Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» ??? 802.0 ??? 81.2 ????&923 ?602 ????????? ?.?. ??????????? ?602 ???????? ?.?., ????????? ?.?. ???????? ?????? ?????????? ?? ?????????? ????? ?? ???& ?????????? «????????????»: ????.&?????. ???????: ? 2 ?. ? ?. 1. ? ?.: ???&?? ???? ??. ?.?. ???????, 2007. ? 36 ?.: ??. Пособие содержит оригинальные тексты ?? английских и американских научно-технических изданий, лексико-грамматические упражнения, способствующие развитию и закреплению навыков перевода литературы по специальности. Для студентов 3&?? курса факультета «Специальное машиностроение», ??????????? ?? ????????????? «????????????». ??? 802.0 ??? 81.2 ????&923 г ???? ??. ?.?. ???????, 2007 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» ??????????? ? ??????? ???????? ???????????? ?????? ?? ?????????? ? ???& ????????? ??????&??????????? ??????????; ???????, ?????????? ???????? ???????, ??????? ??????? ????????????; ???????&????& ?????????? ??????????, ?????????????? ???????? ? ??????????? ??????? ?????????, ??????????, ???????? ? ????????????? ??????& ???? ?? ?????????? ????? ?? ????????? ?????????????, ? ????? ??& ????? ?????? ????, ????????? ? ??????????????? ?????????. ????????, ?????????????? ? ???????, ????? ?????????????? ?????????? ??? ?? ????? ?????????? ??????? (??? ???????????? ?????????????), ??? ? ? ???????? ??????????????? ??????. ??????? ????????????? ??? ????????? ??????? ?????? ?????????? «??????????? ??????????????». UNIT I New Words and Word Combinations lead n occur v solid n solid ? investigate v investigation n to refer to uniform gas averaged a ?????? ????? ?????, ??????????? ??????? ???? ??????? ???????????, ??????? ???????????? ????????? ?.&?., ????????? ?? ?.&?. ?????????? ??? ??????????? 3 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» exert v altitude n relative to to be related to encounter v fluid n fluid a entire a ordered motion blast n net a angular momentum viscosity n rotational a boundary layer drag n compressibility n to go into alter v shock wave ???????? (??????????), ??????????? (????????) ?????? ??????????? ? ?.&?.; ?? ????????? ? ?.&?. ????? ????????? ? ?&?. ????????????, ??????????? ?????? ????? ???????, ????????????, ?????? ????, ??????, ????? ????????????? ???????? ?????? ?????, ???????? ?????? ????????; ?????? ?????????? ???& ????? ????????; ?????????; ?????????? ?????? ???????? ??????????? ???? ??????? ?????????????, ?????????? ????????? ? ????????? ??????????? ? ??????, ??????????? ????????, ???????????? ??????? ????? 1. Find the transcriptions of the following words in a dictionary. Pronounce them carefully: ?haracteristics, characterize, proton, neutron, neon, oxygen, nitrogen, theory, diatomic, process, gas, through, location, rotational, macro, micro, kinetic, thermodynamic, lead, major, molecule. 2. Translate the following words and word combinations: the air ? the characteristics of air ? the major components of air; the motion ? the individual molecular motions ? the large scale motion; the property ? the gas properties ? the uniform gas properties. 4 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 3. Read and translate the text. Text IA. Gas Properties Definitions Aerodynamics involves the interactions between an object and the surrounding air. To better understand these interactions, we need to know some things about air. Characteristics of Air All matter is made from atoms with the configuration of the atom (number of protons, number of neutrons) determining the kind of matter present (oxygen, lead, silver, neon). Individual atoms can combine with other atoms to form molecules. In particular, oxygen and nitrogen, which are the major components of air, occur in nature as diatomic (2 atom) molecules. Under normal conditions, matter exists as either a solid, a liquid, or a gas. Air is a gas. In any gas, we have a very large number of molecules that are only weakly attracted to each other and are free to move about in space. When studying gases, we can investigate the motions and interactions of individual molecules, or we can investigate the large scale action of the gas as a whole. Scientists refer to the large scale motion of the gas as the macro scale and the individual molecular motions as the micro scale. Some phenomena are easier to understand and explain based on the macro scale, while other phenomena are more easily explained 5 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» on the micro scale. Macro scale investigations are based on things that we can easily observe and measure. But micro scale investigations are based on rather simple theories because we cannot actually observe an individual gas molecule in motion. Macro scale and micro scale investigations are just two views of the same thing. Large Scale Motion of a Gas ? Macro Scale Air is treated as a uniform gas with properties that are averaged from all the individual components (oxygen, nitrogen, water vapor). On the macro scale, we are dealing with large scale effects that we can measure, such as the gas velocity, the pressure exerted on the surroundings, or the temperature of the gas. a gas does not have a fixed shape or size but will expand to fill any container. Because the molecules are free to move about in a gas, the mass of the gas is normally characterized by the density. On the macro scale, the properties of the gas can change with altitude and depend on the thermodynamic state of the gas. The state of the gas can be changed by thermodynamic processes. Individual Molecular Motion of a Gas ? Micro Scale On the micro scale, air is modeled by the kinetic theory of gases. The model assumes that the molecules are very small relative to the distance between molecules. The molecules have the standard physical properties of mass, momentum, and energy. And these properties are related to the macro properties of density, pressure, and temperature. The interactions of the molecules introduce some other properties that we normally do not encounter when dealing with solids. In a solid, the location of the molecules relative to each other remains almost constant. But in a fluid, the molecules can move around and interact with each other and with their surroundings in different ways. As mentioned above, there is always a random component of molecular motion. But the entire fluid can be made to move as well in an ordered motion. As the molecules move, the properties of the fluid move as well. If the properties are transported by the random motion, the process is called diffusion. (an example of diffusion is the spread of an odor in a perfectly still room). If the properties are transported by the ordered motion, the process is called convection. (An example of convection is a blast of cold weather brought down from somewhere in the North.) 6 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» If the flow of a gas produces a net angular momentum, we say the flow is rotational. (No net angular momentum in the fluid is irrotational.) Viscosity As an object moves through the air, the viscosity (stickiness) of the air becomes very important. Air molecules stick to any surface, creating a layer of air near the surface (called a boundary layer) that, in effect, changes the shape of the object. To make things more confusing, the boundary layer may lift off or ?separate? from the body and create an effective shape much different from the physical shape of an object. And to make it even more confusing, the flow conditions in and near the boundary layer are often unsteady (changing in time). The boundary layer is very important in determining both the drag and lift of an object. Compressibility As an object moves through the air, the compressibility of the air also becomes important. Air molecules move around an object as it passes through. If the object passes at a low speed (typically less than 200 mph), the density of the fluid remains constant. But for high speeds, some of the energy of the object goes into compressing the fluid, moving the molecules closer together and changing the air density, which alters the amount of the resulting force on the object. This effect is more important as speed increases. Near and beyond the speed of sound (about 700 mph), shock waves are produced that affect both the lift and drag of an object. 4. Answer the questions to the text. 1. What are the major components of air? 2. What states of substances can you come across in nature? 3. Why do scientists refer to the large scale motion of the gas as the macro scale and the individual molecular motions as the mi& cro scale? 4. What gas parameters can be measured? 5. What affects the gas properties? 6. Does gas have a fixed shape or size? Why? 7. When do we say the flow is rotational? 8. What effect do we have when the speed increases ? 9. What are the physical properties of the molecule? 7 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 5. Give the meanings of the words with the prefixes: atomic?diatomic, action ? interaction, to understand ? to misunder& stand, normally ? abnormally, to change ? unchanged, steady ? unsteady, rotational ? irrotational, relative ? non&relative, defined ? undefined, moving ? immoving, important ? unimportant, compressibility ? incompressibility. 6. Fill in the gaps with the words and word combinations from the box: shock waves, molecules, lift, averaged, drag, kinetic theory, weakly attracted 1. As ________ move, the properties of the fluid move as well. 2. Near and beyond the speed of sound _____ are produced. 3. The boundary layer is very important in determining both ____ and _____ of an object. 4. On the micro scale air is modeled by ____ of gases. 5. In any gas we have a very large number of molecules that are only _____ to each other. 6. Air is treated as a uniform gas with properties that are _____ from all the individual components. 7. Complete the sentences using the information from the text. 1. Under normal conditions, matter exists _______. 2. Macro scale investigations are based on ______. 3. a gas does not have a fixed shape or size but _____. 4. The molecules have the standart physical properties of ______. 5. The state of the gas can be changed by ______. 8. Give the verbs in the brackets in the correct form. 1. Air (to be) a gas. 2. Matter (to exist) as either a solid, a liquid, or a gas. 3. Marco scale investigations (to be) based on things we can easily (to observe) and (to measure). 4. a gas does not (to have) a fixed shape or a size but (to expand) to fill any container. 5. We do not encounter other properties when (to deal) with solids. 8 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 6. (To make) things more confusing, the boundary layer (to lift) off or (to separate) from the body. 7. Air molecules move around the object as it (to pass) through. 8. Molecules are free (to move) about in a gas. 9. Say what parts of speech do the underlined words belong to. Translate them. 1. The mass of the gas is normally characterized by the density. 2. a gas does not have a fixed shape. 3. We are dealing with large scale effects that we can measure, such as the gas velocity, the pressure exerted on the surroundings. 4. As mentioned above, there is always a random component of mo& lecular motion. 5. Air molecules stick to any surface, creating a layer of air near the surface. 6. But for high speeds some of the energy of the object goes into compressing the fluid, moving molecules closer together and changing the air density. 7. When studying gases, we can investigate the motions and interactions of individual molecules. 10. Translate the sentences from Russian into English using the words from the text. 1. Изучая свойства газов, мы можем исследовать взаимодействие отдельных молекул. 2. Исследования наших ученых основываются на довольно простых теориях. 3. ????????????? ????? ???????? ????? ????????? ????????? ? ???????? ???????????. 4. ???????? ???????? ??????? ?????? ??????? ????? ??????. 5. Если свойства газа переносятся в процессе упорядоченного движения молекул, то этот процесс называется конвекцией. 6. ??? ???????? ????? ?????????? ??????? ?????, ??????? ?????? ?? ????????? ???? ??????? ? ?? ??? ??????? ?????& ????????. 11. Read and translate the text using a dictionary if necessary. 9 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» Text IB. Gas Pressure An important property of any gas is its pressure. We have some experience with gas pressure that we don?t have with such properties like viscosity and compressibility. Every day we hear the TV meteorologist give value of the barometric pressure of the atmosphere (29.8 inches of mercury, for example). And most of us have blown up a balloon or used a pump to inflate a bicycle tire or a basketball. There are two ways to look at pressure: (1) the small scale action of individual air molecules or (2) the large scale action of a large number of molecules. Molecular Definition of Pressure From the kinetic theory of gases, a gas is composed of a large number of molecules that are very small relative to the distance between molecules. The molecules of a gas are in constant, random motion and frequently collide with each other and with the walls of any container. The molecules pocess the physical properties of mass, momentum, and energy. The momentum of a single molecule is the product of its mass and velocity, while the kinetic energy is one half the mass times the square of the velocity. As the gas molecules collide with the walls of a container, as shown on the left of the figure, the molecules impart momentum to the walls, producing a force perpendicular to the wall. The sum of the forces of all the molecules striking the wall divided by the area of 10 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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 11 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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 12 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» ?n 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 equilibrium very quickly. With these three thermodynamic principles, we can construct a device for measuring temperature, a thermometer, which assigns a number to the temperature of an object. When the thermometer is brought into contact with another object, it quickly establishes a ther& 13 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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. 14 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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 immerse v flow n streamline n maintain v denote v airfoil n rear n infinitely small contribution n vary v net force impose v respond v ?????????, ???????? ? ????????, ????????? ?????, ????? ????? ?????????? ??????, ????? ??????& ???; ?????????? ????? ????????? ?????????, ?????????? ???????????????? ???????????, ??????? ???; ??????, ??????? ??????? ?????????? ????? ?????, ????? ?????????? ???????????????? (??????????????) ???? ???????? ???????????, ???????? 15 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» distribution v to add up edge ????????????? ??????????, ???????????? ??????, ????, ??????? 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. 16 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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 (S). 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 · ? · 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. 17 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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? 18 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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. ?? ????? ?????? ?????????? ?????????. 3. ????? ???????????? ????????? ?????? ????? (S). 4. ???? ????????? ?? ?????????? ????? ??????? ???????????. 5. ???????? ???? ????? ????????, ???????????? ?? ???????. 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. 19 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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. a=b a+b a?b a<b a>b a?b 106 am ab = a · b a/b ac/bd S dy/dx n! т a equals b / a is equal to b a plus b a minus b a is less than b a is greater than b a is much greater than b the sixth power of ten / ten to the sixth power a sub m / a subscript m / a mth a times b / a multiplied b a divided by b a times c over b times d summation derivative of y with respect to x n factorial the integral of 9. Try to read English formulae given in text IIA . F=SpA·n F = т(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? 20 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» Drag is a mechanical force. It is generated by the interaction and contact of a solid body with a fluid (liquid or gas). For drag to be gener& ated, the solid body must be in contact with the fluid. If there is no fluid, there is no drag. Drag is generated by the difference in velocity between the solid object and the fluid. There must be motion between the object and the fluid. If there is no motion, there is no drag. It makes no differ& ence whether the object moves through a static fluid or whether the fluid moves past a static solid object. Drag acts in a direction that opposes the motion. (Lift acts perpendicular to the motion.) We can think of drag as aerodynamic friction, and one of the sources of drag is the skin friction between the molecules of the air and the solid surface of the aircraft. Because the skin friction is an interaction between a solid and a gas, the magnitude of the skin friction depends on properties of both solid and gas. For the solid, a smooth, waxed surface produces less skin friction than a roughened surface. For the gas, the magnitude depends on the viscosity of the air and the relative magnitude of the viscous forces to the motion of the flow, expressed as the Reynolds number. Along the solid surface, a boundary layer of low energy flow is generated. And the magnitude of the skin friction depends on the state of this flow. We can also think of drag as aerodynamic resistance to the motion of the object through the fluid. This source of drag depends on the shape of the aircraft and is called form drag. As air flows around a body, the local velocity and pressure are changed. Since pressure is a measure of the mo& mentum of the gas molecules and a change in momentum produces a force, a varying pressure distribution will produce a force on the body. We can determine the magnitude of the force by integrating (or adding up) the local pressure times the surface area around the entire body. The component of the aerodynamic force that is opposed to the motion is the drag; the component perpendicular to the motion is the lift. Both the lift and drag force act through the center of pressure of the object. There is an additional drag component caused by the generation of lift . Aerodynamicists have named this component the induced drag. This drag occurs because the flow near the wing tips is distorted spanwise as a result of the pressure difference from the top to the bottom of the wing. Swirling vortices are formed at the wing tips, and there is an energy associated with these vortices. The induced drag is an indication of the amount of energy lost to the tip vortices. The magnitude of induced drag depends on the amount of lift being generated by the wing and on 21 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» the wing geometry. Long, thin (chordwise) wings have low induced drag; short wings with a large chord have high induced drag. Additional sources of drag include wave drag and ram drag. As an aircraft approaches the speed of sound, shock waves are generated along the surface. There is an additional drag penalty (called wave drag) that is associated with the formation of the shock waves. The magnitude of the wave drag depends on the Mach number of the flow. Ram drag is associated with slowing down the free stream air as air is brought inside the aircraft. Jet engines and cooling inlets on the aircraft are sources of ram drag. Text IIC. What Is Lift? Lift is the force that holds an aircraft in the air. Lift can be generated by any part of the airplane, but most of the lift on a normal airliner is generated by the wings. Lift is an aerodynamic force produced by the motion of a fluid past an object. Lift acts through the center of pressure of the object and is defined to be perpendicular to the flow direction. How Is Lift Generated? There are many explanations for the generation of lift found in encyclopedias, in basic physics textbooks, and on Web sites. Unfortunately, many of the explanations are misleading and incorrect. Theories on the generation of lift have become a source of great controversy and a topic for heated arguments. To help you understand lift and it?s origins, a series of pages will describe The various theories and how some of The popular theories fail. Lift occurs when a flow of gas is turned by a solid object. The flow is turned in one direction, and the lift is generated in the opposite direction, according to Newton?s Third Law of action and reaction. Because air is a gas and the molecules are free to move about, any solid surface can deflect a flow. For an airfoil, both the upper and lower surfaces contribute to the flow turning. Neglecting the upper surface?s part in turning the flow leads to an incorrect theory of lift. No Fluid, No Lift. Lift is a mechanical force. It is generated by the interaction and contact of a solid body with a fluid (liquid or gas). It is not generated by a force field, in the sense of a gravitational field, or an electromagnetic field, where one object can affect another object 22 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» without being in physical contact. For lift to be generated, the solid body must be in contact with the fluid: no fluid, no lift. (The space shuttle does not stay in space because of lift from its wings but because of orbital mechanics related to its speed. Space is nearly a vacuum. Without air, there is no lift generated by the wings.) No Motion, No Lift. Lift is generated by the difference in velocity between the solid object and the fluid. There must be motion between the object and the fluid: no motion, no lift. It makes no difference whether the object moves through a static fluid, or the fluid moves past a static solid object. Lift acts perpendicular to the motion. (Drag acts in the direction opposed to the motion.) Text IID. What Is Weight? Weight is the force generated by the gravitational attraction of the earth, on the airplane. We are more familiar with weight than with the other forces acting on an airplane, because each of us have our own weight which we can measure every another thing is light. But weight, the gravitational force, is fundamentally different from the aerodynamic forces, lift and drag. Aerodynamic forces are mechanical forces and the airplane has to be in physical contact with the air which generates the force. The gravitational force is a field force; the source of the force does not have to be in physical contact with the object (The airplane). The nature of the gravitational force has been studied by scientists for many years and is still being investigated by theoretical physicists. For an object the size of an airplane, the descriptions given three hundred years ago by Sir Isaac Newton work quite well. Newton developed his theory of gravitation when he was only 23 years old and published the theories with his laws of motion some years later. The gravitational force between two objects depends on the mass of the objects and the inverse of the square of the distance between the objects. Larger objects create greater forces and the farther apart the objects are the weaker the attraction. Newton was able to express the relationship in a single weight equation. For an airplane, weight is a force which is always directed towards the center of the earth. The magnitude of this force depends on the mass of all of the parts of the airplane itself, plus the amount of fuel, plus any payload on board (people, baggage, freight...). The weight is distributed throughout the airplane, but we can often think of it as collected and 23 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» acting through a single point called the center of gravity. In flight, the airplane rotates about the center of gravity, but the direction of the weight force always remains toward the center of the earth. During a flight the aircraft burns up its fuel, so the weight of the airplane constantly changes. Also, the distribution of the weight and the center of gravity can change, so the pilot must constantly adjust the controls to keep the airplane balanced. The dream remains that, if we could really understand gravity, we could create anti&gravity devices which would revolutionize travel through the sky. Unfortunately, anti&gravity devices only exist in science fiction. Machines like airplanes, or magnetic levitation devices, create forces opposed to the gravitational force, but they do not block out or eliminate the gravitational force. UNIT III New Words and Word Combinations slip n disturb v springiness n to slow down collision n stall n transfer n heat transfer inlet n scope n three&dimensional a conservation displacement n laminar a turbulent a swirling flow uniformly adv gluey a 24 ??????????, ????? ?????????, ????????? ???????????, ????????? ????????? ???????????? ???? ?????? ??????? ???????????? ????? ???????, ???????, ????? ?????????? ?????????? ???????? ?????????? ???????????? ???????? (???????????) ????? ?????????? ???????, ?????? Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 1. Translate the following words and word combinations: the value ? the stream value ? the free steam value; the drag ? the friction drag ? the skin friction drag; the inlet ? the aircraft inlet ? the high speed aircraft inlet; the variation ? the velocity variation ? the steamwise velocity variation. 2. Read and translate the text. Text IIIA. Boundary Layer As an object moves through a fluid, or as a fluid moves past an object, the molecules of the fluid near the object are disturbed and move around the object. Aerodynamic forces are generated between the fluid and the object. The magnitude of these forces depend on the shape of the object, the speed of the object, the mass of the fluid going by the object and on two other important properties of the fluid; the viscosity, or stickiness, and the compressibility, or springiness, of the fluid. То model these effects рroреrly, aerodynamicists use similarity parameters which are ratios of these effects to other forces present in the problem. If two experiments have the same values for the similarity parameters, then the relative importance of the forces are being correctly modeled. Aerodynamic forces depend in a complex way on the viscosity of the fluid. As the fluid moves past the object, the molecules right next to the surface stick to the surface. The molecules just above the surface are slowed down in their collisions with the molecules sticking to the surface. These molecules in turn slow down the flow just above them. The farther one moves away from the surface, the fewer the collisions affected by the object surface. This creates a thin layer of fluid near the surface in which the velocity changes from zero at the surface to the free stream value away from the surface. Engineers call this layer the boundary layer because it occurs on the boundary of the fluid. The details of the flow within the boundary layer are very important for many problems in aerodynamics, including the development of a wing stall, the skin friction drag of an object, the heat transfer that occurs in high speed flight, and the performance of a high speed aircraft inlet. Unfortunately, the physical and mathematical details of boundary layer theory are beyond the scope of this article and are usually studied in late 25 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» undergraduate or graduate school in college. We will only present some of the effects of the boundary layer. On the figure we show the streamwise velocity variation from free stream to the surface. In reality, the effects are three dimensional. From the conservation of mass in three dimensions, a change in velocity in the streamwise direction causes a change in velocity in the other directions as well. There is a small component of velocity perpendicular to the surface which displaces or moves the flow above it. One can define the thickness of the boundary layer to be the amount of this displacement. The displacement thickness depends on the Reynolds number which is the ratio of inertial (resistant to change or motion) forces to viscous (heavy and gluey) forces and is given by the equation: Reynolds number (Re) equals velocity (V) times density (r) times a characteristic length (1) divided by the viscosity coefficient (µ): Re = V · r · 1 / µ. Boundary layers may be either laminar (layered), or turbulent (disordered) depending on the value of the Reynolds number. For lower Reynolds numbers, the boundary layer is laminar and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of the figure. For higher Reynolds numbers, the boundary layer is turbulent and the streamwise velocity is characterized by unsteady (changing with time) swirling flows inside the boundary layer. The external flow reacts to the edge of the boundary layer just as it would to the physical surface of an object. So the boundary layer gives any object an ?effective? shape which is usually slightly different from the physical shape. To make things more confusing, the boundary layer may lift off or ?separate? from the body and create an effective shape much different from the physical shape. This happens because the flow in the boundary has very low energy (relative to the free stream) and is more easily driven by changes in pressure. Flow separation is the reason for wing stall at high angle of attack. The effects of the boundary layer on lift are contained in the lift coefficient and the effects on drag are contained in the drag coefficient. Historical note: The theory which describes boundary layer effects was first presented by Ludwig Prandtl in the early 1900?s. The general fluids equations had been known for many years, but solutions to the equations did not properly describe observed flow effects (like wing stalls) . Prandtl was the first to realize that the relative magnitude of 26 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» the inertial and viscous forces changed from a layer very near the surface to a region far from the surface. He first proposed the interactively coupled, two layer solution which properly models many flow problems. 3. Answer the questions. 1. What does the term boundary layer stand for? 2. What does the magnitude of aerodynamic forces depend on? 3. What do aerodynamicists use to model the effects in the fluid? 4. When can the boundary layers be laminar? When can they be turbulent? 5. Where are the effects of the boundary layer on lift contained? 6. Who was the first to present the theory describing boundary layer affects? 4. Fill in the blanks with the words and word combinations from the box: laminar, uniformly, angle of attack, boundary layer, lift coefficient, disturbed 1. Engineers call this layer the ______ because it occurs on the boundary of the fluid. 2. The molecules of the fluid near the object are ______ and move around the object. 3. For lower Reynolds numbers, the boundary layer is ______ . 4. Velocity changes from zero at the surface to the _______ away from the surface. 5. Flow separation is the reason for wing stall at high _______ . 6. The streamwise velocity changes _______ as one moves away from the wall. 7. The effects of the boundary layer on lift are contained in the ______ . 5. Complete the sentences using the information from the text. 1. Aerodynamic forces depend on _____. 2. In reality the effects in the boundary layer are _____. 3. The Reynolds number is ______. 4. Boundary layers may be either ______. 5. The boundary layer may lift off the body and create an effective shape different from the physical shape because ______. 27 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 6. Translate the sentences into English. 1. 2. 3. 4. 5. 6. Теория пограничного слоя не изучается в нашем курсе. ??? ??????? ?? ????? ??????????. ??????????? ?????????. Разделение потока было причиной этого явления. Величина этой силы зависит от формы объекта. ????? движется вдоль объекта. 7. Match the beginnings of the sentences with their ends. 1. The magnitude of these forces 2. The details of the flow within the boundary layer 3. The farther one moves away from the surface 4. Boundary layers may be 5. The external flow 6. The general fluids equations had been a. very important for many pro& blems in aerodynamics. b. reacts to the edge of the boun& dary layer just as it would to the physical surface of an object. c. known for many years, but solutions did not properly de& scribe observed flow effects. d. depend on the shape of the object. e. either laminar, or turbulent. f. the fewer the collisions affected by the object surface. 8. Give the verbs in the brackets in the correct form. 1. Aerodynamic forces (to generate) between the fluid and the ob& ject. 2. The molecules (to slow down) the flow just above them. 3. The streamwise velocity (to change) uniformly. 4. The theory of boundary layer (to present) first by Ludwig Prandtl in 1900?s. 5. Solutions to the equations (not to describe) properly observed flow effects. 6. The effects of the boundary layer on lift (to contain) in the lift coefficient. 7. A change in velocity in the streamwise direction (to cause) a change in velocity in the other directions as well. 28 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 8. The flow in the boundary (to have) low energy and easily (to drive) by changes in pressure. 9. Reynolds number (to give) by the equation. 9. Read and translate the text. Write out the terms from it. Text IIIB. Equation of State Ideal Gas. Properties V = C2 · T Density = r, Pressure = p, Temperature = Т, Volume = V, Mass = m. Observation. Boil: For a given mass, at constant temperature, the pressure times the volume is a constant: p · V = С1. Charles and Gay&Lussaс: For a given mass, at constant pressure, the volume is directly proportional to the temperature: Combine: pV / Т = nR R = 8.31 J / mole / K(Universal) pV = nRT, n = number of moles. Divide by mass: Specific Volume = v = volume / mass = 1 / r pv = nRT / m or pv = RT op = RrT, R = Constant value for each gas = 286 kJ / kg / K (for air). Air is a gas. Gases have various properties that we can observe with our senses, including the gas pressure (p), temperature (Т), mass (m), and volume (V) that contains the gas. Careful, scientific observation has determined that these variables are related to one another, and the values of these properties determine the state of the gas. If we fix any two of the properties we can determine the nature of the relationship between the other two. If the pressure and temperature are held constant, the volume of the gas depends directly on the mass, or amount of gas. This allows us to define a single additional property called the gas density (r), which is the ratio of mass to volume. If the mass and 29 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» temperature are held constant, the product of the pressure and volume are observed to be nearly constant for a real gas. (The product of pressure and volume is exactly a constant for an ideal gas.) This relationship between pressure and volume is called Boyle?s Law in honor of Robert Boyle who first observed it in 1660. Finally, if the mass and pressure are held constant, the volume is directly proportional to the temperature for an ideal gas. This relationship is called Charles and Gay&Lussac?s Law in honor of the two French scientists who discovered the relationship. The gas laws of Boyle and Charles and Gay&Lussac can be combined into a single equation of state: p · V / Т = n · R where ? · ? denotes multi& plication and / denotes division. To account for the effects of mass, we have defined the constant to contain two parts: a universal constant (R) and the mass of the gas expressed in moles (n). Performing a little algebra, we obtain the more familiar form: p · V = n · R · T. Aerodynamicists use a slightly different form of the equation of state that is specialized for air. If we divide both sides of the general equation by the mass of the gas, the volume becomes the specific volume, which is the inverse of the gas density. We also define a new gas constant (R), which is equal to the universal gas constant divided by the mass per mole of the gas. The value of the new constant depends on the type of gas as opposed to the universal gas constant, which is the same for all gases. The value of the equation of state for air is given as 286 kilo Joule per kilogram per degree Kelvin . The equation of state can be written in terms of the specific volume or in terms of the air density as p · v = R · T or p = r · R · T. Notice that the equation of state given here applies only to an ideal gas, or a real gas that behaves like an ideal gas. There are in fact many different forms for the equation of state for different gases. Also be aware that the temperature given in the equation of state must be an absolute temperature that begins at absolute zero. In the metric system of units, we must specify the temperature in degrees Kelvin (not Celsius). In the English system, absolute temperature is in degrees Rankine (not Fahrenheit). 10. Give a summary of text IIIB. 11. Read and translate the text using a dictionary if necessary. 30 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» Text IIIC. Flow Characteristics Although the Mach number is used to define the occurrence of some flow features, the basic parameters defining the speed characteristics are three: Reynolds number; Mach number; Knudsen number. Reynolds Number Effects: Viscosity The Reynolds number (first introduced by L. Prandtl) dominates the viscous effects by defining the size of the boundary layers. Almost all aerodynamic flows occur at high Reynolds number, which implies viscous phenomena are limited to narrow boundary layers. 6 The notion high is somewhat arbitrary, although the value of 0.5 · 10 is often the switching boundary. 6 6 Flows at Reynolds numbers in the range 0.1 · 10 < Re < 0.5 · 10 are called Low&Reynolds Number Aerodynamics . Flows at very small Reynolds numbers are dominated by viscosity and are better described with the use of Stanton number. These flows (sometimes called creeping motions or Stokes flows) are not considered proper domain of aerodynamics. Mach Number Effects: Compressibility The Mach number (introduced by J. Ackeret, 1992 ) defines the appearance of compressibility effects and the charges associated with the shock waves. In the subsonic speed range of the compressibility of the flow is negligible. At transonic speeds there are pockets of flow below and above the speed sound. The main feature of this speed range is the presence of compression and expansion shock waves. ? supersonic flow is exclusively above the speed of sound. Supersonic aerodynamics differs from aerodynamics at lower speeds because the flow is highly compressible. The Reynolds and Mach numbers are independent and are both needed to define the characteristics of speeds in the transonic regime. At subsonic speeds the flow is generally treated as a constant&density flow and the Mach number influence is neglected. Knudsen Number Effects: Molecular Flow Flows at higher Mach numbers are object of hypersonics (a term due to Tsien, 1946). Other definitions sometimes used for this speed regime is 31 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» gasdynamics, rarefied gasdynamics and magnetigasdynamics for yet higher speeds . Two more dimensionless parameters are useful to describe the physics: the Knudsen number and the Damkolner ratio (e. g. the ratio between a characteristic time and the molecular relaxation time). The Knudsen number is not quite independent, since it can also be written as ratio between Mach and Reynolds numbers. Flows at Knudsen numbers Kn ? 1 are basically collisionless flows (artificial satellites in orbital motion above the Earth); flows at Kn < 1 are in regime of slight rarefaction and are called slip flows; flows at inter& mediate Knudsen numbers are called transitional flows. These flows re& quire some modeling of the molecular gas, and are beyond the domain of validity of the Navier&Stokes equations. At speeds above M = 5 there are changes in the physics of the flow, because of changes in the medium and of the aero&thermodynamic heating . At M > 7 the medium becomes chemically reactive; at M > 12 it is also ionized . The energy produced by the propulsion system is used to overcome the resistance of the flight vehicle (drag), and is converted into compression work on the surrounding medium. 12. Read and explain the formulae given in texts IIIA , IIIB and IIIC: Kn ? 1 0.1 Ч 106 < Re < 0.5 Ч 106 Re = V · r · l / µ V = C2 · T pv = nRT / m. 13. Give a summary of text IIIC. Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» ?????? ?????????? ? ?????? ?????&??????? ??????????????? ???????: ? 2 ?. / ???.&????. ?.?. ???????. ? ?????: ???????, 2004. ??????? ?????&??????? ???????: ? 2 ?. / ??? ???. ?.?. ????????& ??. ??.: ??????? ????, 1987. ?????? ?.?. ??????? ???????????? ???????????: ?? ?????????? ?????, ???????? ? ???????????? ??????&??????????? ??????????: 2&? ???., ???????. ? ???. ? ?.: ?. ??????, 2006. ??????? ?.?. ?????? ? ??????? ?????????? ??????&??????????? ??????????: ???????&???????. ??????????. ? ?.: ???, 2003. th Hornby F.S. Oxford Advanced Learner?s Dictionary, 7 ed. ? Oxford: Oxford Univ. Press, 2006. Longman Dictionary of Scientific Usage: The Reprint Edition. ? Moscow: Longman, 1988. Macmillan English Dictionary for Advanced Learners: International Student Edition. ? L.: Macmillan Education, 2006. www.en.wikipedia.org/wiki/Aerodynamics www.grc.nasa.gov Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» Contents ??????????? .................................................................................................. Unit I ................................................................................................................. New Words and Word Combinations ........................................................ Text IA: Gas Properties Definitions ...................................................... Text IB: Gas Pressure ............................................................................... Text 1C: Gas Temperature ...................................................................... Unit II .............................................................................................................. New Words and Word Combinations ................................................... Text IIA: Aerodynamic Forces ................................................................ Text IIB: What Is Drag? .......................................................................... Text IIC: What Is Lift? ............................................................................ Text IID: What Is Weight? ..................................................................... Unit III ............................................................................................................. New Words and Word Combinations ................................................... Text IIIA: Boundary Layer ...................................................................... Text IIIB: Equation of State .................................................................. Text IIIC: Flow Characteristics ............................................................. ?????? ?????????? ? ?????? .................................................................... 3 3 3 5 10 12 15 15 16 20 22 23 24 24 25 29 31 33 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» ??????? ??????? ???????? ??????? ?????????? ????????? ???? ???????????? ???????? ?????? ?????????? ?? ?????????? ????? ?? ????????????? «?????????????» ???????? ?.?. ??????? ????????? ?.?. ??????? ???????????? ??????? ?.?. ???????? ????????? ? ?????? 12.12. 2007. ?????? 60Ч 84/16. ?????? ????????. ???. ???. ?. 2,09. ??.&???. ?. 1,95. ????? 100 ???. ???. № 63. ????? ???????????? ???? ??. ?.?. ??????? ?????????? ???? ??. ?.?. ??????? 105005, ??????, 2&? ?????????? ??., 5 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» ??? ??????? е содержит оригинальные тексты ?? английских и американских научно-технических изданий, лексико-грамматические упражнения, способствующие развитию и закреплению навыков перевода литературы по специальности. Для студентов 3&?? курса факультета «Специальное машиностроение», ??????????? ?? ????????????? «????????????». ??? 802.0 ??? 81.2 ????&923 г ???? ??. ?.?. ???????, 2007 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» ??????????? ? ??????? ???????? ???????????? ?????? ?? ?????????? ? ???& ????????? ??????&??????????? ??????????; ???????, ?????????? ???????? ???????, ??????? ??????? ????????????; ???????&????& ?????????? ??????????, ?????????????? ???????? ? ??????????? ??????? ?????????, ??????????, ???????? ? ????????????? ??????& ???? ?? ?????????? ????? ?? ????????? ?????????????, ? ????? ??& ????? ?????? ????, ????????? ? ??????????????? ?????????. ????????, ?????????????? ? ???????, ????? ?????????????? ?????????? ??? ?? ????? ?????????? ??????? (??? ???????????? ?????????????), ??? ? ? ???????? ??????????????? ??????. ??????? ????????????? ??? ????????? ??????? ?????? ?????????? «??????????? ??????????????». UNIT I New Words and Word Combinations lead n occur v solid n solid ? investigate v investigation n to refer to uniform gas averaged a ?????? ????? ?????, ??????????? ??????? ???? ??????? ???????????, ??????? ???????????? ????????? ?.&?., ????????? ?? ?.&?. ?????????? ??? ??????????? 3 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» exert v altitude n relative to to be related to encounter v fluid n fluid a entire a ordered motion blast n net a angular momentum viscosity n rotational a boundary layer drag n compressibility n to go into alter v shock wave ???????? (??????????), ??????????? (????????) ?????? ??????????? ? ?.&?.; ?? ????????? ? ?.&?. ????? ????????? ? ?&?. ????????????, ??????????? ?????? ????? ???????, ????????????, ?????? ????, ??????, ????? ????????????? ???????? ?????? ?????, ???????? ?????? ????????; ?????? ?????????? ???& ????? ????????; ?????????; ?????????? ?????? ???????? ??????????? ???? ??????? ?????????????, ?????????? ????????? ? ????????? ??????????? ? ??????, ??????????? ????????, ???????????? ??????? ????? 1. Find the transcriptions of the following words in a dictionary. Pronounce them carefully: ?haracteristics, characterize, proton, neutron, neon, oxygen, nitrogen, theory, diatomic, process, gas, through, location, rotational, macro, micro, kinetic, thermodynamic, lead, major, molecule. 2. Translate the following words and word combinations: the air ? the characteristics of air ? the major components of air; the motion ? the individual molecular motions ? the large scale motion; the property ? the gas properties ? the uniform gas properties. 4 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 3. Read and translate the text. Text IA. Gas Properties Definitions Aerodynamics involves the interactions between an object and the surrounding air. To better understand these interactions, we need to know some things about air. Characteristics of Air All matter is made from atoms with the configuration of the atom (number of protons, number of neutrons) determining the kind of matter present (oxygen, lead, silver, neon). Individual atoms can combine with other atoms to form molecules. In particular, oxygen and nitrogen, which are the major components of air, occur in nature as diatomic (2 atom) molecules. Under normal conditions, matter exists as either a solid, a liquid, or a gas. Air is a gas. In any gas, we have a very large number of molecules that are only weakly attracted to each other and are free to move about in space. When studying gases, we can investigate the motions and interactions of individual molecules, or we can investigate the large scale action of the gas as a whole. Scientists refer to the large scale motion of the gas as the macro scale and the individual molecular motions as the micro scale. Some phenomena are easier to understand and explain based on the macro scale, while other phenomena are more easily explained 5 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» on the micro scale. Macro scale investigations are based on things that we can easily observe and measure. But micro scale investigations are based on rather simple theories because we cannot actually observe an individual gas molecule in motion. Macro scale and micro scale investigations are just two views of the same thing. Large Scale Motion of a Gas ? Macro Scale Air is treated as a uniform gas with properties that are averaged from all the individual components (oxygen, nitrogen, water vapor). On the macro scale, we are dealing with large scale effects that we can measure, such as the gas velocity, the pressure exerted on the surroundings, or the temperature of the gas. a gas does not have a fixed shape or size but will expand to fill any container. Because the molecules are free to move about in a gas, the mass of the gas is normally characterized by the density. On the macro scale, the properties of the gas can change with altitude and depend on the thermodynamic state of the gas. The state of the gas can be changed by thermodynamic processes. Individual Molecular Motion of a Gas ? Micro Scale On the micro scale, air is modeled by the kinetic theory of gases. The model assumes that the molecules are very small relative to the distance between molecules. The molecules have the standard physical properties of mass, momentum, and energy. And these properties are related to the macro properties of density, pressure, and temperature. The interactions of the molecules introduce some other properties that we normally do not encounter when dealing with solids. In a solid, the location of the molecules relative to each other remains almost constant. But in a fluid, the molecules can move around and interact with each other and with their surroundings in different ways. As mentioned above, there is always a random component of molecular motion. But the entire fluid can be made to move as well in an ordered motion. As the molecules move, the properties of the fluid move as well. If the properties are transported by the random motion, the process is called diffusion. (an example of diffusion is the spread of an odor in a perfectly still room). If the properties are transported by the ordered motion, the process is called convection. (An example of convection is a blast of cold weather brought down from somewhere in the North.) 6 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» If the flow of a gas produces a net angular momentum, we say the flow is rotational. (No net angular momentum in the fluid is irrotational.) Viscosity As an object moves through the air, the viscosity (stickiness) of the air becomes very important. Air molecules stick to any surface, creating a layer of air near the surface (called a boundary layer) that, in effect, changes the shape of the object. To make things more confusing, the boundary layer may lift off or ?separate? from the body and create an effective shape much different from the physical shape of an object. And to make it even more confusing, the flow conditions in and near the boundary layer are often unsteady (changing in time). The boundary layer is very important in determining both the drag and lift of an object. Compressibility As an object moves through the air, the compressibility of the air also becomes important. Air molecules move around an object as it passes through. If the object passes at a low speed (typically less than 200 mph), the density of the fluid remains constant. But for high speeds, some of the energy of the object goes into compressing the fluid, moving the molecules closer together and changing the air density, which alters the amount of the resulting force on the object. This effect is more important as speed increases. Near and beyond the speed of sound (about 700 mph), shock waves are produced that affect both the lift and drag of an object. 4. Answer the questions to the text. 1. What are the major components of air? 2. What states of substances can you come across in nature? 3. Why do scientists refer to the large scale motion of the gas as the macro scale and the individual molecular motions as the mi& cro scale? 4. What gas parameters can be measured? 5. What affects the gas properties? 6. Does gas have a fixed shape or size? Why? 7. When do we say the flow is rotational? 8. What effect do we have when the speed increases ? 9. What are the physical properties of the molecule? 7 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 5. Give the meanings of the words with the prefixes: atomic?diatomic, action ? interaction, to understand ? to misunder& stand, normally ? abnormally, to change ? unchanged, steady ? unsteady, rotational ? irrotational, relative ? non&relative, defined ? undefined, moving ? immoving, important ? unimportant, compressibility ? incompressibility. 6. Fill in the gaps with the words and word combinations from the box: shock waves, molecules, lift, averaged, drag, kinetic theory, weakly attracted 1. As ________ move, the properties of the fluid move as well. 2. Near and beyond the speed of sound _____ are produced. 3. The boundary layer is very important in determining both ____ and _____ of an object. 4. On the micro scale air is modeled by ____ of gases. 5. In any gas we have a very large number of molecules that are only _____ to each other. 6. Air is treated as a uniform gas with properties that are _____ from all the individual components. 7. Complete the sentences using the information from the text. 1. Under normal conditions, matter exists _______. 2. Macro scale investigations are based on ______. 3. a gas does not have a fixed shape or size but _____. 4. The molecules have the standart physical properties of ______. 5. The state of the gas can be changed by ______. 8. Give the verbs in the brackets in the correct form. 1. Air (to be) a gas. 2. Matter (to exist) as either a solid, a liquid, or a gas. 3. Marco scale investigations (to be) based on things we can easily (to observe) and (to measure). 4. a gas does not (to have) a fixed shape or a size but (to expand) to fill any container. 5. We do not encounter other properties when (to deal) with solids. 8 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 6. (To make) things more confusing, the boundary layer (to lift) off or (to separate) from the body. 7. Air molecules move around the object as it (to pass) through. 8. Molecules are free (to move) about in a gas. 9. Say what parts of speech do the underlined words belong to. Translate them. 1. The mass of the gas is normally characterized by the density. 2. a gas does not have a fixed shape. 3. We are dealing with large scale effects that we can measure, such as the gas velocity, the pressure exerted on the surroundings. 4. As mentioned above, there is always a random component of mo& lecular motion. 5. Air molecules stick to any surface, creating a layer of air near the surface. 6. But for high speeds some of the energy of the object goes into compressing the fluid, moving molecules closer together and changing the air density. 7. When studying gases, we can investigate the motions and interactions of individual molecules. 10. Translate the sentences from Russian into English using the words from the text. 1. Изучая свойства газов, мы можем исследовать взаимодействие отдельных молекул. 2. Исследования наших ученых основываются на довольно простых теориях. 3. ????????????? ????? ???????? ????? ????????? ????????? ? ???????? ???????????. 4. ???????? ???????? ??????? ?????? ??????? ????? ??????. 5. Если свойства газа переносятся в процессе упорядоченного движения молекул, то этот процесс называется конвекцией. 6. ??? ???????? ????? ?????????? ??????? ?????, ??????? ?????? ?? ????????? ???? ??????? ? ?? ??? ??????? ?????& ????????. 11. Read and translate the text using a dictionary if necessary. 9 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» Text IB. Gas Pressure An important property of any gas is its pressure. We have some experience with gas pressure that we don?t have with such properties like viscosity and compressibility. Every day we hear the TV meteorologist give value of the barometric pressure of the atmosphere (29.8 inches of mercury, for example). And most of us have blown up a balloon or used a pump to inflate a bicycle tire or a basketball. There are two ways to look at pressure: (1) the small scale action of individual air molecules or (2) the large scale action of a large number of molecules. Molecular Definition of Pressure From the kinetic theory of gases, a gas is composed of a large number of molecules that are very small relative to the distance between molecules. The molecules of a gas are in constant, random motion and frequently collide with each other and with the walls of any container. The molecules pocess the physical properties of mass, momentum, and energy. The momentum of a single molecule is the product of its mass and velocity, while the kinetic energy is one half the mass times the square of the velocity. As the gas molecules collide with the walls of a container, as shown on the left of the figure, the molecules impart momentum to the walls, producing a force perpendicular to the wall. The sum of the forces of all the molecules striking the wall divided by the area of 10 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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 11 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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 12 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» ?n 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 equilibrium very quickly. With these three thermodynamic principles, we can construct a device for measuring temperature, a thermometer, which assigns a number to the temperature of an object. When the thermometer is brought into contact with another object, it quickly establishes a ther& 13 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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. 14 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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 immerse v flow n streamline n maintain v denote v airfoil n rear n infinitely small contribution n vary v net force impose v respond v ?????????, ???????? ? ????????, ????????? ?????, ????? ????? ?????????? ??????, ????? ??????& ???; ?????????? ????? ????????? ?????????, ?????????? ???????????????? ???????????, ??????? ???; ??????, ??????? ??????? ?????????? ????? ?????, ????? ?????????? ???????????????? (??????????????) ???? ???????? ???????????, ???????? 15 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» distribution v to add up edge ????????????? ??????????, ???????????? ??????, ????, ??????? 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. 16 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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 (S). 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 · ? · 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. 17 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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? 18 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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. ?? ????? ?????? ?????????? ?????????. 3. ????? ???????????? ????????? ?????? ????? (S). 4. ???? ????????? ?? ?????????? ????? ??????? ???????????. 5. ???????? ???? ????? ????????, ???????????? ?? ???????. 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. 19 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 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. a=b a+b a?b a<b a>b a?b 106 am ab = a · b a/b ac/bd S dy/dx n! т a equals b / a is equal to b a plus b a minus b a is less than b a is greater than b a is much greater than b the sixth power of ten / ten to the sixth power a sub m / a subscript m / a mth a times b / a multiplied b a divided by b a times c over b times d summation derivative of y with respect to x n factorial the integral of 9. Try to read English formulae given in text IIA . F=SpA·n F = т(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? 20 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» Drag is a mechanical force. It is generated by the interaction and contact of a solid body with a fluid (liquid or gas). For drag to be gener& ated, the solid body must be in contact with the fluid. If there is no fluid, there is no drag. Drag is generated by the difference in velocity between the solid object and the fluid. There must be motion between the object and the fluid. If there is no motion, there is no drag. It makes no differ& ence whether the object moves through a static fluid or whether the fluid moves past a static solid object. Drag acts in a direction that opposes the motion. (Lift acts perpendicular to the motion.) We can think of drag as aerodynamic friction, and one of the sources of drag is the skin friction between the molecules of the air and the solid surface of the aircraft. Because the skin friction is an interaction between a solid and a gas, the magnitude of the skin friction depends on properties of both solid and gas. For the solid, a smooth, waxed surface produces less skin friction than a roughened surface. For the gas, the magnitude depends on the viscosity of the air and the relative magnitude of the viscous forces to the motion of the flow, expressed as the Reynolds number. Along the solid surface, a boundary layer of low energy flow is generated. And the magnitude of the skin friction depends on the state of this flow. We can also think of drag as aerodynamic resistance to the motion of the object through the fluid. This source of drag depends on the shape of the aircraft and is called form drag. As air flows around a body, the local velocity and pressure are changed. Since pressure is a measure of the mo& mentum of the gas molecules and a change in momentum produces a force, a varying pressure distribution will produce a force on the body. We can determine the magnitude of the force by integrating (or adding up) the local pressure times the surface area around the entire body. The component of the aerodynamic force that is opposed to the motion is the drag; the component perpendicular to the motion is the lift. Both the lift and drag force act through the center of pressure of the object. There is an additional drag component caused by the generation of lift . Aerodynamicists have named this component the induced drag. This drag occurs because the flow near the wing tips is distorted spanwise as a result of the pressure difference from the top to the bottom of the wing. Swirling vortices are formed at the wing tips, and there is an energy associated with these vortices. The induced drag is an indication of the amount of energy lost to the tip vortices. The magnitude of induced drag depends on the amount of lift being generated by the wing and on 21 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» the wing geometry. Long, thin (chordwise) wings have low induced drag; short wings with a large chord have high induced drag. Additional sources of drag include wave drag and ram drag. As an aircraft approaches the speed of sound, shock waves are generated along the surface. There is an additional drag penalty (called wave drag) that is associated with the formation of the shock waves. The magnitude of the wave drag depends on the Mach number of the flow. Ram drag is associated with slowing down the free stream air as air is brought inside the aircraft. Jet engines and cooling inlets on the aircraft are sources of ram drag. Text IIC. What Is Lift? Lift is the force that holds an aircraft in the air. Lift can be generated by any part of the airplane, but most of the lift on a normal airliner is generated by the wings. Lift is an aerodynamic force produced by the motion of a fluid past an object. Lift acts through the center of pressure of the object and is defined to be perpendicular to the flow direction. How Is Lift Generated? There are many explanations for the generation of lift found in encyclopedias, in basic physics textbooks, and on Web sites. Unfortunately, many of the explanations are misleading and incorrect. Theories on the generation of lift have become a source of great controversy and a topic for heated arguments. To help you understand lift and it?s origins, a series of pages will describe The various theories and how some of The popular theories fail. Lift occurs when a flow of gas is turned by a solid object. The flow is turned in one direction, and the lift is generated in the opposite direction, according to Newton?s Third Law of action and reaction. Because air is a gas and the molecules are free to move about, any solid surface can deflect a flow. For an airfoil, both the upper and lower surfaces contribute to the flow turning. Neglecting the upper surface?s part in turning the flow leads to an incorrect theory of lift. No Fluid, No Lift. Lift is a mechanical force. It is generated by the interaction and contact of a solid body with a fluid (liquid or gas). It is not generated by a force field, in the sense of a gravitational field, or an electromagnetic field, where one object can affect another object 22 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» without being in physical contact. For lift to be generated, the solid body must be in contact with the fluid: no fluid, no lift. (The space shuttle does not stay in space because of lift from its wings but because of orbital mechanics related to its speed. Space is nearly a vacuum. Without air, there is no lift generated by the wings.) No Motion, No Lift. Lift is generated by the difference in velocity between the solid object and the fluid. There must be motion between the object and the fluid: no motion, no lift. It makes no difference whether the object moves through a static fluid, or the fluid moves past a static solid object. Lift acts perpendicular to the motion. (Drag acts in the direction opposed to the motion.) Text IID. What Is Weight? Weight is the force generated by the gravitational attraction of the earth, on the airplane. We are more familiar with weight than with the other forces acting on an airplane, because each of us have our own weight which we can measure every another thing is light. But weight, the gravitational force, is fundamentally different from the aerodynamic forces, lift and drag. Aerodynamic forces are mechanical forces and the airplane has to be in physical contact with the air which generates the force. The gravitational force is a field force; the source of the force does not have to be in physical contact with the object (The airplane). The nature of the gravitational force has been studied by scientists for many years and is still being investigated by theoretical physicists. For an object the size of an airplane, the descriptions given three hundred years ago by Sir Isaac Newton work quite well. Newton developed his theory of gravitation when he was only 23 years old and published the theories with his laws of motion some years later. The gravitational force between two objects depends on the mass of the objects and the inverse of the square of the distance between the objects. Larger objects create greater forces and the farther apart the objects are the weaker the attraction. Newton was able to express the relationship in a single weight equation. For an airplane, weight is a force which is always directed towards the center of the earth. The magnitude of this force depends on the mass of all of the parts of the airplane itself, plus the amount of fuel, plus any payload on board (people, baggage, freight...). The weight is distributed throughout the airplane, but we can often think of it as collected and 23 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» acting through a single point called the center of gravity. In flight, the airplane rotates about the center of gravity, but the direction of the weight force always remains toward the center of the earth. During a flight the aircraft burns up its fuel, so the weight of the airplane constantly changes. Also, the distribution of the weight and the center of gravity can change, so the pilot must constantly adjust the controls to keep the airplane balanced. The dream remains that, if we could really understand gravity, we could create anti&gravity devices which would revolutionize travel through the sky. Unfortunately, anti&gravity devices only exist in science fiction. Machines like airplanes, or magnetic levitation devices, create forces opposed to the gravitational force, but they do not block out or eliminate the gravitational force. UNIT III New Words and Word Combinations slip n disturb v springiness n to slow down collision n stall n transfer n heat transfer inlet n scope n three&dimensional a conservation displacement n laminar a turbulent a swirling flow uniformly adv gluey a 24 ??????????, ????? ?????????, ????????? ???????????, ????????? ????????? ???????????? ???? ?????? ??????? ???????????? ????? ???????, ???????, ????? ?????????? ?????????? ???????? ?????????? ???????????? ???????? (???????????) ????? ?????????? ???????, ?????? Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 1. Translate the following words and word combinations: the value ? the stream value ? the free steam value; the drag ? the friction drag ? the skin friction drag; the inlet ? the aircraft inlet ? the high speed aircraft inlet; the variation ? the velocity variation ? the steamwise velocity variation. 2. Read and translate the text. Text IIIA. Boundary Layer As an object moves through a fluid, or as a fluid moves past an object, the molecules of the fluid near the object are disturbed and move around the object. Aerodynamic forces are generated between the fluid and the object. The magnitude of these forces depend on the shape of the object, the speed of the object, the mass of the fluid going by the object and on two other important properties of the fluid; the viscosity, or stickiness, and the compressibility, or springiness, of the fluid. То model these effects рroреrly, aerodynamicists use similarity parameters which are ratios of these effects to other forces present in the problem. If two experiments have the same values for the similarity parameters, then the relative importance of the forces are being correctly modeled. Aerodynamic forces depend in a complex way on the viscosity of the fluid. As the fluid moves past the object, the molecules right next to the surface stick to the surface. The molecules just above the surface are slowed down in their collisions with the molecules sticking to the surface. These molecules in turn slow down the flow just above them. The farther one moves away from the surface, the fewer the collisions affected by the object surface. This creates a thin layer of fluid near the surface in which the velocity changes from zero at the surface to the free stream value away from the surface. Engineers call this layer the boundary layer because it occurs on the boundary of the fluid. The details of the flow within the boundary layer are very important for many problems in aerodynamics, including the development of a wing stall, the skin friction drag of an object, the heat transfer that occurs in high speed flight, and the performance of a high speed aircraft inlet. Unfortunately, the physical and mathematical details of boundary layer theory are beyond the scope of this article and are usually studied in late 25 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» undergraduate or graduate school in college. We will only present some of the effects of the boundary layer. On the figure we show the streamwise velocity variation from free stream to the surface. In reality, the effects are three dimensional. From the conservation of mass in three dimensions, a change in velocity in the streamwise direction causes a change in velocity in the other directions as well. There is a small component of velocity perpendicular to the surface which displaces or moves the flow above it. One can define the thickness of the boundary layer to be the amount of this displacement. The displacement thickness depends on the Reynolds number which is the ratio of inertial (resistant to change or motion) forces to viscous (heavy and gluey) forces and is given by the equation: Reynolds number (Re) equals velocity (V) times density (r) times a characteristic length (1) divided by the viscosity coefficient (µ): Re = V · r · 1 / µ. Boundary layers may be either laminar (layered), or turbulent (disordered) depending on the value of the Reynolds number. For lower Reynolds numbers, the boundary layer is laminar and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of the figure. For higher Reynolds numbers, the boundary layer is turbulent and the streamwise velocity is characterized by unsteady (changing with time) swirling flows inside the boundary layer. The external flow reacts to the edge of the boundary layer just as it would to the physical surface of an object. So the boundary layer gives any object an ?effective? shape which is usually slightly different from the physical shape. To make things more confusing, the boundary layer may lift off or ?separate? from the body and create an effective shape much different from the physical shape. This happens because the flow in the boundary has very low energy (relative to the free stream) and is more easily driven by changes in pressure. Flow separation is the reason for wing stall at high angle of attack. The effects of the boundary layer on lift are contained in the lift coefficient and the effects on drag are contained in the drag coefficient. Historical note: The theory which describes boundary layer effects was first presented by Ludwig Prandtl in the early 1900?s. The general fluids equations had been known for many years, but solutions to the equations did not properly describe observed flow effects (like wing stalls) . Prandtl was the first to realize that the relative magnitude of 26 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» the inertial and viscous forces changed from a layer very near the surface to a region far from the surface. He first proposed the interactively coupled, two layer solution which properly models many flow problems. 3. Answer the questions. 1. What does the term boundary layer stand for? 2. What does the magnitude of aerodynamic forces depend on? 3. What do aerodynamicists use to model the effects in the fluid? 4. When can the boundary layers be laminar? When can they be turbulent? 5. Where are the effects of the boundary layer on lift contained? 6. Who was the first to present the theory describing boundary layer affects? 4. Fill in the blanks with the words and word combinations from the box: laminar, uniformly, angle of attack, boundary layer, lift coefficient, disturbed 1. Engineers call this layer the ______ because it occurs on the boundary of the fluid. 2. The molecules of the fluid near the object are ______ and move around the object. 3. For lower Reynolds numbers, the boundary layer is ______ . 4. Velocity changes from zero at the surface to the _______ away from the surface. 5. Flow separation is the reason for wing stall at high _______ . 6. The streamwise velocity changes _______ as one moves away from the wall. 7. The effects of the boundary layer on lift are contained in the ______ . 5. Complete the sentences using the information from the text. 1. Aerodynamic forces depend on _____. 2. In reality the effects in the boundary layer are _____. 3. The Reynolds number is ______. 4. Boundary layers may be either ______. 5. The boundary layer may lift off the body and create an effective shape different from the physical shape because ______. 27 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 6. Translate the sentences into English. 1. 2. 3. 4. 5. 6. Теория пограничного слоя не изучается в нашем курсе. ??? ??????? ?? ????? ??????????. ??????????? ?????????. Разделение потока было причиной этого явления. Величина этой силы зависит от формы объекта. ????? движется вдоль объекта. 7. Match the beginnings of the sentences with their ends. 1. The magnitude of these forces 2. The details of the flow within the boundary layer 3. The farther one moves away from the surface 4. Boundary layers may be 5. The external flow 6. The general fluids equations had been a. very important for many pro& blems in aerodynamics. b. reacts to the edge of the boun& dary layer just as it would to the physical surface of an object. c. known for many years, but solutions did not properly de& scribe observed flow effects. d. depend on the shape of the object. e. either laminar, or turbulent. f. the fewer the collisions affected by the object surface. 8. Give the verbs in the brackets in the correct form. 1. Aerodynamic forces (to generate) between the fluid and the ob& ject. 2. The molecules (to slow down) the flow just above them. 3. The streamwise velocity (to change) uniformly. 4. The theory of boundary layer (to present) first by Ludwig Prandtl in 1900?s. 5. Solutions to the equations (not to describe) properly observed flow effects. 6. The effects of the boundary layer on lift (to contain) in the lift coefficient. 7. A change in velocity in the streamwise direction (to cause) a change in velocity in the other directions as well. 28 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» 8. The flow in the boundary (to have) low energy and easily (to drive) by changes in pressure. 9. Reynolds number (to give) by the equation. 9. Read and translate the text. Write out the terms from it. Text IIIB. Equation of State Ideal Gas. Properties V = C2 · T Density = r, Pressure = p, Temperature = Т, Volume = V, Mass = m. Observation. Boil: For a given mass, at constant temperature, the pressure times the volume is a constant: p · V = С1. Charles and Gay&Lussaс: For a given mass, at constant pressure, the volume is directly proportional to the temperature: Combine: pV / Т = nR R = 8.31 J / mole / K(Universal) pV = nRT, n = number of moles. Divide by mass: Specific Volume = v = volume / mass = 1 / r pv = nRT / m or pv = RT op = RrT, R = Constant value for each gas = 286 kJ / kg / K (for air). Air is a gas. Gases have various properties that we can observe with our senses, including the gas pressure (p), temperature (Т), mass (m), and volume (V) that contains the gas. Careful, scientific observation has determined that these variables are related to one another, and the values of these properties determine the state of the gas. If we fix any two of the properties we can determine the nature of the relationship between the other two. If the pressure and temperature are held constant, the volume of the gas depends directly on the mass, or amount of gas. This allows us to define a single additional property called the gas density (r), which is the ratio of mass to volume. If the mass and 29 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» temperature are held constant, the product of the pressure and volume are observed to be nearly constant for a real gas. (The product of pressure and volume is exactly a constant for an ideal gas.) This relationship between pressure and volume is called Boyle?s Law in honor of Robert Boyle who first observed it in 1660. Finally, if the mass and pressure are held constant, the volume is directly proportional to the temperature for an ideal gas. This relationship is called Charles and Gay&Lussac?s Law in honor of the two French scientists who discovered the relationship. The gas laws of Boyle and Charles and Gay&Lussac can be combined into a single equation of state: p · V / Т = n · R where ? · ? denotes multi& plication and / denotes division. To account for the effects of mass, we have defined the constant to contain two parts: a universal constant (R) and the mass of the gas expressed in moles (n). Performing a little algebra, we obtain the more familiar form: p · V = n · R · T. Aerodynamicists use a slightly different form of the equation of state that is specialized for air. If we divide both sides of the general equation by the mass of the gas, the volume becomes the specific volume, which is the inverse of the gas density. We also define a new gas constant (R), which is equal to the universal gas constant divided by the mass per mole of the gas. The value of the new constant depends on the type of gas as opposed to the universal gas constant, which is the same for all gases. The value of the equation of state for air is given as 286 kilo Joule per kilogram per degree Kelvin . The equation of state can be written in terms of the specific volume or in terms of the air density as p · v = R · T or p = r · R · T. Notice that the equation of state given here applies only to an ideal gas, or a real gas that behaves like an ideal gas. There are in fact many different forms for the equation of state for different gases. Also be aware that the temperature given in the equation of state must be an absolute temperature that begins at absolute zero. In the metric system of units, we must specify the temperature in degrees Kelvin (not Celsius). In the English system, absolute temperature is in degrees Rankine (not Fahrenheit). 10. Give a summary of text IIIB. 11. Read and translate the text using a dictionary if necessary. 30 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» Text IIIC. Flow Characteristics Although the Mach number is used to define the occurrence of some flow features, the basic parameters defining the speed characteristics are three: Reynolds number; Mach number; Knudsen number. Reynolds Number Effects: Viscosity The Reynolds number (first introduced by L. Prandtl) dominates the viscous effects by defining the size of the boundary layers. Almost all aerodynamic flows occur at high Reynolds number, which implies viscous phenomena are limited to narrow boundary layers. 6 The notion high is somewhat arbitrary, although the value of 0.5 · 10 is often the switching boundary. 6 6 Flows at Reynolds numbers in the range 0.1 · 10 < Re < 0.5 · 10 are called Low&Reynolds Number Aerodynamics . Flows at very small Reynolds numbers are dominated by viscosity and are better described with the use of Stanton number. These flows (sometimes called creeping motions or Stokes flows) are not considered proper domain of aerodynamics. Mach Number Effects: Compressibility The Mach number (introduced by J. Ackeret, 1992 ) defines the appearance of compressibility effects and the charges associated with the shock waves. In the subsonic speed range of the compressibility of the flow is negligible. At transonic speeds there are pockets of flow below and above the speed sound. The main feature of this speed range is the presence of compression and expansion shock waves. ? supersonic flow is exclusively above the speed of sound. Supersonic aerodynamics differs from aerodynamics at lower speeds because the flow is highly compressible. The Reynolds and Mach numbers are independent and are both needed to define the characteristics of speeds in the transonic regime. At subsonic speeds the flow is generally treated as a constant&density flow and the Mach number influence is neglected. Knudsen Number Effects: Molecular Flow Flows at higher Mach numbers are object of hypersonics (a term due to Tsien, 1946). Other definitions sometimes used for this speed regime is 31 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» gasdynamics, rarefied gasdynamics and magnetigasdynamics for yet higher speeds . Two more dimensionless parameters are useful to describe the physics: the Knudsen number and the Damkolner ratio (e. g. the ratio between a characteristic time and the molecular relaxation time). The Knudsen number is not quite independent, since it can also be written as ratio between Mach and Reynolds numbers. Flows at Knudsen numbers Kn ? 1 are basically collisionless flows (artificial satellites in orbital motion above the Earth); flows at Kn < 1 are in regime of slight rarefaction and are called slip flows; flows at inter& mediate Knudsen numbers are called transitional flows. These flows re& quire some modeling of the molecular gas, and are beyond the domain of validity of the Navier&Stokes equations. At speeds above M = 5 there are changes in the physics of the flow, because of changes in the medium and of the aero&thermodynamic heating . At M > 7 the medium becomes chemically reactive; at M > 12 it is also ionized . The energy produced by the propulsion system is used to overcome the resistance of the flight vehicle (drag), and is converted into compression work on the surrounding medium. 12. Read and explain the formulae given in texts IIIA , IIIB and IIIC: Kn ? 1 0.1 Ч 106 < Re < 0.5 Ч 106 Re = V · r · l / µ V = C2 · T pv = nRT / m. 13. Give a summary of text IIIC. Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» ?????? ?????????? ? ?????? ?????&??????? ??????????????? ???????: ? 2 ?. / ???.&????. ?.?. ???????. ? ?????: ???????, 2004. ??????? ?????&??????? ???????: ? 2 ?. / ??? ???. ?.?. ????????& ??. ??.: ??????? ????, 1987. ?????? ?.?. ??????? ???????????? ???????????: ?? ?????????? ?????, ???????? ? ???????????? ??????&??????????? ??????????: 2&? ???., ???????. ? ???. ? ?.: ?. ??????, 2006. ??????? ?.?. ?????? ? ??????? ?????????? ??????&??????????? ??????????: ???????&???????. ??????????. ? ?.: ???, 2003. th Hornby F.S. Oxford Advanced Learner?s Dictionary, 7 ed. ? Oxford: Oxford Univ. Press, 2006. Longman Dictionary of Scientific Usage: The Reprint Edition. ? Moscow: Longman, 1988. Macmillan English Dictionary for Advanced Learners: International Student Edition. ? L.: Macmillan Education, 2006. www.en.wikipedia.org/wiki/Aerodynamics www.grc.nasa.gov Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» Contents ??????????? .................................................................................................. Unit I ................................................................................................................. New Words and Word Combinations ........................................................ Text IA: Gas Properties Definitions ...................................................... Text IB: Gas Pressure ............................................................................... Text 1C: Gas Temperature ...................................................................... Unit II .............................................................................................................. New Words and Word Combinations ................................................... Text IIA: Aerodynamic Forces ................................................................ Text IIB: What Is Drag? .......................................................................... Text IIC: What Is Lift? ............................................................................ Text IID: What Is Weight? ..................................................................... Unit III ............................................................................................................. New Words and Word Combinations ................................................... Text IIIA: Boundary Layer ...................................................................... Text IIIB: Equation of State .................................................................. Text IIIC: Flow Characteristics ............................................................. ?????? ?????????? ? ?????? .................................................................... 3 3 3 5 10 12 15 15 16 20 22 23 24 24 25 29 31 33 Copyright ??? «??? «??????» & ??? «A???????? K????-C?????» ??????? ??????? ???????? ??????? ?????????? ????????? ???? ???????????? ???????? ?????? ?????????? ?? ?????????? ????? ?? ????????????? «???????????

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