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# U1. FLUIDS AND THE CONTINUUM MODEL

Редактор і коректор

Т. А. Осипова

Дизайн

Л. Н. Кисельової

Комп'ютерна верстка

Т. С. Сировєтнік

Технолог

В. А. Бєлова

ISBN 978-5-88689-061-7

Підписано до друку 05.02.2009. Формат 70 х 100/16.

Гарнітура РetersburgС. Папір офсетний.

Друк офсетний. Ум. печ. л. 34,45. Тираж 1000 екземплярів. Зак. тип. № 1065.

Санкт-Петербурзька державна

академія театрального мистецтва 191028,

Санкт-Петербург, Мохова вул., 34.

Надруковано в ТОВ «Друкарня« Береста »

196006, м.Санкт-Петербург, вул. Коли Томчак, 28.

Методичний посібник з дисципліни

«Гідромеханіки»

Для студентів IV курсу МФ

Іопія А. В.

РОДИНА Е. Ю.

зміст

1. U1 Fluid and continuum model
2. U2 Properties of fluid
3. U3 Stress and Pressure
4. U4 Hydrostatic Pressure
5. U5 Hydrostatic Pressure at a Point
6. U6 Pressure Field
7. U7 Fluid having a Uniform Acceleration

U1. FLUIDS AND THE CONTINUUM MODEL

In nature, matter exists in either of three states; these are the solid, liquid, or gaseous states. Solids have a specific shape and a significant degree of rigidity. From strength of materials, we know that solids may be measurably deformed by sufficiently large forces. If a liquid is placed into a container, it will take the shape of the container except for the top surface. If a gas is allowed to flow into an evacuated container, it will completely fill the container. It takes a relatively large force to change the total volume of a liquid. Thus, for many problems, liquids may be considered to be incompressible. That is, the total volume of an element of liquid remains unchanged as it flows through or past a device of interest. However, gases are readily compressed. Both gases and liquids are classified as fluids

From the molecular viewpoint, the state of a substance results from the intermolecular forces within the material, from the spacing between molecules, and from the degree of freedom of motion of the molecules. The intermolecular forces in a solid are greater than the intermolecular forces in a liquid, and those of a liquid are greater than the intermolecular forces in a gas. The spacing between the molecules in a solid is less than the spacing between the molecules in a liquid, which is less than the spacing between the molecules in a gas.

For mechanical analysis, a fluid is treated as a continuum. That is, matter is assumed to exist continuously with mathematically continuous properties. Thus, we may take the value of a property at two adjacent points, subtract them, divide the result by the distance between the adjacent points, and take the limit as the distance between the points approaches zero, thus obtaining the derivative of that property with respect to distance. Of course, this is a mathematical abstraction since, as the distance between adjacent points gets as small as the intermolecular spacing, matter becomes discrete. That is, the region will consist of a molecule, a void, a molecule, a void, and so on. However, this does not disturb us, since the measuring instruments used in fluid mechanics can not depict this fine structure. These instruments provide us with property measurements that result from the average behavior of many molecules, and they are therefore attuned to the continuum model. The interrelationship between molecular and continuum behavior is treated in the kinetic theory of gases and in statistical mechanics.

The study of fluid mechanics is concerned with fluids both at rest and in motion. Fluids at rest are studied under the heading of fluid statics. When a fluid is static, it is in equilibrium; thus, the equations of equilibrium used in statics also apply for the case of a static fluid.

1. Look through the first two paragraphs. Find key words and make your own sentences with them.
2. a) Complete the table according to the parts of speech.

Matter, degree, fill, solid, significant, measurably, deform, device, substance, container, depict, relatively, classify, molecular, value, readily, assume, adjacent.

b) Which of these words are international?

1. Match the words with their definitions.
1. liquid
2. matter
3. solid
4. space

a) a firm object that has a fixed shape

b) substance that flows, is not a solid or a gas, has no fixed shape

c) substance of which a thing is made

d) area or volume, interval or distance between two or more objects

1. Make nouns from these verbs.
1. to divide
2. to compress
3. to treat
4. to exist
5. to disturb
1. free
2. relative
3. rigid
4. specific
5. proper
6. distant
7. significant
8. complete
9. continuous
1. Use some of the adverbs from exercise V to complete the sentences.
1. Liquid is a substance that flows ___.
2. Matter exists ___.
3. Solids are ___ deformed by large forces.
4. Changing the volume of a liquid takes a ___ large force.
5. Gases are ___ compressed.
6. When following, gas ___ fills the container.

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