Обучение чтению литературы на английском языке по специальности «Аэродинамика». В 2 ч. Ч. 1 (96

the wall is defined to be the pressure. The pressure of a gas is then a measure of the average linear momentum of the moving molecules of a gas. The pressure acts perpendicular (normal) to the wall; the tangential (shear) component of the force is related to the viscosity of the gas.

Scalar Quantity

Let us look at a static gas, one that does not appear to move or flow. While the gas as a whole does not appear to move, the individual molecules of the gas, which we cannot see, are in constant random motion.

Because we are dealing with a nearly infinite number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per area (The pressure) is the same. We can shrink the size of our “container” down to an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has a magnitude but no direction associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.

If the gas as a whole is moving, the measured pressure is different in the direction of the motion. The ordered motion of the gas produces an ordered component of the momentum in the direction of the motion. We associate an additional pressure component, called dynamic pressure, with this fluid momentum. The pressure measured in the direction of the motion is called the total pressure and is equal to the sum of the static and dynamic pressure as described by Bernoulli’s equation.

Macro Scale Definition of Pressure

Turning to the larger scale, pressure is a state variable of a gas, like temperature and density. The change in pressure during any process is governed by the laws of thermodynamic. Although pressure itself is a scalar, we can define a pressure force to be equal to the pressure (force/area) times the surface area in a direction perpendicular to the surface. The pressure force is a vector quantity.

Pressure forces have some unique qualities as compared to gravitational or mechanical forces. In the figure shown above, we have a gas that is confined in a box. a mechanical force is applied to the top of the box. The pressure force within the box opposes the applied force according to Newton’s third law of motion. The scalar pressure equals

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the external force divided by the area of the top of the box. Inside the gas, the pressure acts in all directions. So the pressure pushes on the bottom of the box and on the sides. This is different from simple solid mechanics. If the gas was a solid, there would be no forces applied to the sides of the box; the applied force would be simply transmitted to the bottom. But in a gas, because the molecules are free to move about and collide with one another, a force applied in the vertical direction causes forces in the horizontal direction.

12.Answer the questions to the text.

1.What do you know about gas pressure?

2.What is a measure of the average linear momentum of a gas?

3.Why don’t we detect any motion of the individual molecules?

4.What is called dynamic pressure?

5.What is called the total pressure and what is it equal to?

6.What are the unique qualities of the pressure forces?

13.Speak on the topics using the information from text IB.

1.Molecular definition of pressure.

2.Scalar quantity.

3.Macro scale definition of pressure.

14.Read and translate the text using a dictionary if necessary.

Text IC. Gas Temperature

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Аn important property of any gas is temperature. We have some experience with temperature that we don’t have with properties like viscosity and compressibility. We’ve heard the TV meteorologist give the daily value of the temperature of the atmosphere (15 degrees Celsius, for example). We know that a hot object has a high temperature, and a cold object has a low temperature. And we know that the temperature of an object changes when we heat the object or cool it.

Scientists, however, must be more precise than simply describing an object as “hot” or “cold”. an entire branch of physics, called thermodynamics, is devoted to studying the temperature of objects and the transfer of heat between objects of different temperatures.

The temperature of a gas is a measure of the average translational kinetic energy of the molecules. In a hot gas, the molecules move faster than in a cold gas; the mass remains the same, but the kinetic energy, and hence the temperature, is greater because of the increased velocity of the molecules.

The temperature of a gas is something that we can determine quali& tatively with our senses. We can sense that one gas is hotter than another gas and therefore has a higher temperature. But to determine the tem& perature quantitatively, to assign a number, we must use some principles from thermodynamics:

–the first principle is the observation that the temperature of an ob& ject can affect some physical property of the object, such as the length of a solid, or the gas pressure in a closed vessel, or the electrical resistance of a wire;

–the second principle is the definition of thermodynamic equilibrium between two objects.

Two objects are in thermodynamic equilibrium when they have the same temperature.

– the final principle is the observation that if two objects of different temperatures are brought into contact with one another, they will eventually establish a thermodynamic equilibrium.

The word “eventually” is important. Insulating materials reach equilibrium after a very long time, while conducting materials reach

a number to the temperature of an object. When the thermometer is brought into contact with another object, it quickly establishes a ther&

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modynamic equilibrium. By measuring the thermodynamic effect on some physical property of the thermometer at some fixed conditions, like the boiling point and freezing point of water, we can establish a scale for assigning temperature values.

The number assigned to the temperature depends on what we pick for the reference condition. So several different temperature scales have arisen. The Celsius scale, designated with a C, uses the freezing point of pure water as the zero point and the boiling point as 100 degrees with a linear scale in between these extremes. The Fahrenheit scale, desig& nated with an F, is a lot more confusing. It originally used the freezing point of sea water as the zero point and the freezing point of pure water as 30 degrees, which made the temperature of a healthy person equal to 96 degrees. On this scale, the boiling point of pure water was 212 degrees. So Fahrenheit adjusted the scale to make the boiling point of pure water 212 and the freezing point of pure water 32, which gave 180 degrees between the two reference points. 180 degrees was chosen because it is evenly divisible by 2, 3, 4, 5 and 6. On the new temperature scale, the temperature of a healthy person is 98.6 degrees F. Because there are 100 degrees C and 180 degrees F between the same reference conditions:

1 degree C = 1 degree F · 10 / 180 = 1 degree F · 5 / 9.

Since the scales start at different zero points, we can convert from the temperature on the Fahrenheit scale (TF) to the temperature on the Celsius scale (TC) by using this equation:

TF = 32 + (9 / 5) · TC.

Of course, you can have temperatures below the freezing point of water and these are assigned negative numbers. When scientists began to study the coldest possible temperature, they determined an absolute zero at which molecular kinetic energy is a minimum (but not strictly zero!). They found this value to be at –273.16 degrees C. Using this point as the new zero point we can define another temperature scale called the absolute temperature. If we keep the size of a single degree to be the same as the Celsius scale, we get a temperature scale which has been named after Lord Kelvin and designated with a K. Then:

K = C + 273.16.

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There is a similar absolute temperature corresponding to the Fa& hrenheit degree. It is named after the scientist Rankine and designated with an R:

R = F + 459.69.

Absolute temperatures are used in the equation of state, the derivation of the state variables enthalpy, and entropy, and determining the speed of sound.

Temperature, like pressure, is a scalar quantity. Temperature has a magnitude, but no direction associated with it. It has just a single value at every location in a gas. The value can be changed from location to location, but there is no direction connected to the temperature.

15.A. Make up questions to find out about:

(1)an important property of any gas;

(2)three principles of thermodynamics;

(3)different temperature scales;

(4)a thermometer.

B. Make up dialogues using your questions.

UNIT II

New Words and Word Combinations

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1. Translate the following words and word combinations:

the check – the quick units check;

the section of the object – the small section – the limit of infinitely small sections;

the surface – the closed surface – the pressure on a closed surface; the force – the net force – the component of the net force.

2. Read and translate the text.

Text IIA. Aerodinamic Forces

When two solid objects interact in a mechanical process, forces are transmitted, or applied, at the point of contact. But when a solid object interacts with a fluid, things are more difficult to describe because the fluid can change its shape. For a solid body immersed in a fluid, the “point of contact” is every point on the surface of the body. The fluid can flow around the body and maintain physical contact at all points.

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The transmission, or application, of mechanical forces between a solid body and a fluid occurs at every point on the surface of the body. And the transmission occurs through the fluid pressure.

Variation in Pressure

The magnitude of the force acting over a small section of an object equals the pressure times the area of the section. a quick units check shows that pressure (force/area) times area produces a force. Pressure is a scalar quantity related to the momentum of the molecules of a fluid. Since a force is a vector quantity, having both magnitude and direction, we must determine the direction of the force. Pressure acts perpendicular (or normal) to the solid surface of an object. So the direction of the force on the small section of the object is along the normal to the surface. We denote this direction by the letter n.

The normal direction changes from the front of the airfoil to the rear and from the top to the bottom. To obtain the net mechanical force over the entire solid object, we must sum the contributions from all the small sections. Mathematically, the summation is indicated by the Greek letter sigma ( ). The aerodynamic force F is equal to the sum of the product of the pressure p times the area a in the normal direction:

F = p · А · n.

In the limit of infinitely small sections, this gives the integral of the pressure times the area around the closed surface. If the pressure on a closed surface is a constant, there is no net force produced because the summation of the directions of the normal adds up to zero. (For every small section there is another small section whose normal points in exactly the opposite direction.)

Definitions of Lift and Drag

For a fluid in motion, the velocity will have different values at different locations around the body. The local pressure is related to the local velocity, so the pressure will also vary around the closed surface and a net force is produced. Summing (or integrating) the pressure perpendicular to the surface times the area around the body produces a net force. Since the fluid is in motion, we can define a flow direction along the motion. The component of the net force perpendicular (or normal) to the flow direction is called the lift; the component of the net force along the flow direction is called the drag. These are definitions.

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In reality, there is a single, net, integrated force caused by the pressure variations along a body. This aerodynamic force acts through the average location of the pressure variation which is called the center of pressure.

Velocity Distribution

For an ideal fluid with no boundary layers, the surface of an object is a streamline. If the velocity is low, and no energy is added to the flow, we can use Bernoulli’s equation along a streamline to determine the pressure distribution for a known velocity distribution. If boundary layers are present, things are a little more confusing, since the external flow re& sponds to the edge of the boundary layer and the pressure on the surface is imposed from the edge of the boundary layer. If the boundary layer separates from the surface, it gets even more confusing. How do we deter& mine the velocity distribution around a body? Specifying the velocity is the source of error in two of the more popular incorrect theories of lift. To correctly determine the velocity distribution, we have to solve equations expressing a conservation of mass, momentum, and energy for the fluid passing the object.

Summary

So, to summarize, for any object immersed in a fluid, the me& chanical forces are transmitted at every point on the surface of the body. The forces are transmitted through the pressure, which acts perpendicular to the surface. The net force can be found by integrating (or summing) the pressure times the area around the entire surface. For a moving flow, the pressure will vary from point to point because the velocity varies from point to point. For some simple flow problems we can determine the pressure distribution (and the net force) if we know the velocity distri& bution by using Bernoulli’s equation.

3.Answer the questions using the information from the text.

1.What is pressure related to?

2.What is the “point of contact” for a solid body immersed in a fluid?

3.Will the velocity have the same values at different locations around the body?

4.How does the lift act?

5.What equation can we use to determine the pressure distribution for known velocity distribution for an ideal fluid?

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6.How can we determine the velocity distribution?

7.Why will the pressure vary from point to point for a moving flow?

4.Fill in the blanks with the proper words from the box. maintain, streamline, caused by, net force, vector quantity

1.For an ideal fluid the surface of an object is _____.

2.There is a force ______ the pressure variations.

3.We can determine the pressure distribution and the ____ if we know the velocity distribution.

4.The fluid can _____ physical contact at all points.

5.A force is a ______ .

5.Translate the sentences into English.

1.Когда два твердых тела взаимодействуют, сила приложена в точке контакта.

2.Мы можем решить упрощенное уравнение.

3.Сумма обозначается греческой буквой сигма ( ).

4.Силы действуют на бесконечно малые участки поверхности.

5.Величина силы равна давлению, помноженному на площадь.

6.Направление перпендикуляра изменяется от верхней к нижней части.

6.Complete the sentences using the information from text IIA.

1.The forces are transmitted through the pressure, which _____.

2.We can use Bernulli’s equation along a streamline to ______.

3.Since the fluid is in motion, we ______.

4.The aerodynamic force is equal to the sum of ______.

5.The direction of the force on the small section of the object is

______.

7.Translate the sentences into Russian paying attention to the Modal verbs.

1.The fluid can flow around the body.

2. Things are more difficult to describe because the fluid can change its shape.

3.We must sum the contributions from all the small sections.

4.We can define the flow direction along the motion.

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5.We have to solve equations expressing a conservation of mass, momentum, and energy for the fluid passing the object.

6.The net force can be found by summing the pressure times the area around the entire surface.

7.If we have a liquid flowing in a pipe, the same amount of liquid must be flowing past any point in the pipe regardless of how the pipe is shaped.

8.Unless the spacecraft reaches the speed of 7 miles per second it will not be able to leave the Earth.

8.Learn to read mathematical symbols.

Ssummation

the integral of

9.Try to read English formulae given in text IIA .

F = p A · n

F = p · n) dA

P = F / s

10. Read texts IIB, IIC and IID with a dictionary if necessary. Give a summary of one of the texts by your choice.

Text IIB. What Is Drag?

Drag is the aerodynamic force that opposes an aircraft’s motion through the air. Drag is generated by every part of the airplane (even the engines). How is drag generated?

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