1、Chapter 1 Fluid statics 流体静力学1. 连续介质假定(Continuum assumption)：The real fluid is considered as no-gap continuous media, called the basic assumption of continuity of fluid, or the continuum hypothesis of fluid. 流体是由连续分布的流体质点(fluid particle)所组成，彼此间无间隙。它是流体力学中最基本的假定，1755 年由欧拉提出。在连续性假设之下，表征流体状态的宏观物理量在空间和时
2、间上都是连续分布的，都可以作为空间和时间的函数。2. 流体质点（Fluid particle）: A fluid element that is small enough with enough moles to make sure that the macroscopic mean density has definite value is defined as a Fluid Particle. 宏观上足够小，微观上足够大。3. 流体的粘性（Viscosity ）: is an internal property of a fluid that offers resistance to s
3、hear deformation. It describes a fluids internal resistance to flow and may be thought as a measure of fluid friction. 流体在运动状态下抵抗剪切变形的性质，称为黏性或粘滞性。它表示流体的内部流动阻力，也可当做一个流体摩擦力量。The viscosity of a gas increases with temperature, the viscosity of a liquid decreases with temperature.4. 牛顿内摩擦定律（Newtons law o
4、f viscosity）：5. The dynamic viscosity（动力黏度）is also called absolute viscosity（绝对黏度）. The kinematic viscosity（运动黏度）is the ratio of dynamic viscosity to density. 6. Compressibility（压缩性）：As the temperature is constant, the magnitude of compressibility is expressed by coefficient of volume compressibilit
5、y (体积压缩系数) , a relative variation rate（相对变化率） of volume per unit pressure. The bulk modulus of elasticity (体积弹性模量) E is the reciprocal of coefficient of volume compressibility. 7. 流体的膨胀性(expansibility; dilatability)：The coefficient of cubical expansion (体积热膨胀系数) t is the relative variation rate of v
6、olume per unit temperature change.8. 表面张力 Surface tension: A property resulting from the attractive forces between duz2dmNVp1dEVo1K,CTdVaTmolecules. -单位长度所受拉力9. 表面力 Surface forceis the force exerted on the contact surface by the contacted fluid or other body. Its value is proportional to contact are
7、a. 作用在所研究流体外表面上与表面积大小成正比的力。Stress （应力） is the surface force on per unit area.10. 质量力 Mass forceThe force acting on every fluid mass particle within the control body. Its value is proportional to its mass. Mass force is also known as body force. 作用在流体的每一个流体质点上，其大小与流体所具有的质量成正比。 11. Euler Equilibrium E
8、quations 欧拉平衡微分方程（分量式） 1775 年Physical Meaning: For the fluid in equilibrium, surface force components per mass fluid are equal to mass force components per mass fluid. Pressure variation rate in axes directions are equal to mass force components per unit volume in axes directions respectively12. con
9、stant-pressure Surface(等压面)a surface that the pressure of every point in liquid is equal. Common constant-pressure surfaces are free liquid surface and interface of two unmixed fluids in equilibrium.平衡流体中压强相等的点所组成的平面或曲面。13. Pressure Distribution in the Static Fluid 重力场中流体的平衡Conclusions:1. Pressure a
10、t a point in a static fluid under gravity increases linearly with depth.2. Pressure at a point in a static fluid under gravity is equal to the sum of the pressure at the free surface and the fluid specific weight timing depth.3. constant-pressure surface in a static fluid under gravity is a horizont
11、al plane.4. Extended: while the pressure at a point and the depth difference between two points are known, the pressure at another point can be calculated.14. Absolute pressure(绝对压力), Gage pressure(相对压力, 又称“表压力”), and Vacuum(真空度 ): 表压力绝对压力大气压力; 真空度大气压力绝对压力15. Fluid in Relative Equilibrium(相对静止流体) Eq
12、uation of constant-pressure surface(等压面方程): a) Uniform Linear Acceleration 等加速度直线运动流体: 11xyzpffpf(,)pxyz(,)xyzff0pCd或 CgpzCgzpcosd(in)d0ayagzb) Uniform Rotation about a Vertical Axis 等角速度旋转流体:Chapter 2 basic equations of fluid mechanics16. 迹线 pathline：the trace after a single particle travels in a f
13、ield of flow over a period of time. 流体质点的运动轨迹曲线17. 流线 streamline ： a curve that show the direction of a number of particles at the same instant of time.某一时刻处处与速度矢量相切的空间曲线-瞬时性。18. Stream-tube(流管)Consider a closed curve(not streamline) in the flow field, then draw streamlines through every point on it
14、, so as to form a tube-shaping space whose walls are streamlines. This tube is called the stream-tube. 在流场中任取一个有流体从中通过的封闭曲线，在曲线上的每一个质点都可以引出一条流线，这些流线簇围成的管状曲面称为流管。19. Tube-flow 流束Fluid fulling the stream tube is called the tube-flow and the limit of a tube-flow is a streamline. 流管内的全部流体称为流束。20. Mini s
15、tream-tube 微小流束 The stream tube with an infinitesimal section is said to be mini-stream tube. Streamline is the extreme case of mini-stream tube. 截面无穷小的流束。21. Total flow 总流Total of countless mini-stream tubes is called total flow. 包含流动中所有的微小流束。22. Cross section(过水断面)- The section is perpendicular to
16、 the direction of fluid flow. (such as pipe flow and channel flow) 与流束或总流流线 成正交的断面。23. Discharge (流量)-Amount of fluid pass through a cross section per unit time (such as the section in the channel or pipe).单位时间内通过某一过水断面的流体体积称为体积流量，简称流量。24. Mean velocity 断面平均流速 -The velocities of points on the same c
17、ross section in the total flow are different, so usually an average velocity is used instead of the real velocity (,)(,)(,)dxdydzuyztvztwxytdtzxtzvdytzyux, ,dAover the cross section, this average velocity is called the mean velocity.25. Uniform flow 均匀流： is defined as uniform flow when in the flow f
18、ield the velocity and other hydrodynamic parameters do not change from point to point at any instant of time (in which the cross section of each stream tube remains unchanged. 流场中每一空间点的各运动参数（速度，压力）不随空间位置而变化。26. Nonuniform flow 非均匀流： Flow such that the velocity varies from place to place at any insta
19、nt.27. Steady flow 恒定流 ： the flow whose motion factors dont change with time. 流场中所有的运动要素不随时间变化. 28. Unsteady flow 非恒定流：the flow that at least one of its motion factors changes with time.流场中至少有一个运动要素随时间变化. 29. One dimensional flow (一元流动) - all main variables in the flow field can be completely specif
20、ied by a single coordinate if the variation of flow parameters transverse to the mainstream direction can be neglected.流动参数只与一个坐标变量有关。30. Two dimensional flow(二元流动)- fluid motion factors are function of two space coordinates. 流动参数与两个坐标变量有关。31. Three-dimensional Flow (三元流动): Fluid flows motion factor
21、s are functions of three space coordinates.流动参数与三个坐标变量有关。32. System（系统） is a set of definite fluid particles selected in the interest of researcher.由确定的流体质点组成的流体团或流体体积 V(t)。系统边界面 S(t)在流体的运动过程中不断发生变化。 反映了拉格朗日观点 33. Control volume (控制体 CV)is defined as an invariably hollow volume or frame fixed in spa
22、ce or moving with constant velocity through which the fluid flows.相对于坐标系固定不变的空间体积 V 。是为了研究问题方便而取定的。反映了欧拉观点 For a CV:1) its shape, volume and its cs can not change with time. 2) it is stationary in the coordinate system. (in this book)3) there may be the exchange of mass and energy on the cs.34. Cont
23、rol surface 控制面 : the surface area completely encloses the CV. 边界面 S 称为控制面。35. differential form of continuity equation 微分形式的连续性方程 ()0Av0yxzvtFor incompressible fluidFor 2-D incompressible flowPhysical meaning: The net mass discharge entering the control volume is equal to the mass increased in unit
24、 time due to the change in density.Fit for: Steady flow, unsteady flow, compressible and incompressible fluid, ideal fluid and real fluid.36. Integral form of continuity equation 积分形式的连续方程Physical meaning：在单位时间内，由于控制体内密度变化引起的质量变化量（增加量或减少量）与通过控制体表面的质量净流出量（流出与流入的质量差）之和等于零。Steady flow 定常流动 incompressib
25、le fluid 不可压缩流体 37. Motion Differential Equation 运动微分方程For IDEAL FLOWfor Viscous Flow0yxzvyxd0nVStv0nCSvdAnCS12v11xxxxx yzy yyxyzzzzvvpftftvvpft2222()1()xxxxxxxx yzyyyy yy xyzzzzzzz xyzvvvvf tpf tvvvvf tx38. Bernoulli Equation 伯努利方程（1 ） steady flow 定常流动（2 ） incompressible flow 不可压缩（3 ） integration a
26、long a streamline 沿流线积分（4 ） mass force is a potential force 质量力有势For streamline For compressible flow in gravity fieldFor compressible flow with fluid machinery in gravity fieldz(m) the elevation height above datum surface o-o, called the elevation head (位置水头).p/( g)rising height of fluid with unit
27、weight under the action of pressure P, called the pressure head (压力水头). u2/(2g) rising height of fluid with unit weight under the action of velocity V, called the velocity head (速度水头 ), denoted as hu fh the lost mechanical energy from 1 to 2 points per unit weight fluid THThe effective energy obtain
28、ed after the unit weight of the liquid flows through the pump.单位重量液体流经泵后获得的有效能量。 Head of delivery 扬程The sum of them is called the total head (总水头) , denoted as H.Pump power 泵功率：For the ideal-fluid total flow 理想流体总流的伯努利方程for the real-fluid total flow 实际流体总流的伯努利方程39. momentum integral equation 动量积分方程2
29、pvzCg22112fVpVpzzhgg22112TfH221121HpvzgwTPQ22112pvpvzzgg221 fuuzzhFor CV d()ddS nSV VStvvnfpAAsum of the fluid momentum change in CV and the net outflow momentum in CS, is equal to the resultant force. Steady flow：()ddnSVSvnfp40. Moment-of-momentum integral equation 动量矩积分方程()d()d()d()dnS SV VStrvrvn
30、rfrpFor steady flow： ()()()nS SVrvnrfr流出动量矩 CS 流入动量矩 CS = 合外力矩 CV+CS 41. Forces on bend(弯头）42. fluid jets on deflector(导流板）43. Sprinkler(喷水器）角速度：固定所需力矩Chapter 3 Pipe Flow and Boundary Layer Theory (管流和边界层概述)21122cos)()()cosaaxQvpAFp22insiny 2y22sin()sinavpRA1122(co()cosax p12122()4()vrQrd21212()()rM
31、vrd44. Laminar flow (层流) ： In the fluid flow the fluid particles move along smooth path in layers without transverse velocity in the direction of main flow, one layer glides smoothly over an adjacent layer. 45. Turbulent flow (紊流, 湍流 ) or Turbulence ：If the fluid particles have a transverse velocity
32、 normal to the main flow direction, that leads to particles mixing up each other, with a violent transverse interchange of momentum. This is turbulent flow (紊流, 湍流) or turbulence.46. Reynolds number 雷诺数：is used to describe the characteristic of flow.47. Wetted perimeter (湿润长度)：The length of wall con
33、tacted with liquid.48. the hydraulic diameter (水力直径 ) DH: The characteristic dimension of noncircular tube.49. Head Loses（能头损失，或水头损失 )：the total energy losses per unit weight （单位重量流体所损失的机械能为能头损失(水头) ）, which due to the resistance between two sections of gradually varied flow. （流体流动,克服粘性内摩擦力,消耗机械能为热能
34、.）50. Friction Loss 沿程水头损失( h ): In the flow through a straight tube with constant cross section, the energy loss increases linearly in the direction of flow and the loss is called friction loss. (原因: 粘性内摩擦力, 以及与管壁的摩擦阻力 )Darcy-Weisbch (达西- 韦斯巴赫 ) Equation: : the coefficient of friction loss 沿程阻力系数,
35、与流态和壁面有关51. Local losses 局部水头损失(h ) ：When the shape of flow path changes, such as section enlargement and so on, it will give rise to a change in the distribution of velocity for the flow. The change results in energy loss, which is called minor loss or local loss. 原因: 流速急剧变化, 流体质点剧烈撞击和摩擦. ： minor l
36、oss coefficient or local loss coefficient 为局部阻力系数,与障碍物形式有关52. Head losses 总能量损失(h f=h +h )53. LAMINAR FLOW THROUGH CIRCULAR TUBE 圆管中的层流Velocity distribution in cross sectionVRe2LvhDg2vhgf2()()4purRrL214wDrRDischarge Hagen-Poiseuille (哈根- 泊肃叶) equation. Distribution of shear stress 切应力分布 ：壁面剪切力54. He
37、ad loss along the path 沿程能量( 阻力)损失pressure drop 压强损失 Head loss 水头损失：the coefficient of friction loss：64RevdPower loss(功率损失) ：55. Pulsation Phenomenon （脉动现象）：The phenomenon that the physical parameter fluctuates around a certain average value is called pulsation phenomenon （脉动现象）.u=+ u 2max4puRL28pRv
38、L()vdqArdmax1u0vr 20 ()4RprdL4 8RpL2max u vvAqd204RprdL48RpL412D24rdA2dur2wpRL28evF2p28LvR8v48vLqpR412vd28LvR23hghg48vq41vLgd28Lvg23vWghqvpA224481vvLqRdwhere: is time-average velocity (时均速度); u -the component of random fluctuating velocity(脉动速度).56. hydraulic smooth (水力光滑 ): If viscous sublayer more
39、 than absolute roughness (ie. ), the effect of for the core of turbulent flow is very little, namely, the influence of in the energy loss is very little. 57. hydraulic rough (水力粗糙): If viscous sublayer less than absolute roughness (ie. 10，the head, pressure, velocity on the section will NOT be chang
40、ed with the height.65. free outflow（自由出流）：the jet flows into atmosphere directly, the pressure on the contracted section was BAR, pc=pa.66. submerged outflow（淹没出流）：the jet flows down to the water.67. Contracted section 收缩断面： the streamlines were contracted after the hole, and the section reached the
41、 minimum at d/2, which was the contracted section CC.68. contraction coefficient 收缩系数： the ratio between the contracted section area and the hole area, labeled as Cc : 69. The discharge calculation of steady free flow in orifice 孔口恒定自由出流流量计算Cv is the velocity coefficient 流速系数discharge coefficient 流量
42、系数70. gap flow between stationary 固定平板间的缝隙流动velocity distributiondischargeaverage velocity /1cAgHvvc 21cQAcvCrAr212dpuzCx22/max8hLpuhz2003()2hhvBBpqzzhLL1vqApressure loss71. gap flow between relatively moved parallel plates 具有相对运动的两平行平板间的流动velocity discharge 压差与平板运动方向相同取正号；方向相反取负号72. gap flow betwee
43、n concentric cylinders 同心圆环间的缝隙流动discharge Chap. 5 Similitude and Dimensional Analysis相似理论和量纲分析73. The three similarities are essential conditions of Dynamic Similitude of Fluid Motion(流动相似), in which, at any time, all the parameters of the model and prototype are in the same ratio throughout the en
44、tire flow field. Dynamic Similitude of Fluid Motion(流动相似) includes Geometric similarity 几何相似, Kinematic similarity 运动相似, and Dynamic similarity 动力相似; Geometric similarity 几何相似 is the basic and the most obvious requirement; Kinematic similarity 运动相似 is the result; Dynamic similarity 动力相似 is the condi
45、tions. dynamic similarity includes kinematic similarity, while kinematic similarity includes geometric similarity. Hence, ratios of force, time and length are same under dynamic similarity, and other quantities are also equal. 动力相似包括运动相似，而运动相似又包括几何相似。所以动力相似包括力、时间和长度三个基本物理量相似。两系统的其它物理量由它们决定，也必然相似。The
46、 initial conditions(初始条件)and boundary conditions(边界条件) also must be coincident for dynamic similitude of fluid flow except above three similarities. 74. Newton number(牛顿数), NevlF2312vLqpBh2()UuzzLh31vBhpq312vdhpUqL75. Reynolds number 雷诺数76. Froud number 弗劳德数77. Strouhal number 斯特洛哈尔数78. Euler number
47、 欧拉数79. Dimension 量纲 ：Unit types of physical variables (物理量测量单位的类别); For one quantity, only one dimension, but different units(同一量,可以有不同的单位,单仅有一个量纲).80. Dimensional Homogeneity 量纲齐次性/Dimension concordant principle 量纲和谐原理）:The dimensions on both sides of equation are correspondingly equal.(等式两边各项的量纲对
48、应相等)81. -theorem (-定理): The number of independent dimensionless groups of variables needed to correlate the variables in a given process is equal to n-m, where n is the number of variables involved and m is the number dimensions included in the variables. 若一个物理现象可由 n 个物理量构成的物理方程式描述，在 n 个物理量中有 m 个独立的物理量，则该物理现象也可以用这些量组成的（nm）个无量纲群的关系来描述。 Chapter 6 1-D compressible gas flow 可压缩气体的一元流动82. isothermal process 等温过程 21Vp83. adiabatic pr
