Fluid mechanics
Fluid mechanics is a science concerned with the response of fluids to forces exerted upon them. It is a branch of classical physics with applications of great importance in hydraulic and aeronautical engineering, chemical engineering, meteorology, and zoology. The most familiar fluid is of course water, and an encyclopedia of the 19th century probably would have dealt with the subject under the separate headings of hydrostatics, the science of water at rest, and hydrodynamics, the science of water in motion. Archimedes founded hydrostatics in about 250 BC when, according to legend, he leapt out of his bath and ran naked through the streets of Syracuse crying “Eureka!”; it has undergone rather little development since. The foundations of hydrodynamics, on the other hand, were not laid until the 18th century when mathematicians such as Leonard Euler and Daniel Bernoulli began to explore the consequences, for a virtually continuous medium like water, of the dynamic principles that Newton had enunciated for systems composed of discrete particles. Their work was continued in the 19th century by several mathematicians and physicists of the first rank, notably G.G. Stokes and William Thomson. By the end of the century explanations had been found for a host of intriguing phenomena having to do with the flow of water through tubes and orifices, the waves that ships moving through water leave behind them, raindrops on windowpanes, and the like. There was still no proper understanding, however, of problems as fundamental as that of water flowing past a fixed obstacle and exerting a drag force upon it; the theory of potential flow, which worked so well in other contexts, yielded results that at relatively high flow rates were grossly at variance with experiment. This problem was not properly understood until 1904, when the German physicist Ludwig Prandtl introduced the concept of the boundary layer. Prandtl's career continued into the period in which the first manned aircraft were developed. Since that time, the flow of air has been of as much interest to physicists and engineers as the flow of water, and hydrodynamics has, as a consequence, become fluid dynamics. The term fluid mechanics embraces both fluid dynamics and the subject still generally referred to as hydrostatics. One other representative of the 20th century who deserves mention here besides Prandtl is Geoffrey Taylor of England. Taylor remained a classical physicist while most of his contemporaries were turning their attention to the problems of atomic structure and quantum mechanics, and he made several unexpected and important discoveries in the field of fluid mechanics. The richness of fluid mechanics is due in large part to a term in the basic equation of the motion of fluids which is nonlinear - i.e., one that involves the fluid velocity twice over. It is characteristic of systems described by nonlinear equations that under certain conditions they become unstable and begin behaving in ways that seem at first sight to be totally chaotic. In the case of fluids, chaotic behaviour is very common and is called turbulence. Mathematicians have now begun to recognize patterns in chaos that can be analyzed fruitfully, and this development suggests that fluid mechanics will remain a field of active research well into the 21st century.
Essential vocabulary: 1. to exert – оказывать 2. to be concerned with smth. – касаться чего-либо, относиться 3. response – ответ, реакция 4. aeronautical - авиационный 5. heading - заголовок 6. to leap out - выпрыгивать 7. consequence - последствие 8. to enunciate - выговаривать 9. discrete particles – дискретные частицы 10. host – хозяин, главный 11. orifice - отверстие 12. obstacle - препятствие 13. drag force – сила тяги 14. to yield - давать 15. boundary layer – пограничная зона, слой 16. manned – пилотируемый, управляемый человеком 17. to embrace – охватывать, заключать 18. to refer to smth. – ссылаться на что-либо, отсылать 19. representative - представитель 20. to deserve - заслуживать 21. mention - упоминание 22. to be due to smth. – благодаря чему-либо, из-за 23. contemporary – 1) (сущ.) современник; 2) (прилаг.) современный 24. equation - уравнение 25. under certain conditions – при определенных условиях 26. nonlinear - нелинейный 27. to involve – включать, заключать в себе 28. behaviour - поведение 29. to recognize patterns – распознавать образцы 30. to analyze fruitfully – тщательно анализировать
I. Find the English equivalents of the following words and phrases in the text. Compose your own sentences with these words: · движение воды · к концу века · нелинейное уравнение · течение воды по трубе · поток воздуха · механика жидкостей · согласно легенде · правильное понимание
II. Answer the following questions: 1. What is fluid mechanics? 2. What is the most familiar fluid to you? 3. When did Archimedes find hydrostatics? 4. What problem was not properly understood until 1904? 5. What does the term “fluid mechanics” embrace? 6. Why does Geoffrey Taylor still remain a classical physicist? 7. Why does the development of fluid mechanics still remain a field of active research? Give your reasons.
Basic properties of fluids (from fluid mechanics)
Fluids are not strictly continuous media in the way that all the successors of Euler and Bernoulli have assumed, for they are composed of discrete molecules. The molecules, however, are so small and, except in gases at very low pressures, the number of molecules per millilitre is so enormous that they need not be viewed as individual entities. There are a few liquids, known as liquid crystals, in which the molecules are packed together in such a way as to make the properties of the medium locally anisotropic, but the vast majority of fluids (including air and water) are isotropic. In fluid mechanics, the state of an isotropic fluid may be completely described by defining its mean mass per unit volume, or density (ρ), its temperature (T), and its velocity (v) at every point in space, and just what the connection is between these macroscopic properties and the positions and velocities of individual molecules is of no direct relevance. A word perhaps is needed about the difference between gases and liquids, though the difference is easier to perceive than to describe. In gases the molecules are sufficiently far apart to move almost independently of one another, and gases tend to expand to fill any volume available to them. In liquids the molecules are more or less in contact, and the short-range attractive forces between them make them cohere; the molecules are moving too fast to settle down into the ordered arrays that are characteristic of solids, but not so fast that they can fly apart. Thus, samples of liquid can exist as drops or as jets with free surfaces, or they can sit in beakers constrained only by gravity, in a way that samples of gas cannot. Such samples may evaporate in time, as molecules one by one pick up enough speed to escape across the free surface and are not replaced. The lifetime of liquid drops and jets, however, is normally long enough for evaporation to be ignored. There are two sorts of stress that may exist in any solid or fluid medium, and the difference between them may be illustrated by reference to a brick held between two hands. If the holder moves his hands toward each other, he exerts pressure on the brick; if he moves one hand toward his body and the other away from it, then he exerts what is called a shear stress. A solid substance such as a brick can withstand stresses of both types, but fluids, by definition, yield to shear stresses no matter how small these stresses may be. They do so at a rate determined by the fluid’s viscosity. This property is a measure of the friction that arises when adjacent layers of fluid slip over one another. It follows that the shear stresses are everywhere zero in a fluid at rest and in equilibrium, and from this it follows that the pressure (that is, force per unit area) acting perpendicular to all planes in the fluid is the same irrespective of their orientation (Pascal’s law). For an isotropic fluid in equilibrium there is only one value of the local pressure (p) consistent with the stated values for ρ and T. These three quantities are linked together by what is called the equation of state for the fluid.
Essential vocabulary: 1. entity – сущность, объект 2. property - свойство 3. volume - объем 4. velocity - скорость 5. relevance - релевантность 6. density - плотность 7. to perceive - воспринимать 8. to cohere - слипаться 9. to settle down - устраиваться 10. solid – твердое вещество 11. drop - капля 12. jet - струя 13. surface - поверхность 14. beaker – химический стакан, колба 15. to constrain - ограничивать 16. to evaporate - испарять 17. to pick up - приобретать 18. to escape - исчезать 19. to exert - оказывать 20. a shear stress – свободное напряжение 21. to withstand - выдерживать 22. to yield – давать, уступать, сдаваться 23. to determine - устанавливать 24. viscosity – вязкость 25. friction - трение 26. adjacent - смежный 27. to slip over – выскальзывать, скользить 28. equilibrium - равновесие 29. plane - плоскость 30. irrespective - безотносительный 31. consistent - последовательный 32. equation - уравнение
I. Work in pairs. Discuss which sentence in B best continues the sentence in A:
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