流体的定义和流体流动的分类

1、PAGE 2 Part Fluid Mechanics and Fluid Machines1.1 Definition of a Fluid and Classification of Fluid Flow流体的定义和流体流动的分类A fluid is a substance that deforms continuously when subjected to a shear stress, no matter how small that shear stress may be. A shear force is the force component tangent to a surf

2、ace, and this force divided by the area of the surface is the average shear stress over the area. Shear stress at a point is the limiting value of shear force to area as the area is reduced to the point. 无论受到多么小的剪切力都会发生连续变形的物质叫做流体。剪切力是与表面相切方向上的分力，该力除以面积便得此面积上的平均切应力，当面积缩成一点时，即为该点上的切应力。In Fig. 1-1 a s

3、ubstance is placed between two closely spaced parallel plates, so large that conditions at their edges may be neglected. The lower plate is fixed, and a force F is applied to the upper plate, which exerts a shear F/A on any substance between the plates. A is the area of the upper plate. When the for

4、ce F causes the upper plate to move with a steady ( nonzero ) velocity, no matter how small the magnitude of F, one may conclude that substance between the two plates is a fluid. 如图1-1a所示，两块平行放置非常靠近的平板间充满某种物质，平板很大，因此平板四周边缘处的情况可以不予考虑。固定下平板，对上板施加一作用力F，平板间的物质便会受到剪切力F/A的作用，其中A是上板面积。只要作用力F能使上板以恒定（不等于零）的速

5、度运动，而不论力F的量值多么小，你就可以断定板间的物质是一种流体。The fluid in immediate contact with a solid boundary has the same velocity as the boundary, i.e., there is no slip at the boundary. This is an experimental fact which has been verified in countless tests with various kinds of fluids and boundary materials. The fluid

6、in area abcd flows to the new position abcd , each fluid particle moving parallel to the plate and velocity u varying uniformly from zero at the stationary plate to U at the upper plate. Experiments show that, other quantities being held constant, F is directly proportional to A and to U and is inve

7、rsely proportional to thickness t. In equation form in which is the proportionality factor and includes the effect of the particular fluid. If =F/A for the shear stress,The ratio U/t is the angular velocity of line ab, or it is the rate of angular deformation of the fluid, i.e., the rate of decrease

8、 of angle bad. The angular velocity may also be written du/dy, as both U/t and du/dy express the velocity change divided by the distance over which the change occurs. However, du/dy is more general, as it holds for situations in which the angular velocity and shear stress change with y. the velocity

9、 gradient du/dy may also be visualized as the rate at which one layer moves relative to an adjacent layer. In differential form, (1-1)is the relation between shear stress and rate of angular deformation for one-dimensional flow of a fluid. The proportionality factor is called the viscosity of the fl

10、uid, and Eq. (1-1) is Newtons law of viscosity.紧贴固体边壁的流体其速度与边壁速度相同，也就是说交界处并无滑移，这一事实已为不同流体和不同边壁材料进行的千万次试验所证实。面积abcd里的流体流到新的位置abcd处，各流体质点均平行于平板运动，其速度u从固定平板上的零值均匀地变化到上板处的U。实验表明，保持其他参数不变，F正比于AU，且反比于厚度t。可以表示成公式形式：式中是与特定流体有关的比例系数，令=F/A代表剪切应力，则有比值U/t是线段ab的角速度，或者说是流体的角变形速度，即角bad减小的速度。角速度也可以表达为du/dy,，因为U/t和d

11、u/dy这两者都表示的是速度的变化量除以发生该变化所需的距离。然而，du/dy更具普遍性，因为它适用于角速度和切应力随y变化的情况。速度梯度du/dy还可以形象地看作是某层相对于其邻层流体间的速度。表示成微分形式为：上式即为流体一元流动中切应力同角变形率间的关系。比例系数称为流体的粘度。方程（1-1）称为牛顿粘性定律。Materials other than fluids cannot satisfy the definition of a fluid. A plastic substance will deform a certain amount proportional to the f

12、orce, but not continuously when the stress applied is below its yield shear stress. A complete vacuum between the plates would cause deformation at an ever-increasing rate. If sand were placed between the two plates, Coulomb friction would require a finite force to cause a continuous motion. Hence,

13、plastics and solids are excluded from the classification of fluids. 非流体材料就不能满足流体的定义。塑性物质会随着所施加作用力的大小而发生一定的变形，但当作用其上的切应力小于屈服切应力时，变形即终止。若两平板间完全真空，变形速率将不断增大。若将沙粒填充于两平板之间，那么库伦摩擦要求作用力必须超过某一数值才会引起连续运动，因此塑料和固体均无法归入流体的分类。Fluids may be classified as Newtonian or non-Newtonian. In Newtonian fluid there is a l

14、inear relation between the magnitude of applied shear stress and the resulting rate of angular deformation (constant in Eq. 1-1). In non-Newtonian fluid there is a nonlinear relation between the magnitude of applied shear stress and the rate of angular deformation. 流体可分为牛顿流体和非牛顿流体，牛顿型流体中施加的切应力的大小同其所

15、引起的角变形速率之间的关系是线性的（方程1-1中的为常数）；非牛顿型流体中施加的切应力的大小同其所引起的角变形速率间有着非线性的关系An ideal plastic has a definite yield stress and a constant linear relation of to du/dy. A thixotropic substance, such as printer s ink, has a viscosity that is dependent upon the immediately prior angular deformation of the substance

16、 and has a tendency to take a set when at rest. Gases and thin liquids tend to be Newtonian fluids, while thick long-chained hydrocarbons may be non-Newtonnian. 理想塑性流体有一确定的屈服应力，同时其中的与du/dy之间有一定的线性关系。触变性物质，如油墨之类，其粘度依该物质当时经历的角变形而定，且在静止不动时趋于凝聚态。各种气体和稀薄液体近乎牛顿型流体，而粘稠的长链碳氢化合物则常为非牛顿型流体。For purposes of anal

17、ysis, the assumption is frequently made that a fluid is nonviscous. With zero viscosity the shear stress is always zero, regardless of the motion of the fluid. If the fluid is considered to be nonviscous, it is then called an ideal fluid. 为了分析为题起见，通常假定流体是无粘性的。粘度为零时，不管流体是否流动，切应力总等于零。若把流体看成是无粘性的，那么这就称

18、为理想流体。Fluid flow may be classified in many ways, such as steady or nonsteady, rotational or irrotational, compressible or incompressible, and viscous or nonviscous. 流体的流动可用多种方式加以分类，如定常流或非定常流；有旋流或无旋流；可压缩流或不可压缩流；以及粘性流动或无粘性流等。Fluid flow can be steady or nonsteady. When the fluid velocity at any given p

19、oint is constant in time, the fluid motion is said to be steady. That is, at any given point in a steady flow the velocity of each passing fluid particle is always the same. At some other point a particle may travel with a different velocity, but every other particle which passes this second point b

20、ehaves there just as this particle did when it passed this point. These conditions can be achieved at low flow speeds, a gently flowing stream is an example. In nonsteady flow, as in a tidal bore, the velocities are a function of the time. In the case of turbulent flow, such as rapids or a waterfall

21、, the velocities vary erratically from point to point as well as from time to time.流体的流动可以是定常的或非定常的。如果在任一给定点处流体的速度不随时间而变化，这种流体的流动就称为定常流，也就是说流经定常流中任一给定点的每一流体质点的速度总是相同的；在另一点上某质点的流动速度可能不同，但任一通过该第二点上的其它质点恰好同该质点经过此点时的速度相同。在低的流动速度下就可能出现这种情形，徐缓的溪流便是其中一例。非定常流方面，可以举出涨潮时的激浪为例，其速度是时间的函数，诸如激流或瀑布紊流情形里，各点间以及不同时刻下

22、的速度均变化不定。Fluid flow can be rotational or irrotational. If the element of fluid at each point has no net angular velocity about that point, the fluid flow is irrotational. We can imagine a small paddle wheel immersed in the moving fluid. If the wheel moves without rotating, the motion is irrotational

23、; otherwise it is rotational. Rotational flow includes vortex motion, such as whirlpools. 流体流动可以是有旋的或者无旋的。如果每个点上的流体微团绕该店均无净角速度，这时的流体流动便是无旋的；我们不妨设想在运动流体中有一个小的自行车蹬，只要车蹬运动时不发生旋转，这种运动便是无旋的，否则就是有旋的，有旋运动包含像一些漩涡那样的涡旋运动。Fluid flow can be compressible or incompressible. Liquids can usually be considered as f

24、lowing incompressible. But even a highly compressible gas may sometimes undergo unimportant changes in density. Its flow is then practically incompressible. In flight at speeds much lower than the speed of sound in air (described by subsonic aerodynamics ), the motion of the air relative to the wing

25、s is one of nearly incompressible flow. 流体可以是可压缩的或者不可压缩的。各种液体通常可作为不可压缩流动看待。不过即使是某种有高度压缩性的气体，有时它的密度并未表现出多大的变化，这样的流体实际上仍是不可压缩的。飞行速度远小于空气中的声速时（用亚声速空气动力学来描述），空气相对于飞机机翼的运动便是一种不可压缩流动。Fluid flow can be viscous or nonviscous. Viscosity in fluid motion is the analogy of friction in the motion of solids. In m

26、any cases, such as in lubrication problems, it is extremely important. Sometimes, however, it is negligible. Viscosity introduces tangential forces between layers of fluid in relative motion and results in dissipation of mechanical energy.流体流动还可以是粘性的或者无粘性的。流体流动中的粘性可以比作固体运动中的摩擦。许多情形里，比如在润滑问题中这是极其重要的，

27、但有时又可以予以忽略。粘性引起流体相对运动各层间的切向力，从而导致了机械能的损耗。Historical Development of Fluid Mechanics流体力学的发展史The science of fluid mechanics began with the need to control water for irrigation and navigation purposes in ancient China, Egypt, Mesopotamia, and India. Although these civilizations understood the nature of

28、channel flow, there is no evidence that any quantitative relationships had been developed to guide them in their work. It was not until 250 B. C. that Archimedes discovered and recorded the principles of hydrostatics and buoyancy. In spite of the fact that the empirical understanding of hydrodynamic

29、s continued to improve with the development of fluid machinery, better sailing vessels, and more intricate channel systems, the fundamental principles of classical hydrodynamics were not founded until the seventeenth and eighteenth centuries. Newton, Daniel Bernoulli, and Leonard Euler made the grea

30、test contributions to the founding of these principles. 流体力学这门科学起源于古代中国、埃及、美索布达美亚和印度，它是随着水利灌溉和舟船航行的需要对水进行治理而出现的。虽然这些文明古国都谙熟河道水流的本质，但尚无根据说明他们曾经提出过什么定量规律以指导其工作。直到公元前250年，阿基米德才发现并记载了有关水静力学及浮力方向的一些定理。尽管随着流体机械的发展、更好的帆船的制造以及日益错综复杂的运河水系的建成，人们关于流体动力学方面的实际知识也在不断发展，然而经典水动力学方面的一些基本定理直到17、18世纪才建立起来。牛顿、丹尼尔伯努利、列昂

31、纳德欧拉都曾为这些定理的建立做出过最大的贡献。In the nineteenth century, two schools of thought arose in the treatment of fluid mechanics, one dealing with the theoretical and the other with practical aspects of fluid flow. Classical hydrodynamics, though a fascinating subject that appealed to mathematicians, was not appl

32、icable to many practical problems because the theory was based on inviscid fluids. The practicing engineers at that time needed design procedures that involved the flow of viscous fluids; consequently, they developed empirical equations that were usable but narrow in scope. Thus, on the one hand, th

33、e mathematicians and physicists developed theories that in many cases could not be used by the engineers, and on the other hand, engineers used empirical equations that could not be used outside the limited range of application from which they were derived. In a sense, these two schools of thought h

34、ave persisted to present day, resulting in the mathematical field of hydrodynamics and the practical science of hydraulics. 19世纪，流体力学领域里形成了两种想法不同的学派，一派从理论角度处理流体流动，另一派则从实际流动情况出发。经典水动力学虽然作为一门吃香的学科吸引了一批数学家，但因其理论均从无粘性流体出发，所以无法用到许多实际问题里去。当时潜心于实际工作的工程们正需要一些设计方法以对付有粘性的流体，因而他们提出了各种有用的、但使用范围有限的经验公式。于是就出现了这样的

35、局面，一方面数学家和物理学家提出了一些工程师在许多场合下无法应用的理论，另一方面，工程师所使用的经验公式又只能在其导出范围以内应用。从某种意义上来说，这两派不同想法一直绵延至今，形成了数学领域里的水动力学以及实用科学中的水力学。Near the beginning of the twentieth century, however, it was necessary to merge the general approach of the physicists and mathematicians with the experimental approach of the engineer t

36、o bring about significant advances in the understanding of flow processed. Osborne Reynoldspaper in 1883 on turbulence and later papers on the basic equations of liquid motion contributed immeasurably to the development of fluid mechanics. After the turn of the century, in 1904, Ludwing Prandtl prop

37、osed the concept of the boundary layer. In his short, convincing paper Prandtl, at a stroke, provided an essential link between ideal and real fluid motion for fluids with a small viscosity and provided the basis for much of modern fluid mechanics. 然而，在接近20世纪之初，人们为了在认清流动过程方面能取得重大进展，数学家与物理学家的一般的概括性的方

38、法同工程师的实验方法殊途同归，融合在一起，便成为势所必然。1883年，奥斯本雷诺的一篇关于紊流的文章，以及随后的几篇有关液体运动基本方程的论文，无可估量的促进了流体力学的发展。进入20世纪之始，1904年，路德维希普朗特提出了边界层的概念。普朗特在他这篇短小而有说服力的文章里，对各种粘性不大的流体，一举提出了理想流体与实际流体两种运动间的本质联系，由此在很大程度上奠定了现代流体力学的基础。The development of fluid mechanics in the twentieth century may be divided into four periods. 流体力学在20世纪的

39、发展可分为四个时期：1Low speed aerodynamics, 1900-1935The fist development of fluid mechanics was closely associated with aeronautical science. Because of the stringent requirement on weight, one needs reliable theoretical prediction to practical problems. As a result, one has to combine the essential feature

40、s of old hydrodynamics and hydraulics into one rational science of fluid mechanics. Some of the important development in these periods are: (a) Prandtl s boundary layer theory; (b) Kutta-Joukowski s wing theory to explain the phenomenon of air lift ;(c) the theory of turbulent flow by von karman and

41、 others. In this period, the velocity of the fluid flow is low and the temperature difference in the flow is small. Consequently, we may neglect the compressibility effect of the fluid. Both the gas and the liquid may be treated by the same method of analysis. There is practically no difference in p

42、rinciple for hydrodynamics and aerodynamics. 低速空气动力学，1900-1935年流体力学开始的发展是同航空科学密切相关的。由于载重方面的严格要求，人们需要能对实际问题进行可靠的理论上的预先估计。因此，出现了把古老的水动力学与水力学中的基本要点结合起来而构成的理论流体力学学科。这个时期的重要发展有：（1）普朗特的边界层理论；（2）库塔和儒可夫斯基的翼展理论，它可以解释空气升力现象；（3）冯卡门等人的紊流理论。在此时期内，流体的流动速度不大，而且流动中的温差也小，从而我们可以把流体的压缩性忽略不计。气体与液体均可按同一分析方法处理。实际上水动力学与空气

43、动力学并无区别。2. Aerothermodynamics, 1935-1950The speed of the gas flow was gradually increased from subsonic to supersonic speed. The compressibility effect of the gas is no longer negligible. We have to treat gas and liquid separately. For gasdynamics, we have to consider the mechanics of the flow simul

44、taneously with the thermodynamics of the gas. Hence the term of aerothermodynamics was suggested for this new branch of fluid mechanics. In this field the most important parameter is the Mach number. However, the temperature range of the gas or air was still below 2000K and the air may be considerd

45、as an ideal gas with constant specific heat. The molecular structure has very little influence on the gas flow and we may use the same formula to deal with monatomic gas and polyatomic gas. Many new phenomena, such as shock wave, supersonic flow, etc. , were analyzed in this period. 空气热力学，1935-1950年

46、气体流动的速度渐次地由亚声速增大为超声速。气体的压缩性效应便不能再予以忽略。气体与液体就必须加以区别对待。在气体动力学里，我们必须同时考虑到流体流动的力学与气体热力学，因而空气热力学这个术语便应运而生，以反映流体力学这个新的分支。这方面最重要的参数是马赫数。但此时气体或空气的温度范围仍在2 000K以下，因此空气仍可看成是比容不变的理想气体。分子结构对气体流动几乎没有影响，不管是单原子气体还是多原子气体，仍都适用于同样的方程。像激波、超声速流动等许多新现象在此时期内也已被加以分析。3. Physics of fluid, 1950-1960This is the start of the sp

47、ace age. The speed of the flow and the temperature of the fluid are high enough so that we have to consider the interaction of mechanics of fluid with other branches of physics and that the molecular structure of the gas has a large influence on the fluid flow. We have to consider the influence on d

48、issociation, ionization, and thermal radiation. New subjects such as aerothermochemistry, magnetogasdynamics, and plasma dynamics, and radiation gasdynamics have been extensively studied. We have to deal with the whole physics of fluids. 流体物理学，1950-1960年这是空间时代的开始。流体速度与流体温度之高足以使我们必须考虑到流体力学同物理学中其他分支学科

49、之间的相互影响，必须考虑到气体分子结构对流体的流动大有影响。我们必须考虑到离解、电离和热辐射的影响。许多新学科诸如空气热力学、磁性气体动力学、等离子体动力学以及辐射气体动力学等已经将研究延伸开去。我们不得不面对整门流体物理学。4. New era of fluid mechanics, 1960 and on In the above three periods, our main interests are still the flow of fluids which consists of liquid, gas, or plasma only. During the recent yea

50、rs, the interest of many technical developments is so broad that we have to deal with flow problems beyond those of fluid alone. For instance, we have to deal with the mixture of solid and fluid, the so-called two-phase flow. In many rheological problems, the fluids behave partly as ordinary fluid a

51、nd partly as solid. In the above three periods, we treat the fluid flow problems mainly according to the principles of classical physics. In many new problems of fluid flow, we have to consider the principles beyond those of classical physics such as superfluid for which the quantum effects are impo

52、rtant even for macroscopic properties ( quantum fluid mechanics ); relativistic fluid mechanics in which the relativistic mechanics should be used because the velocity of the flow is no longer negligible in comparison with the speed of light. We are also interested in bio-fluid mechanics in which we

53、 study the interaction between the physical science of fluid flow and biological science. Modern developments in fluid mechanics, as in all fields, involve the use of highspeed computers in the solution of problems. Remarkable progress has been made in this area, and there is an increasing use of th

54、e computer in fluid dynamic design.流体力学的新纪元，1960年至现在在以上三个时期内，我们主要关心的还只是单一液体、气体或者等离子体的流体流动。近些年来，许多技术部门发展之广，使我们必须同不仅只有单独一种流体的流动打交道。比如，我们必须处理固体和液体的混合流，即所谓的两相流问题。在许多流变学问题中，一些流体的性质既有点像普通流体，又有点像固体那样。以上三个时期里，我们主要根据经典物理学原理处理流体流动问题。在许多流体流动的新问题中，我必须考虑经典物理学之外的一些原理如超流体，超流体即使究其宏观性质而论，量子效应也有举足轻重的作用（量子流体力学）。又如相对论流

55、体力学，因其流速同光速相比已不能忽略而必须用到相对论力学。我们还关注于生物流体力学，其中要研究到流体流动的物理学学科同生物学学科之间的相互影响。同各行各业一样，流体力学的现代发展也离不开借助高速计算机来解题。这方面已取得重大进展，流体动力设计方面正愈来愈多地用到计算机。It should be noted that even though we divide the development of modern fluid mechanics into the above four periods, there are overlaps in time for these periods as

56、far as the study of various subjects are concerned. For instance, the study of turbulent flow of low speed fluid flow which was one of the major subjects in the first period is still a very active research subject at the present time and many basic problems are far from being solved yet.应当指出，尽管我们把现代

57、流体力学划分成以上四个时期，但就各门学科所涉及的研究而言，在这些时期内还有相互的交叉重叠。例如，低速流动的紊流研究虽然作为第一时期中的主要学科，但至今仍然是十分热门的研究题目，其中的许多基本课题还远未获得解决。1.3 The Characteristics of Fluids 流体的特征A fluid is a substance which may flow; that is, its constituent particles may continuously change their positions relative to one another. Moreover, it offe

58、rs no lasting resistance to the displacement, however great, of one layer over another. This means that, if the fluid is at rest, no shear force (that is a force tangential to the surface on which it acts )can exist in it. A solid, on the other hand, can resist a shear force while at rest; the shear

59、 force may cause some displacement of one layer over another, but the material does not continue to move indefinitely. In a fluid, however, shear forces are possible only while relative movement between layers is actually taking place. A fluid is further distinguished from a solid in that a given am

60、ount of it owes its shape at any particular time to that of a vessel containing it, or to forces which in some way restrain its movement. 流体是可以流动的物质，也就是说，组成流体的质点可以连续的改变它们的相对位置。而且，不管层与层之间的相对位移有多大都不会产生持久的抵抗力。这意味着流体在静止状态下是不会存在剪切力的（剪切力是与其作用表面相切的力）。另一方面，固体在静止时却可以抵抗剪切力，其中的剪切力也可以使层与层之间发生相对位移，但是固体材料却不一定会有连续