流體力學(xué)英文版復(fù)習(xí)

1、General Review 總復(fù)習(xí),雙 語 課 程,Chapter 1. FLUID PROPERTIES 第一章 流體性質(zhì),2024/3/19,In physics, a fluid is a substance that continually deforms under an applied shear stress, no matter how small it is.,流體是一種一受到切力作用（不論多么?。┚蜁B續(xù)

2、變形的物體。,Definition of a fluid,2024/3/19,(1) Density （密度）,Density is the ratio of the mass of fluid to its volume.,(1.12),Specific volume (比容) : volume occupied by unit mass.,(1.13),The specific volume is the reciprocal (

3、倒數(shù)) of density.,(kg/m3 ),(m3/kg ),2024/3/19,,,(2) Specific Weight （重度）,It’s the weight per unit volume,,(1.14),in which ? is the specific weight of fluid, N/m3; G is the weight of fluid, N.,(1.14a),Or the product of den

4、sity ? and acceleration of gravity g.,,2024/3/19,(3) Relative density and specific gravity,The relative density (相對密度) RD of a fluid is the ratio of its density to the density of a given reference material.,The reference

5、 material is water at 4?C i.e., ?ref=?water.=1000kg/m3,dimensionless quantity無量綱,The specific gravity (比重) SG of a fluid is the ratio of its weight to the weight of an equal volume of water at standard conditions(標(biāo)準(zhǔn)狀態(tài)).,

6、dimensionless quantity無量綱,2024/3/19,(4) Compressibility（壓縮性）,The volume of fluid changes under different pressure. As the temperature is constant, the magnitude of compressibility is expressed by coefficient of volume co

7、mpressibility (體積壓縮系數(shù)) ?p , a relative variation rate（相對變化率） of volume per unit pressure.,(1.15),The bulk modulus of elasticity (體積彈性模量) K is the reciprocal of coefficient of volume compressibility ?p.,(1.16),（Pa）,（Pa?1）

8、,2024/3/19,A mineral oil in cylinder has a volume of 1000cm3 at 0.1MN/m2 and a volume of 998 cm3 at 3.1MN/m2. What is its bulk modulus of elasticity?,Example 1.1,Solution:,2024/3/19,Predominant Cause: Cohesion is the c

9、ause of viscosity of liquid. Transfer of molecular momentum is the cause of viscosity of gas.,(5) Viscosity,Viscosity is an internal property of a fluid that offers resistance to shear deformation. It describes a flui

10、d's internal resistance to flow and may be thought as a measure of fluid friction. The resistance of a fluid to shear depends upon its cohesion(內(nèi)聚力) and its rate of transfer of molecular momentum(分子動量交換).,2024/

11、3/19,Newton’s law of viscosity,Figure 1.5 Deformation resulting from application of constant shear force,In Fig.1.5, a substance is filled to the space between two closely spaced parallel plates（平行板）. The lower plate is

12、 fixed, the upper plate with area A move with a constant velocity V, a force F is applied to the upper plate.,2024/3/19,Experiment shows that F is directly proportional to A and to V and is inversely proportional （反比）to

13、thickness h.,(1.18),If the shear stress is ? =F/A, it can be expressed as,The ratio V/h is the angular velocity of line ab, or it is the rate of angular deformation of the fluid.,2024/3/19,(1.19),The angular velocity may

14、 also be written as du/dz, so Newton’s law of viscosity is,The proportionality factor (比例因子）? is called the viscosity coefficient（黏性系數(shù)，黏度）.,Fluids may be classified as Newtonian or non-Newtonian. Newtonian fluid:

15、 ? is constant. (gases and thin liquids稀液) Non-Newtonian fluid: ? is not constant. (thick稠的, long- chained hydrocarbons長鏈碳氫化合物),2024/3/19,Dynamic viscosity and Kinematic viscosity,The dynamic viscosity（動力黏度

16、）is also called absolute viscosity（絕對黏度）. From （1.19）,SI unit ：kg/(m?s) or N?s/m2 U.S. customary unit：dyne?s/cm2 （達因?秒/厘米2）cgs unit： Poise (P, 泊). 1P=100cP (厘泊) 1P=0.1Pa?s (帕?秒),The kinematic viscosity （運動黏度）is th

17、e ratio of dynamic viscosity to density.,SI unit：m2/s U.S. customary unit：ft2/s （英尺2/秒） cgs unit：stokes (St, 斯). 1cm2/s=1St 1mm2/s=1cSt (厘斯),Chapter 2. FLUID STATICS 第二章 流體靜力學(xué),2024/3/19,Basic equation of

18、hydrostatics under gravity,Gravity G (G=mg) is the only mass force acting on the liquid,fx=0，fy=0，fz= ?g,Figure 2.4 A vessel containing liquid at rest,rewriting,From (2.5),2024/3/19,For the two points 1 and 2 in the sta

19、tic fluid,For the two points 0 and 1,Figure 2.4 A vessel containing liquid at rest,The pressure at a point in liquid at rest consists of two parts: the surface pressure, and the pressure caused by the weight of column of

20、 liquid.,2024/3/19,Physical meaning,z —— the position potential energy per unit weight of fluid to the base level；,p/?g —— the pressure potential energy (壓強勢能) per unit weight of fluid.,Geometrical meaning,z ——the posi

21、tion height or elevation head (位置水頭),p/?g——the pressure head (壓力水頭) per unit weight of fluid,Sum of the position head (位置水頭) and pressure head is called the hydrostatic head (靜水頭), also known as the piezometric head (測壓管

22、水頭).,2024/3/19,local atmospheric pressure (當(dāng)?shù)卮髿鈮? pa,absolute pressure (絕對壓強) pabs,gauge pressure (表壓, 計示壓強) = relative pressure,vacuum pressure (真空壓強, 真空度) pv , or suction pressure (吸入壓強) , also called negative pressure

23、 (負壓強),relative pressure (相對壓強) p,It is usually measured in the height of liquid column, such as millimeters of mercury (mmHg, 毫米水銀柱), denoted by hv.,Related Pressures,2024/3/19,,,,,,,,,,,Local atmospheric pressure p

24、=pa,Complete vacuum pabs=0,Absolute pressure,Vacuumpressure,Gaugepressure,Figure 2.6 absolute pressure, gauge pressure and vacuum pressure,p,Absolute pressure,2,p<pa,1,p>pa,O,Relationship Graph,2024/3/19,To avoid

25、 any confusion, the convention is adopted throughout this text that a pressure is in gauge pressure unless specifically marked ‘a(chǎn)bs’, with the exception of a gas, which is absolute pressure unit.,Attention:,2024/3/19,Dif

26、ferential manometer[m?’n?mit?](差壓計),used to measure the differences in pressure for two containers or two points in a container.,Structure：,Measurement principle：,,,Figure 2.10 Differential manometer,2,,,,,,,,,,,?A

27、,,A,pA,1,? >?A, ?B,,h,,,,,,,h1,,,,,,?B,,B,pB,h2,,,,,,,,,ρA= ρB= ρ1,For two same air, ρA= ρB= 0,2024/3/19,EXAMPLE 2.1,A pressure measurement apparatus without leakage and friction between piston and cylinder wall is sh

28、own in Fig. 2.11. The piston diameter is d=35mm, the relative density of oil is RDoil=0.92, the relative density of mercury is RDHg=13.6, and the height is h=700 mm. If the piston has a weight of 15N, calculate the value

29、 of height difference of liquid Δh in the differential manometer.,,,1,1,,pa,?h,,,,,,,RDoil=0.92,RDHg=13.6,,,,,,,d,,,h,,,,,,,,,,,,,Figure 2.11 Pressure measurement apparatus,piston,,pa,2024/3/19,The pressure on the pist

30、on under the weight,From the isobaric surface 1-1 the equilibrium equation is,solving for ?h,Solution:,Chapter 3. FLUID FLOW CONCEPTS & BASIC EQUATIONS第三章 流體流動概念和基本方程組,2024/3/19,The space pervaded (彌漫,充滿) the flowi

31、ng fluid is called flow field (流場).,velocity u, acceleration a, density ?, pressure p, temperature T, viscosity force Fv , and so on.,Motion parameters:,2024/3/19,Steady flow and unsteady flow,For steady flow (

32、定常流), motion parameters independent of time. u=u(x, y, z)p=p(x, y, z) Steady flow may be expressed as,The motion parameters are dependent on time, the flow is unsteady flow (非定常流).,u=u(x, y, z, t),p=p(x, y, z, t),20

33、24/3/19,A path line (跡線, 軌跡線) is the trajectory of an individual fluid particle in flow field during a period of time. Streamline (流線) is a continuous line (many different fluid particles) drawn within flu

34、id flied at a certain instant, the direction of the velocity vector at each point is coincided with（與…一致） the direction of tangent at that point in the line.,Path line and streamline,path line,Streamline,2024/3/19,Cross

35、section, flow rate and average velocity,1. Flow section (通流面) The flow section is a section that every area element in the section is normal to mini-stream tube or streamline. The flow section is a curved surface（曲面）

36、. If the flow section is a plane area, it is called a cross section (橫截面).,2024/3/19,The amount of fluid passing through a cross section in unit interval is called flow rate or discharge.,weight flow rate,volumetric flow

37、 rate,mass flow rate,(3.7),For a total flow,2. Flow rate (流量),2024/3/19,3. Average velocity (平均速度),Figure 3.6 Distribution of velocity over cross section,The velocity u takes the maximum umax on the pipe axle and the zer

38、o on the boundary as shown in Fig. 3.6.,The average velocity V according to the equivalency of flow rate is called the section average velocity (截面平均速度).,According to the equivalency of flow rate, VA=∫A udA=Q, therewith,

39、,2024/3/19,3.3.2 Control volume,Control volume (cv, 控制體) is defined as an invariably hollow volume or frame fixed in space or moving with constant velocity through which the fluid flows. The boundary of control

40、volume is called control surface (cs, 控制面).,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 energ

41、y on the cs.,2024/3/19,System vs Control Volume,2024/3/19,3.4.1 Steady flow continuity equation of 1D mini stream tube,The net mass inflow,dM=(?lu1dA1??2u2dA2) dt,For compressible steady flow dM=0,?lu1dA1=?2u2dA2,If inc

42、ompressible, ρl =ρ2=ρ,u1dA1= u2dA2,The formula is the continuity equation for incompressible fluid, steady flow along with mini-stream tube.,(3.23),2024/3/19,3.4.2 Total flow continuity equation for 1D steady flow,?lmV1A

43、1=?2mV2A2 (3.24),For incompressible fluid flow, ρ is a constant.,Q1=Q2 or V1A1=V2A2,Making integrals at both sides of Eq.(3.23),Integrating it,The total flow continuity equation for the incompressible

44、fluid in steady flow.,2024/3/19,3.5.2 Bernoulli’s equation,Eq.(3.8) is used for ideal fluid flows along a streamline in steady. Bernoulli’s equation can be obtained with an integral along a streamline :,(m2/s2)

45、 (3.29),This is an energy equation per unit mass.,It has the dimensions (L/T)2 because m?N/kg=(m?kg?m/s2)/kg=m2/s2.,The meanings,u2/2 ——the kinetic energy per unit mass (mu2/2)/m.,p/? ——the pressure energy per uni

46、t mass. gz ——the potential energy per unit mass.,Eq. (3.29) shows that the total mechanical energy per unit mass of fluid remains constant at any position along the flow path.,2024/3/19,The Bernoulli’s equation per unit

47、 volume is,(N/m2) (3.30),Because the dimension of ?u2/2 is the same as that of pressure, it is called dynamic pressure (動壓強).,The Bernoulli’s equation per unit weight is,(m?N/N, or, m) (3.31),For

48、arbitrary two points 1 and 2 along a streamline,,(3.32),2024/3/19,The mechanical energy per unit weight over the section in gradually varied flow is,Let hw be the energy losses per unit weight of fluid from 1-1 to 2-2,

49、the Bernoulli’s equation for a total flow is,Let hs be the shaft work per unit weight of fluid, the Bernoulli’s equation for a real system is,(3.45),(3.44),3.7.2 The Bernoulli’s equation for the real-fluid total flow,202

50、4/3/19,A centrifugal water pump (離心式水泵) with a suction pipe (吸水管) is shown in Fig. 3.20. Pump output is Q=0.03m3/s, the diameter of suction pipe d=150mm, vacuum pressure that the pump can reach is pv/(?g)=6.8 mH2O, and a

51、ll head losses in the suction pipe hw=1mH2O. Determine the utmost elevation (最大提升) he from the pump shaft to the water surface on the pond.,EXAMPLE 3.6,2024/3/19,Solution,1) two cross sections and the datum plane are sel

52、ected.,The sections should be on the gradually varied flow, the two cross sections here are: 1) the water surface 0-0 on the pond, 2) the section 1-1 on the inlet of pump. Meanwhile, the section 0-0 is taken as the datum

53、 plane, z0=0.,2024/3/19,2) the parameters in the equation are determined.,The pressure p0 and p1 are expressed in relative pressure (gauge pressure).,，and,So,V0=0.,Let ?=1,hw0-1=1 mH2O,，and,，and,2024/3/19,3) calculation

54、for the unknown parameter is carried out.,By substituting V0=0，p0=0，z0=0，p1=?pv，z1=he，α1=1 and V1=1.7 into the Bernoulli’s equation, i.e.,,The values of pv/(?g) and V1 are substituted into above formula and it gives,name

55、ly,,2024/3/19,In the actual flow the velocity over a plane cross section(橫截平面) is not uniform,or,If the un-uniform in velocity over the section is taken into account, Eq. (3.48) may be rewritten as,? is momentum correct

56、ion factor (動量修正系數(shù)). ? = 4/3 in laminar flow for a straight round tube. ? = 1.02~1.05 in turbulent flow and it could be taken as 1.,or,or,(3.49),(3.50),3.8 THE LINEAR-MOMENTUM EQUATION,Chapter 4. FLUI

57、D RESISTANCE 4. 流體阻力,2024/3/19,hw —head losses (水頭損失) comprises of friction losses and minor losses.,1. Friction loss (沿程損失, 摩擦水頭損失) hl In the flow through a straight tube with constant cross section, the energ

58、y loss increases linearly in the direction of flow and the loss is called friction loss.,2. Minor loss (次要損失) or Local loss (局部損失) hm When the shape of flow path changes, such as section enlargement and so on, it w

59、ill 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.,4.1 REYNOLDS NUMBER,2024/3/19,,,,Reynolds number Re is used to describe

60、 the characteristic of flow.,2024/3/19,The discharge（流量） passing through a fixed cross section is,4.2 LAMINAR BETWEEN PARALLEL PLATES,2024/3/19,It can be written as,Suppose the diameter of circular tube is d. Substitutin

61、g known conditions above to the discharge equation, the discharge of circular tube is,,Hagen-Poiseuille (哈根-泊肅葉) equation.,So the average velocity of laminar flow in the circular tube is,4.3 LAMINAR FLOW THROUGH CIRCULAR

62、 TUBE,2024/3/19,Fluid flows in a 3-mm-ID horizontal tube. Find the pressure drop per meter. μ=60 cP, RD=0.83, at Re=200.,,Example 4.2,Solution:,2024/3/19,In the Fig. 4.7, ?p is friction loss of laminar flow in the tube b

63、etween sections 1-1 and 2-2.,Let,the coefficient of friction loss (沿程摩擦系數(shù)，沿程損失系數(shù)),obtains,Darcy-Weisbch (達西-韋斯巴赫) Equation,4.3.3 Frictional loss for laminar flow in horizontal circular tube,It is used to calculate the f

64、rictional pressure drop for laminar flow or turbulent flow in horizontal circular tube. For the convenience of application, it can be written friction loss :,2024/3/19,,The losses just occur locally, which called as mino

65、r energy losses (局部能量損失) or minor pressure losses, denoted by ?pm. It usually is expressed as the following equation.,4.6.5 Minor resistance,? : the minor loss coefficient or local loss coefficient,V : the velocity ove

66、r the cross section, ? : the mass density,2024/3/19,It is that the friction loss is the only factor for energy losses in fluid flow. In the simple pipe problem, assuming that the fluid is incompressible, it involves six

67、 parameters, Q, L, D, hw, ?, ?. In general, the length of pipe, L, kinematic viscosity of fluid, ?, and absolute roughness of pipe, ?, may be determined already.,So, simple pipe problem can be classified into thr

68、ee types: (1) solution for pressure drop hw with Q, L, D; (2) solution for discharge Q with L, D, hw ; (3) solution for diameter D with Q, L, hw.,Table 4.5 Simple pipe problem,“Simple pipe problem”