 | 0,00065 | 0,0093 |
| Glycerin 50% aqueous solution | 20 | 0,0603 | 0,00603 | 0,0598 |
| Glycerin 80% aqueous solution | 20 | 1,2970 | 0,12970 | 1,0590 |
| Glycerin anhydrous | 20 | 14,990 | 1,4990 | 11,890 |
| Kerosene | 15 | 0,0217 | 0,00217 | 0,0270 |
| Mazut | 18 | 38,700 | 3,8700 | 20,000 |
| Milk whole | 20 | 0,0183 | 0,00183 | 0,0174 |
| Oil is light | 18 | 0,178 | 0,0178 | 0,250 |
| Heavy oil | 18 | 1,284 | 0,01284 | 1,400 |
| Syrup | 18 | 888 | 0,888 | 600 |
| Mercury | 18 | 0,0154 | 0,00154 | 0,0011 |
| Turpentine | 16 | 0,0160 | 0,00160 | 0,0183 |
| Ethanol | 20 | 0,0119 | 0,00119 | 0,0154 |
| Ether | 20 | 0,0246 | 0,00246 | 0,00327 |
The value of the coefficients of the kinematic and dynamic viscosity of fresh water
A source:Wilner Ya.M. Reference manual for hydraulics, hydraulic and hydraulic drives.
Comments on this article !!
Answer DROGHKIN: What to do students who are interested in the table viscosity of water in the SSS system? If the school is taught only in SI, then in the university after the course of mechanics you will send this si far and for a long time. Because it is simply uncomfortable in it.
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Definition
Viscosity Call one of the types of transfer phenomena. It is associated with the property of flowable substances (gases and liquids), resist the movement of one layer relative to the other. This phenomenon is caused by the movement of the particles that make up the substance.
Select dynamic viscosity and kinematic.
Consider the movement of gas with viscosity as moving flat parallel layers. We assume that the change in the rate of motion of the substance occurs in the direction of the axis x, which is perpendicular to the direction of the gas speed direction (Fig. 1).
In the direction of the Y axis, the speed of movement at all points is the same. So, speed is a function. In this case, the friction force module between the gas layers (F), which acts per unit area of \u200b\u200bthe surface, which separates two adjacent layers, is described by the equation:
where - the gradient of the speed () along the X axis. The x axis is rebounded by the direction of movement of the substance layers (Fig. 1).
Definition
The coefficient () included in equation (1) is called a dynamic viscosity coefficient (internal friction ratio). It depends on the properties of the gas (liquid). It is numerically equal to the amount of movement that is transferred per unit of time through the site of a unit area under a speed gradient equal to one, in the direction of the perpendicular area. Or is numerically equal to force, which acts per unit area under a speed gradient equal to one.
Internally friction - the reason for the flow of gas (liquid) through the pipe is needed pressure difference. In this case, the greater the viscosity coefficient of the substance, the greater the pressure difference should be to give a given flow rate.
The coefficient of kinematic viscosity is usually denoted. It is equal:
where is the gas density (liquid).
Coefficient of internal gas friction
In accordance with the kinetic theory of gases, the viscosity coefficient can be calculated using the formula:
where is the average heat movement of the gas molecules, is the average length of the free mileage of the molecule. Expression (3) shows that at the bottom of the pressure (rack gas), the viscosity is almost independent of pressure, since 
But this conclusion is fair until the moment the ratio of the length of the free mileage of the molecule to the linear dimensions of the vessel will not be approximately equal to one. With increasing temperature, the viscosity of the gases is usually growing, since
Liquid viscosity coefficient
Considering that the viscosity coefficient is determined by the interaction of the molecules of the substance, which depend on the average distance between them, the viscosity coefficient is determined by the Bachinsky experimental formula:
where is the molar volume of fluid, A and B are constant values.
The viscosity of liquids with increasing temperature decreases, with an increase in pressure grows.
Formula Poiseil
The viscosity coefficient is included in the formula that establishes the relationship between the volume (V) of the gas, which flows per unit of time through the pipe cross section and the pressure difference () required for this:
where is the length of the pipe, the radius of the pipe.
The number of Reynolds
The nature of the gas movement (liquid) is determined by the dimensionless number of Reynolds ():
Units Measuring Viscosity Coefficient
The main unit of measurement of the dynamic viscosity coefficient in the SI system is:
1pa C \u003d 10 PUAZ
The main unit of measurement of the coefficient of kinematic viscosity in the SI system is:
Examples of solving problems
Example 1.
| The task | Dynamically viscosity of water is equal to PA s. What the magnitude of the limit diameter of the pipe will allow the flow of water to remain laminar, if for 1 s through the cross-section flows the volume of water equal? |
| Decision | The condition of the fluid flow laminarity is: Where are the Reynolds number by the formula:
Water flow rate Find as: In the expression (1.3) - the height of the water cylinder having the volume: Under the condition \u003d 1 s. We will substitute for the expression for the Ranishds number (1.4), we have: Density of water at N.U. kg / m 3. We carry out the calculations, we get: |
| Answer | M. |
Example 2.
| The task | A ball having a density and diameter D pops up in a density fluid at speed. What is the kinematic viscosity of the liquid? |
| Decision | Make a drawing. |
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