流體的定義和流體流動的分類

1、PAGE 2 Part Fluid Mechanics and Fluid Machines1.1 Definition of a Fluid and Classification of Fluid Flow流體的定義和流體流動的分類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. 無論受到多么小的剪切力都會發(fā)生連續(xù)變形的物質(zhì)叫做流體。剪切力是與表面相切方向上的分力，該力除以面積便得此面積上的平均切應(yīng)力，當(dāng)面積縮成一點時，即為該點上的切應(yīng)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. 如圖1-1a所示，兩塊平行放置非?？拷钠桨彘g充滿某種物質(zhì)，平板很大，因此平板四周邊緣處的情況可以不予考慮。固定下平板，對上板施加一作用力F，平板間的物質(zhì)便會受到剪切力F/A的作用，其中A是上板面積。只要作用力F能使上板以恒定（不等于零）的速

5、度運動，而不論力F的量值多么小，你就可以斷定板間的物質(zhì)是一種流體。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.緊貼固體邊壁的流體其速度與邊壁速度相同，也就是說交界處并無滑移，這一事實已為不同流體和不同邊壁材料進行的千萬次試驗所證實。面積abcd里的流體流到新的位置abcd處，各流體質(zhì)點均平行于平板運動，其速度u從固定平板上的零值均勻地變化到上板處的U。實驗表明，保持其他參數(shù)不變，F(xiàn)正比于AU，且反比于厚度t?？梢员硎境晒叫问剑菏街惺桥c特定流體有關(guān)的比例系數(shù)，令=F/A代表剪切應(yīng)力，則有比值U/t是線段ab的角速度，或者說是流體的角變形速度，即角bad減小的速度。角速度也可以表達(dá)為du/dy,，因為U/t和d

11、u/dy這兩者都表示的是速度的變化量除以發(fā)生該變化所需的距離。然而，du/dy更具普遍性，因為它適用于角速度和切應(yīng)力隨y變化的情況。速度梯度du/dy還可以形象地看作是某層相對于其鄰層流體間的速度。表示成微分形式為：上式即為流體一元流動中切應(yīng)力同角變形率間的關(guān)系。比例系數(shù)稱為流體的粘度。方程（1-1）稱為牛頓粘性定律。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. 非流體材料就不能滿足流體的定義。塑性物質(zhì)會隨著所施加作用力的大小而發(fā)生一定的變形，但當(dāng)作用其上的切應(yīng)力小于屈服切應(yīng)力時，變形即終止。若兩平板間完全真空，變形速率將不斷增大。若將沙粒填充于兩平板之間，那么庫倫摩擦要求作用力必須超過某一數(shù)值才會引起連續(xù)運動，因此塑料和固體均無法歸入流體的分類。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. 流體可分為牛頓流體和非牛頓流體，牛頓型流體中施加的切應(yīng)力的大小同其所

15、引起的角變形速率之間的關(guān)系是線性的（方程1-1中的為常數(shù)）；非牛頓型流體中施加的切應(yīng)力的大小同其所引起的角變形速率間有著非線性的關(guān)系A(chǔ)n 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. 理想塑性流體有一確定的屈服應(yīng)力，同時其中的與du/dy之間有一定的線性關(guān)系。觸變性物質(zhì)，如油墨之類，其粘度依該物質(zhì)當(dāng)時經(jīng)歷的角變形而定，且在靜止不動時趨于凝聚態(tài)。各種氣體和稀薄液體近乎牛頓型流體，而粘稠的長鏈碳?xì)浠衔飫t常為非牛頓型流體。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. 為了分析為題起見，通常假定流體是無粘性的。粘度為零時，不管流體是否流動，切應(yīng)力總等于零。若把流體看成是無粘性的，那么這就稱

18、為理想流體。Fluid flow may be classified in many ways, such as steady or nonsteady, rotational or irrotational, compressible or incompressible, and viscous or nonviscous. 流體的流動可用多種方式加以分類，如定常流或非定常流；有旋流或無旋流；可壓縮流或不可壓縮流；以及粘性流動或無粘性流等。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.流體的流動可以是定常的或非定常的。如果在任一給定點處流體的速度不隨時間而變化，這種流體的流動就稱為定常流，也就是說流經(jīng)定常流中任一給定點的每一流體質(zhì)點的速度總是相同的；在另一點上某質(zhì)點的流動速度可能不同，但任一通過該第二點上的其它質(zhì)點恰好同該質(zhì)點經(jīng)過此點時的速度相同。在低的流動速度下就可能出現(xiàn)這種情形，徐緩的溪流便是其中一例。非定常流方面，可以舉出漲潮時的激浪為例，其速度是時間的函數(shù)，諸如激流或瀑布紊流情形里，各點間以及不同時刻下

22、的速度均變化不定。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. 流體流動可以是有旋的或者無旋的。如果每個點上的流體微團繞該店均無凈角速度，這時的流體流動便是無旋的；我們不妨設(shè)想在運動流體中有一個小的自行車蹬，只要車蹬運動時不發(fā)生旋轉(zhuǎn)，這種運動便是無旋的，否則就是有旋的，有旋運動包含像一些漩渦那樣的渦旋運動。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. 流體可以是可壓縮的或者不可壓縮的。各種液體通?？勺鳛椴豢蓧嚎s流動看待。不過即使是某種有高度壓縮性的氣體，有時它的密度并未表現(xiàn)出多大的變化，這樣的流體實際上仍是不可壓縮的。飛行速度遠(yuǎn)小于空氣中的聲速時（用亞聲速空氣動力學(xué)來描述），空氣相對于飛機機翼的運動便是一種不可壓縮流動。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.流體流動還可以是粘性的或者無粘性的。流體流動中的粘性可以比作固體運動中的摩擦。許多情形里，比如在潤滑問題中這是極其重要的，

27、但有時又可以予以忽略。粘性引起流體相對運動各層間的切向力，從而導(dǎo)致了機械能的損耗。Historical Development of Fluid Mechanics流體力學(xué)的發(fā)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. 流體力學(xué)這門科學(xué)起源于古代中國、埃及、美索布達(dá)美亞和印度，它是隨著水利灌溉和舟船航行的需要對水進行治理而出現(xiàn)的。雖然這些文明古國都諳熟河道水流的本質(zhì)，但尚無根據(jù)說明他們曾經(jīng)提出過什么定量規(guī)律以指導(dǎo)其工作。直到公元前250年，阿基米德才發(fā)現(xiàn)并記載了有關(guān)水靜力學(xué)及浮力方向的一些定理。盡管隨著流體機械的發(fā)展、更好的帆船的制造以及日益錯綜復(fù)雜的運河水系的建成，人們關(guān)于流體動力學(xué)方面的實際知識也在不斷發(fā)展，然而經(jīng)典水動力學(xué)方面的一些基本定理直到17、18世紀(jì)才建立起來。牛頓、丹尼爾伯努利、列昂

31、納德歐拉都曾為這些定理的建立做出過最大的貢獻。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世紀(jì)，流體力學(xué)領(lǐng)域里形成了兩種想法不同的學(xué)派，一派從理論角度處理流體流動，另一派則從實際流動情況出發(fā)。經(jīng)典水動力學(xué)雖然作為一門吃香的學(xué)科吸引了一批數(shù)學(xué)家，但因其理論均從無粘性流體出發(fā)，所以無法用到許多實際問題里去。當(dāng)時潛心于實際工作的工程們正需要一些設(shè)計方法以對付有粘性的流體，因而他們提出了各種有用的、但使用范圍有限的經(jīng)驗公式。于是就出現(xiàn)了這樣的

35、局面，一方面數(shù)學(xué)家和物理學(xué)家提出了一些工程師在許多場合下無法應(yīng)用的理論，另一方面，工程師所使用的經(jīng)驗公式又只能在其導(dǎo)出范圍以內(nèi)應(yīng)用。從某種意義上來說，這兩派不同想法一直綿延至今，形成了數(shù)學(xué)領(lǐng)域里的水動力學(xué)以及實用科學(xué)中的水力學(xué)。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世紀(jì)之初，人們?yōu)榱嗽谡J(rèn)清流動過程方面能取得重大進展，數(shù)學(xué)家與物理學(xué)家的一般的概括性的方

38、法同工程師的實驗方法殊途同歸，融合在一起，便成為勢所必然。1883年，奧斯本雷諾的一篇關(guān)于紊流的文章，以及隨后的幾篇有關(guān)液體運動基本方程的論文，無可估量的促進了流體力學(xué)的發(fā)展。進入20世紀(jì)之始，1904年，路德維希普朗特提出了邊界層的概念。普朗特在他這篇短小而有說服力的文章里，對各種粘性不大的流體，一舉提出了理想流體與實際流體兩種運動間的本質(zhì)聯(lián)系，由此在很大程度上奠定了現(xiàn)代流體力學(xué)的基礎(chǔ)。The development of fluid mechanics in the twentieth century may be divided into four periods. 流體力學(xué)在20世紀(jì)的

39、發(fā)展可分為四個時期：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. 低速空氣動力學(xué)，1900-1935年流體力學(xué)開始的發(fā)展是同航空科學(xué)密切相關(guān)的。由于載重方面的嚴(yán)格要求，人們需要能對實際問題進行可靠的理論上的預(yù)先估計。因此，出現(xiàn)了把古老的水動力學(xué)與水力學(xué)中的基本要點結(jié)合起來而構(gòu)成的理論流體力學(xué)學(xué)科。這個時期的重要發(fā)展有：（1）普朗特的邊界層理論；（2）庫塔和儒可夫斯基的翼展理論，它可以解釋空氣升力現(xiàn)象；（3）馮卡門等人的紊流理論。在此時期內(nèi)，流體的流動速度不大，而且流動中的溫差也小，從而我們可以把流體的壓縮性忽略不計。氣體與液體均可按同一分析方法處理。實際上水動力學(xué)與空氣

43、動力學(xué)并無區(qū)別。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. 空氣熱力學(xué)，1935-1950年

46、氣體流動的速度漸次地由亞聲速增大為超聲速。氣體的壓縮性效應(yīng)便不能再予以忽略。氣體與液體就必須加以區(qū)別對待。在氣體動力學(xué)里，我們必須同時考慮到流體流動的力學(xué)與氣體熱力學(xué)，因而空氣熱力學(xué)這個術(shù)語便應(yīng)運而生，以反映流體力學(xué)這個新的分支。這方面最重要的參數(shù)是馬赫數(shù)。但此時氣體或空氣的溫度范圍仍在2 000K以下，因此空氣仍可看成是比容不變的理想氣體。分子結(jié)構(gòu)對氣體流動幾乎沒有影響，不管是單原子氣體還是多原子氣體，仍都適用于同樣的方程。像激波、超聲速流動等許多新現(xiàn)象在此時期內(nèi)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. 流體物理學(xué)，1950-1960年這是空間時代的開始。流體速度與流體溫度之高足以使我們必須考慮到流體力學(xué)同物理學(xué)中其他分支學(xué)科

49、之間的相互影響，必須考慮到氣體分子結(jié)構(gòu)對流體的流動大有影響。我們必須考慮到離解、電離和熱輻射的影響。許多新學(xué)科諸如空氣熱力學(xué)、磁性氣體動力學(xué)、等離子體動力學(xué)以及輻射氣體動力學(xué)等已經(jīng)將研究延伸開去。我們不得不面對整門流體物理學(xué)。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.流體力學(xué)的新紀(jì)元，1960年至現(xiàn)在在以上三個時期內(nèi)，我們主要關(guān)心的還只是單一液體、氣體或者等離子體的流體流動。近些年來，許多技術(shù)部門發(fā)展之廣，使我們必須同不僅只有單獨一種流體的流動打交道。比如，我們必須處理固體和液體的混合流，即所謂的兩相流問題。在許多流變學(xué)問題中，一些流體的性質(zhì)既有點像普通流體，又有點像固體那樣。以上三個時期里，我們主要根據(jù)經(jīng)典物理學(xué)原理處理流體流動問題。在許多流體流動的新問題中，我必須考慮經(jīng)典物理學(xué)之外的一些原理如超流體，超流體即使究其宏觀性質(zhì)而論，量子效應(yīng)也有舉足輕重的作用（量子流體力學(xué)）。又如相對論流

55、體力學(xué)，因其流速同光速相比已不能忽略而必須用到相對論力學(xué)。我們還關(guān)注于生物流體力學(xué)，其中要研究到流體流動的物理學(xué)學(xué)科同生物學(xué)學(xué)科之間的相互影響。同各行各業(yè)一樣，流體力學(xué)的現(xiàn)代發(fā)展也離不開借助高速計算機來解題。這方面已取得重大進展，流體動力設(shè)計方面正愈來愈多地用到計算機。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.應(yīng)當(dāng)指出，盡管我們把現(xiàn)代

57、流體力學(xué)劃分成以上四個時期，但就各門學(xué)科所涉及的研究而言，在這些時期內(nèi)還有相互的交叉重疊。例如，低速流動的紊流研究雖然作為第一時期中的主要學(xué)科，但至今仍然是十分熱門的研究題目，其中的許多基本課題還遠(yuǎn)未獲得解決。1.3 The Characteristics of Fluids 流體的特征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. 流體是可以流動的物質(zhì)，也就是說，組成流體的質(zhì)點可以連續(xù)的改變它們的相對位置。而且，不管層與層之間的相對位移有多大都不會產(chǎn)生持久的抵抗力。這意味著流體在靜止?fàn)顟B(tài)下是不會存在剪切力的（剪切力是與其作用表面相切的力）。另一方面，固體在靜止時卻可以抵抗剪切力，其中的剪切力也可以使層與層之間發(fā)生相對位移，但是固體材料卻不一定會有連續(xù)