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26.Обучение чтению литературы на английском языке по спец. «Аэродинамика»

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?. 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», ??????????? ?? ????????????? «????????????».
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? ??????? ???????? ???????????? ?????? ?? ?????????? ? ???&
????????? ??????&??????????? ??????????; ???????, ??????????
???????? ???????, ??????? ??????? ????????????; ???????&????&
?????????? ??????????, ?????????????? ???????? ? ???????????
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???? ?? ?????????? ????? ?? ????????? ?????????????, ? ????? ??&
????? ?????? ????, ????????? ? ??????????????? ?????????.
????????, ?????????????? ? ???????, ????? ??????????????
?????????? ??? ?? ????? ?????????? ??????? (??? ????????????
?????????????), ??? ? ? ???????? ??????????????? ??????.
??????? ????????????? ??? ????????? ??????? ??????
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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
??????
????? ?????, ???????????
??????? ????
???????
???????????, ???????
????????????
????????? ?.&?., ????????? ?? ?.&?.
?????????? ???
???????????
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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.
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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
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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.)
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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?
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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.
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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.
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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
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the wall is defined to be the pressure. The pressure of a gas is then
a measure of the average linear momentum of the moving molecules of a
gas. The pressure acts perpendicular (normal) to the wall; the tangential
(shear) component of the force is related to the viscosity of the gas.
Scalar Quantity
Let us look at a static gas, one that does not appear to move or flow.
While the gas as a whole does not appear to move, the individual
molecules of the gas, which we cannot see, are in constant random motion.
Because we are dealing with a nearly infinite number of molecules and
because the motion of the individual molecules is random in every
direction, we do not detect any motion. If we enclose the gas within
a container, we detect a pressure in the gas from the molecules colliding
with the walls of our container. We can put the walls of our container
anywhere inside the gas, and the force per area (The pressure) is the same.
We can shrink the size of our ?container? down to an infinitely small point,
and the pressure has a single value at that point. Therefore, pressure is
a scalar quantity, not a vector quantity. It has a magnitude but no
direction associated with it. Pressure acts in all directions at a point inside
a gas. At the surface of a gas, the pressure force acts perpendicular to
the surface.
If the gas as a whole is moving, the measured pressure is different in
the direction of the motion. The ordered motion of the gas produces
an ordered component of the momentum in the direction of the motion.
We associate an additional pressure component, called dynamic pressure,
with this fluid momentum. The pressure measured in the direction of
the motion is called the total pressure and is equal to the sum of the static
and dynamic pressure as described by Bernoulli?s equation.
Macro Scale Definition of Pressure
Turning to the larger scale, pressure is a state variable of a gas, like
temperature and density. The change in pressure during any process is
governed by the laws of thermodynamic. Although pressure itself is
a scalar, we can define a pressure force to be equal to the pressure
(force/area) times the surface area in a direction perpendicular to
the surface. The pressure force is a vector quantity.
Pressure forces have some unique qualities as compared to
gravitational or mechanical forces. In the figure shown above, we have
a gas that is confined in a box. a mechanical force is applied to the top of
the box. The pressure force within the box opposes the applied force
according to Newton?s third law of motion. The scalar pressure equals
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the external force divided by the area of the top of the box. Inside the gas,
the pressure acts in all directions. So the pressure pushes on the bottom of
the box and on the sides. This is different from simple solid mechanics. If
the gas was a solid, there would be no forces applied to the sides of the box;
the applied force would be simply transmitted to the bottom. But in a gas,
because the molecules are free to move about and collide with one another,
a force applied in the vertical direction causes forces in the horizontal
direction.
12. Answer the questions to the text.
1. What do you know about gas pressure?
2. What is a measure of the average linear momentum of a gas?
3. Why don?t we detect any motion of the individual molecules?
4. What is called dynamic pressure?
5. What is called the total pressure and what is it equal to?
6. What are the unique qualities of the pressure forces?
13. Speak on the topics using the information from text IB.
1. Molecular definition of pressure.
2. Scalar quantity.
3. Macro scale definition of pressure.
14. Read and translate the text using a dictionary if necessary.
Text IC. Gas Temperature
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?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&
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modynamic equilibrium. By measuring the thermodynamic effect on
some physical property of the thermometer at some fixed conditions, like
the boiling point and freezing point of water, we can establish a scale for
assigning temperature values.
The number assigned to the temperature depends on what we pick
for the reference condition. So several different temperature scales have
arisen. The Celsius scale, designated with a C, uses the freezing point of
pure water as the zero point and the boiling point as 100 degrees with
a linear scale in between these extremes. The Fahrenheit scale, desig&
nated with an F, is a lot more confusing. It originally used the freezing
point of sea water as the zero point and the freezing point of pure water as
30 degrees, which made the temperature of a healthy person equal to
96 degrees. On this scale, the boiling point of pure water was 212 degrees.
So Fahrenheit adjusted the scale to make the boiling point of pure water
212 and the freezing point of pure water 32, which gave 180 degrees
between the two reference points. 180 degrees was chosen because it is
evenly divisible by 2, 3, 4, 5 and 6. On the new temperature scale,
the temperature of a healthy person is 98.6 degrees F. Because there are
100 degrees C and 180 degrees F between the same reference conditions:
1 degree C = 1 degree F · 10 / 180 = 1 degree F · 5 / 9.
Since the scales start at different zero points, we can convert from
the temperature on the Fahrenheit scale (TF) to the temperature on
the Celsius scale (TC) by using this equation:
TF = 32 + (9 / 5) · TC.
Of course, you can have temperatures below the freezing point of
water and these are assigned negative numbers. When scientists began to
study the coldest possible temperature, they determined an absolute zero
at which molecular kinetic energy is a minimum (but not strictly zero!).
They found this value to be at ?273.16 degrees C. Using this point as
the new zero point we can define another temperature scale called
the absolute temperature. If we keep the size of a single degree to be
the same as the Celsius scale, we get a temperature scale which has been
named after Lord Kelvin and designated with a K. Then:
K = C + 273.16.
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There is a similar absolute temperature corresponding to the Fa&
hrenheit degree. It is named after the scientist Rankine and designated
with an R:
R = F + 459.69.
Absolute temperatures are used in the equation of state,
the derivation of the state variables enthalpy, and entropy, and
determining the speed of sound.
Temperature, like pressure, is a scalar quantity. Temperature has
a magnitude, but no direction associated with it. It has just a single value
at every location in a gas. The value can be changed from location to
location, but there is no direction connected to the temperature.
15. A. Make up questions to find out about:
(1) an important property of any gas;
(2) three principles of thermodynamics;
(3) different temperature scales;
(4) a thermometer.
B. Make up dialogues using your questions.
UNIT II
New Words and Word Combinations
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
?????????, ???????? ? ????????, ?????????
?????, ?????
????? ?????????? ??????, ????? ??????&
???; ?????????? ?????
?????????
?????????, ??????????
???????????????? ???????????, ???????
???; ??????, ??????? ???????
?????????? ?????
?????, ?????
??????????
???????????????? (??????????????) ????
????????
???????????, ????????
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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.
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The transmission, or application, of mechanical forces between a solid
body and a fluid occurs at every point on the surface of the body. And
the transmission occurs through the fluid pressure.
Variation in Pressure
The magnitude of the force acting over a small section of an object
equals the pressure times the area of the section. a quick units check
shows that pressure (force/area) times area produces a force. Pressure is
a scalar quantity related to the momentum of the molecules of a fluid.
Since a force is a vector quantity, having both magnitude and direction,
we must determine the direction of the force. Pressure acts perpendicular
(or normal) to the solid surface of an object. So the direction of the force
on the small section of the object is along the normal to the surface. We
denote this direction by the letter n.
The normal direction changes from the front of the airfoil to the rear
and from the top to the bottom. To obtain the net mechanical force over
the entire solid object, we must sum the contributions from all the small
sections. Mathematically, the summation is indicated by the Greek letter
sigma (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.
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In reality, there is a single, net, integrated force caused by the pressure
variations along a body. This aerodynamic force acts through the average
location of the pressure variation which is called the center of pressure.
Velocity Distribution
For an ideal fluid with no boundary layers, the surface of an object is
a streamline. If the velocity is low, and no energy is added to the flow, we
can use Bernoulli?s equation along a streamline to determine the pressure
distribution for a known velocity distribution. If boundary layers are
present, things are a little more confusing, since the external flow re&
sponds to the edge of the boundary layer and the pressure on the surface
is imposed from the edge of the boundary layer. If the boundary layer
separates from the surface, it gets even more confusing. How do we deter&
mine the velocity distribution around a body? Specifying the velocity is
the source of error in two of the more popular incorrect theories of lift. To
correctly determine the velocity distribution, we have to solve equations
expressing a conservation of mass, momentum, and energy for the fluid
passing the object.
Summary
So, to summarize, for any object immersed in a fluid, the me&
chanical forces are transmitted at every point on the surface of
the body. The forces are transmitted through the pressure, which
acts perpendicular to the surface. The net force can be found by
integrating (or summing) the pressure times the area around
the entire surface. For a moving flow, the pressure will vary from
point to point because the velocity varies from point to point. For
some simple flow problems we can determine the pressure
distribution (and the net force) if we know the velocity distri&
bution by using Bernoulli?s equation.
3. Answer the questions using the information from the text.
1. What is pressure related to?
2. What is the ?point of contact? for a solid body immersed in
a fluid?
3. Will the velocity have the same values at different locations
around the body?
4. How does the lift act?
5. What equation can we use to determine the pressure
distribution for known velocity distribution for an ideal fluid?
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6. How can we determine the velocity distribution?
7. Why will the pressure vary from point to point for a moving
flow?
4. Fill in the blanks with the proper words from the box.
maintain, streamline, caused by, net force, vector quantity
1. For an ideal fluid the surface of an object is _____.
2. There is a force ______ the pressure variations.
3. We can determine the pressure distribution and the ____ if we
know the velocity distribution.
4. The fluid can _____ physical contact at all points.
5. A force is a ______ .
5. Translate the sentences into English.
1.
Когда два твердых тела взаимодействуют, сила
приложена в точке контакта.
2. ?? ????? ?????? ?????????? ?????????.
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.
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5. We have to solve equations expressing a conservation of mass,
momentum, and energy for the fluid passing the object.
6. The net force can be found by summing the pressure times
the area around the entire surface.
7. If we have a liquid flowing in a pipe, the same amount of liquid
must be flowing past any point in the pipe regardless of how
the pipe is shaped.
8. Unless the spacecraft reaches the speed of 7 miles per second it
will not be able to leave the Earth.
8. Learn to read mathematical symbols.
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?
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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
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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
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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
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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
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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
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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 ______.
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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.
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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
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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.
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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
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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
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??????? ???????
???????? ??????? ??????????
????????? ???? ????????????
???????? ?????? ??????????
?? ?????????? ????? ?? ?????????????
«?????????????»
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??? ???????
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
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???????????
? ??????? ???????? ???????????? ?????? ?? ?????????? ? ???&
????????? ??????&??????????? ??????????; ???????, ??????????
???????? ???????, ??????? ??????? ????????????; ???????&????&
?????????? ??????????, ?????????????? ???????? ? ???????????
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???? ?? ?????????? ????? ?? ????????? ?????????????, ? ????? ??&
????? ?????? ????, ????????? ? ??????????????? ?????????.
????????, ?????????????? ? ???????, ????? ??????????????
?????????? ??? ?? ????? ?????????? ??????? (??? ????????????
?????????????), ??? ? ? ???????? ??????????????? ??????.
??????? ????????????? ??? ????????? ??????? ??????
?????????? «??????????? ??????????????».
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
??????
????? ?????, ???????????
??????? ????
???????
???????????, ???????
????????????
????????? ?.&?., ????????? ?? ?.&?.
?????????? ???
???????????
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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.
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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
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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.)
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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?
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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.
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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.
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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
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the wall is defined to be the pressure. The pressure of a gas is then
a measure of the average linear momentum of the moving molecules of a
gas. The pressure acts perpendicular (normal) to the wall; the tangential
(shear) component of the force is related to the viscosity of the gas.
Scalar Quantity
Let us look at a static gas, one that does not appear to move or flow.
While the gas as a whole does not appear to move, the individual
molecules of the gas, which we cannot see, are in constant random motion.
Because we are dealing with a nearly infinite number of molecules and
because the motion of the individual molecules is random in every
direction, we do not detect any motion. If we enclose the gas within
a container, we detect a pressure in the gas from the molecules colliding
with the walls of our container. We can put the walls of our container
anywhere inside the gas, and the force per area (The pressure) is the same.
We can shrink the size of our ?container? down to an infinitely small point,
and the pressure has a single value at that point. Therefore, pressure is
a scalar quantity, not a vector quantity. It has a magnitude but no
direction associated with it. Pressure acts in all directions at a point inside
a gas. At the surface of a gas, the pressure force acts perpendicular to
the surface.
If the gas as a whole is moving, the measured pressure is different in
the direction of the motion. The ordered motion of the gas produces
an ordered component of the momentum in the direction of the motion.
We associate an additional pressure component, called dynamic pressure,
with this fluid momentum. The pressure measured in the direction of
the motion is called the total pressure and is equal to the sum of the static
and dynamic pressure as described by Bernoulli?s equation.
Macro Scale Definition of Pressure
Turning to the larger scale, pressure is a state variable of a gas, like
temperature and density. The change in pressure during any process is
governed by the laws of thermodynamic. Although pressure itself is
a scalar, we can define a pressure force to be equal to the pressure
(force/area) times the surface area in a direction perpendicular to
the surface. The pressure force is a vector quantity.
Pressure forces have some unique qualities as compared to
gravitational or mechanical forces. In the figure shown above, we have
a gas that is confined in a box. a mechanical force is applied to the top of
the box. The pressure force within the box opposes the applied force
according to Newton?s third law of motion. The scalar pressure equals
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the external force divided by the area of the top of the box. Inside the gas,
the pressure acts in all directions. So the pressure pushes on the bottom of
the box and on the sides. This is different from simple solid mechanics. If
the gas was a solid, there would be no forces applied to the sides of the box;
the applied force would be simply transmitted to the bottom. But in a gas,
because the molecules are free to move about and collide with one another,
a force applied in the vertical direction causes forces in the horizontal
direction.
12. Answer the questions to the text.
1. What do you know about gas pressure?
2. What is a measure of the average linear momentum of a gas?
3. Why don?t we detect any motion of the individual molecules?
4. What is called dynamic pressure?
5. What is called the total pressure and what is it equal to?
6. What are the unique qualities of the pressure forces?
13. Speak on the topics using the information from text IB.
1. Molecular definition of pressure.
2. Scalar quantity.
3. Macro scale definition of pressure.
14. Read and translate the text using a dictionary if necessary.
Text IC. Gas Temperature
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?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&
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modynamic equilibrium. By measuring the thermodynamic effect on
some physical property of the thermometer at some fixed conditions, like
the boiling point and freezing point of water, we can establish a scale for
assigning temperature values.
The number assigned to the temperature depends on what we pick
for the reference condition. So several different temperature scales have
arisen. The Celsius scale, designated with a C, uses the freezing point of
pure water as the zero point and the boiling point as 100 degrees with
a linear scale in between these extremes. The Fahrenheit scale, desig&
nated with an F, is a lot more confusing. It originally used the freezing
point of sea water as the zero point and the freezing point of pure water as
30 degrees, which made the temperature of a healthy person equal to
96 degrees. On this scale, the boiling point of pure water was 212 degrees.
So Fahrenheit adjusted the scale to make the boiling point of pure water
212 and the freezing point of pure water 32, which gave 180 degrees
between the two reference points. 180 degrees was chosen because it is
evenly divisible by 2, 3, 4, 5 and 6. On the new temperature scale,
the temperature of a healthy person is 98.6 degrees F. Because there are
100 degrees C and 180 degrees F between the same reference conditions:
1 degree C = 1 degree F · 10 / 180 = 1 degree F · 5 / 9.
Since the scales start at different zero points, we can convert from
the temperature on the Fahrenheit scale (TF) to the temperature on
the Celsius scale (TC) by using this equation:
TF = 32 + (9 / 5) · TC.
Of course, you can have temperatures below the freezing point of
water and these are assigned negative numbers. When scientists began to
study the coldest possible temperature, they determined an absolute zero
at which molecular kinetic energy is a minimum (but not strictly zero!).
They found this value to be at ?273.16 degrees C. Using this point as
the new zero point we can define another temperature scale called
the absolute temperature. If we keep the size of a single degree to be
the same as the Celsius scale, we get a temperature scale which has been
named after Lord Kelvin and designated with a K. Then:
K = C + 273.16.
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There is a similar absolute temperature corresponding to the Fa&
hrenheit degree. It is named after the scientist Rankine and designated
with an R:
R = F + 459.69.
Absolute temperatures are used in the equation of state,
the derivation of the state variables enthalpy, and entropy, and
determining the speed of sound.
Temperature, like pressure, is a scalar quantity. Temperature has
a magnitude, but no direction associated with it. It has just a single value
at every location in a gas. The value can be changed from location to
location, but there is no direction connected to the temperature.
15. A. Make up questions to find out about:
(1) an important property of any gas;
(2) three principles of thermodynamics;
(3) different temperature scales;
(4) a thermometer.
B. Make up dialogues using your questions.
UNIT II
New Words and Word Combinations
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
?????????, ???????? ? ????????, ?????????
?????, ?????
????? ?????????? ??????, ????? ??????&
???; ?????????? ?????
?????????
?????????, ??????????
???????????????? ???????????, ???????
???; ??????, ??????? ???????
?????????? ?????
?????, ?????
??????????
???????????????? (??????????????) ????
????????
???????????, ????????
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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.
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The transmission, or application, of mechanical forces between a solid
body and a fluid occurs at every point on the surface of the body. And
the transmission occurs through the fluid pressure.
Variation in Pressure
The magnitude of the force acting over a small section of an object
equals the pressure times the area of the section. a quick units check
shows that pressure (force/area) times area produces a force. Pressure is
a scalar quantity related to the momentum of the molecules of a fluid.
Since a force is a vector quantity, having both magnitude and direction,
we must determine the direction of the force. Pressure acts perpendicular
(or normal) to the solid surface of an object. So the direction of the force
on the small section of the object is along the normal to the surface. We
denote this direction by the letter n.
The normal direction changes from the front of the airfoil to the rear
and from the top to the bottom. To obtain the net mechanical force over
the entire solid object, we must sum the contributions from all the small
sections. Mathematically, the summation is indicated by the Greek letter
sigma (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.
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In reality, there is a single, net, integrated force caused by the pressure
variations along a body. This aerodynamic force acts through the average
location of the pressure variation which is called the center of pressure.
Velocity Distribution
For an ideal fluid with no boundary layers, the surface of an object is
a streamline. If the velocity is low, and no energy is added to the flow, we
can use Bernoulli?s equation along a streamline to determine the pressure
distribution for a known velocity distribution. If boundary layers are
present, things are a little more confusing, since the external flow re&
sponds to the edge of the boundary layer and the pressure on the surface
is imposed from the edge of the boundary layer. If the boundary layer
separates from the surface, it gets even more confusing. How do we deter&
mine the velocity distribution around a body? Specifying the velocity is
the source of error in two of the more popular incorrect theories of lift. To
correctly determine the velocity distribution, we have to solve equations
expressing a conservation of mass, momentum, and energy for the fluid
passing the object.
Summary
So, to summarize, for any object immersed in a fluid, the me&
chanical forces are transmitted at every point on the surface of
the body. The forces are transmitted through the pressure, which
acts perpendicular to the surface. The net force can be found by
integrating (or summing) the pressure times the area around
the entire surface. For a moving flow, the pressure will vary from
point to point because the velocity varies from point to point. For
some simple flow problems we can determine the pressure
distribution (and the net force) if we know the velocity distri&
bution by using Bernoulli?s equation.
3. Answer the questions using the information from the text.
1. What is pressure related to?
2. What is the ?point of contact? for a solid body immersed in
a fluid?
3. Will the velocity have the same values at different locations
around the body?
4. How does the lift act?
5. What equation can we use to determine the pressure
distribution for known velocity distribution for an ideal fluid?
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6. How can we determine the velocity distribution?
7. Why will the pressure vary from point to point for a moving
flow?
4. Fill in the blanks with the proper words from the box.
maintain, streamline, caused by, net force, vector quantity
1. For an ideal fluid the surface of an object is _____.
2. There is a force ______ the pressure variations.
3. We can determine the pressure distribution and the ____ if we
know the velocity distribution.
4. The fluid can _____ physical contact at all points.
5. A force is a ______ .
5. Translate the sentences into English.
1.
Когда два твердых тела взаимодействуют, сила
приложена в точке контакта.
2. ?? ????? ?????? ?????????? ?????????.
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.
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5. We have to solve equations expressing a conservation of mass,
momentum, and energy for the fluid passing the object.
6. The net force can be found by summing the pressure times
the area around the entire surface.
7. If we have a liquid flowing in a pipe, the same amount of liquid
must be flowing past any point in the pipe regardless of how
the pipe is shaped.
8. Unless the spacecraft reaches the speed of 7 miles per second it
will not be able to leave the Earth.
8. Learn to read mathematical symbols.
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?
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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
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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
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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
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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
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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
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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 ______.
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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
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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
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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.
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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
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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
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31
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??????? ???????
???????? ??????? ??????????
????????? ???? ????????????
???????? ?????? ??????????
?? ?????????? ????? ?? ?????????????
«???????????
1/--страниц
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