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1、Chapter 1.FLUID PROPERTIESFLUID PROPERTIES 第一章 流体性质 2篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 In physics,a fluid is a substance that continually deforms under an applied shear stress,no matter how small it is.流体是一种一流体是一种一受到受到切力作用切力作用（不论多么小）不论多么小）就会就会连续变形连续变形的物体。的物体。Definition of a flui
2、d2023/5/2 3篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统(1)Density（密度）（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(倒数)of density.(kg/m3)(m3/kg)2023/5/2 4篮球比赛是根据运动队在规定的比赛时间里得分多少来
3、决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统(2)Specific Weight（重度）（重度）Its 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 density and acceleration of gravity g.2023/5/2 5篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统(3)Relat
4、ive density and specific gravity The relative density(相相对对密密度度)RD of a fluid is the ratio of its density to the density of a given reference material.The reference material is water at 4C i.e.,ref=water.=1000kg/m3dimensionless quantity无量纲 The specific gravity(比比重重)SG of a fluid is the ratio of its w
5、eight to the weight of an equal volume of water at standard conditions(标准状态).dimensionless quantity无量纲 2023/5/2 6篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统(4)Compressibility（压缩性）（压缩性）The volume of fluid changes under different pressure.As the temperature is constant,the magnitude of comp
6、ressibility is expressed by coefficient of volume compressibility(体体积积压压缩缩系系数数)p,a relative variation rate（相对变化率）of volume per unit pressure.(1.15)The bulk modulus of elasticity(体体积积弹弹性性模模量量)K is the reciprocal of coefficient of volume compressibility p.(1.16)（Pa）（Pa 1）2023/5/2 7篮球比赛是根据运动队在规定的比赛时间里得
7、分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 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 1.1Solution:2023/5/2 8篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统Predominant Cause:p Cohesion is the cause of
8、 viscosity of liquid.p 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 fluids internal resistance to flow and may be thought as a measure of fluid friction.The resista
9、nce of a fluid to shear depends upon its cohesion(内内 聚聚 力力)and its rate of transfer of molecular momentum(分子分子动量交量交换).2023/5/2 9篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统Newtons law of viscosityFigure 1.5 Deformation resulting from application of constant shear force In Fig.1.5,a substan
10、ce is filled to the space between two closely spaced parallel plates（平行板）.The lower plate is fixed,the upper plate with area A move with a constant velocity V,a force F is applied to the upper plate.2023/5/2 10篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 Experiment shows that F is directly
11、 proportional to A and to V and is inversely proportional（反比）to 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.2023/5/2 11篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系
12、统(1.19)The angular velocity may also be written as du/dz,so Newtons law of viscosity is The proportionality factor(比例因子）比例因子）is called the viscosity coefficient（黏性系数，黏度）（黏性系数，黏度）.Fluids may be classified as Newtonian or non-Newtonian.p Newtonian fluid:is constant.(gases and thin liquids稀液)p Non-Newt
13、onian fluid:is not constant.(thick稠的,long-chained hydrocarbons长链碳氢化合物)2023/5/2 12篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 Dynamic viscosity and Kinematic viscosity The dynamic viscosity（动力黏度）is also called absolute viscosity（绝对黏度）.From（1.19）SI unit：kg/(ms)or Ns/m2 U.S.customary unit：dy
14、nes/cm2 （达因秒/厘米2）cgs unit：Poise(P,泊泊).1P=100cP(厘泊厘泊)1P=0.1Pa s(帕帕 秒秒)The kinematic viscosity（运动黏度）is the ratio of dynamic viscosity to density.SI unit：m2/s U.S.customary unit：ft2/s （英尺2/秒）cgs unit：stokes(St,斯斯).1cm2/s=1St 1mm2/s=1cSt(厘斯厘斯)2023/5/2Chapter 2.FLUID STATICS 第二章第二章 流体静力学流体静力学 14篮球比赛是根据运动
15、队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 Basic equation of hydrostatics under gravity Basic equation of hydrostatics under gravityGravity G(G=mg)is the only mass force acting on the liquid fx=0，fy=0，fz=gFigure 2.4 A vessel containing liquid at rest rewritingFrom(2.5)c is the constant of integra
16、tion(积分常数积分常数)determined by the boundary condition.integrating(2.7)2023/5/2 15篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统For the two points 1 and 2 in the static 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 consis
17、ts of two parts:the surface pressure,and the pressure caused by the weight of column of liquid.2023/5/2 16篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统Physical meaning z the position potential energy per unit weight of fluid to the base level；p/g the pressure potential energy (压强势能)per unit
18、 weight of fluid.Geometrical meaning z the position height or elevation head(位置水头)p/gthe pressure head(压力水头)per unit weight of fluid Sum of the position head(位置水头)and pressure head is called the hydrostatic head(静 水 头),also known as the piezometric head(测压管水头).The energy per unit weight of fluid can
19、 be also expressed in terms of the length of column of liquid(液柱液柱),and called the head(水头水头).2023/5/2 17篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 local atmospheric pressure(当地大气压当地大气压)pa absolute pressure(绝对压强绝对压强)pabs gauge pressure(表压表压,计示压强计示压强)=relative pressure vacuum pressure(真空压
20、强真空压强,真空度真空度)pv,or suction pressure(吸入压强吸入压强),also called negative pressure(负压强负压强)relative pressure(相对压强相对压强)p It is usually measured in the height of liquid column,such as millimeters of mercury(mmHg,毫米水银柱毫米水银柱),denoted by hv.Related PressuresRelated Pressures2023/5/2 18篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜
21、负的，因此，篮球比赛的计时计分系统是一种得分类型的系统Local atmospheric pressure p=paComplete vacuum pabs=0Absolute pressureVacuumpressureGaugepressure Figure 2.6 absolute pressure,gauge pressure and vacuum pressure p Absolute pressure2 ppa O Relationship GraphRelationship Graph2023/5/2 19篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛
22、的计时计分系统是一种得分类型的系统 To avoid any confusion,the convention is adopted throughout this text that a pressure is in gauge pressure unless specifically marked abs,with the exception of a gas,which is absolute pressure unit.Attention:2023/5/2 20篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 Differen
23、tial manometerm Differential manometerm nmit(nmit(差压计差压计差压计差压计)used to measure the differences in pressure for two containers or two points in a container.Structure：Measurement principle：Figure 2.10 Differential manometer2A ApA1 A,B hh1B BpBh2A=B=1For two same air,A=B=02023/5/2 21篮球比赛是根据运动队在规定的比赛时间里
24、得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统EXAMPLE 2.1EXAMPLE 2.1 A pressure measurement apparatus without leakage and friction between piston and cylinder wall is shown in Fig.2.11.The piston diameter is d=35mm,the relative density of oil is R Doil=0.92,the relative density of mercury is RDH g=13.6,and the
25、 height is h=700 mm.If the piston has a weight of 15N,calculate the value of height difference of liquid h in the differential manometer.11pahRDoil=0.92RDHg=13.6dhFigure 2.11 Pressure measurement apparatuspistonpa2023/5/2 22篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 The pressure on the p
26、iston under the weight From the isobaric surface 1-1 the equilibrium equation issolving for h Solution:Solution:2023/5/2Chapter 3.FLUID FLOW CONCEPTS&BASIC EQUATIONS第三章第三章 流体流动概念和基本方程组流体流动概念和基本方程组 24篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 The space pervaded(弥漫,充满)the flowing fluid is
27、called flow field(流场).l velocity u,l acceleration a,l density,l pressure p,l temperature T,l viscosity force Fv,and so on.Motion parameters:2023/5/2 25篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 Steady flow and unsteady flow For steady flow(定常流),motion parameters independent of time.u=u(x
28、,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)2023/5/2 26篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 A path line(迹线,轨迹线)is the trajectory of an individual fluid particle in flow field duri
29、ng a period of time.Streamline(流流线线)is a continuous line(many different fluid particles)drawn within fluid flied at a certain instant,the direction of the velocity vector at each point is coincided with（与（与一致）一致）the direction of tangent at that point in the line.Path line and streamline Path line an
30、d streamlinepath lineStreamline2023/5/2 27篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 Cross section,flow rate and average velocity1.Flow section(通流面通流面)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 cu
31、rved surface（曲曲面面）.If the flow section is a plane area,it is called a cross section(横截面).1 1 2 2 IIIu1u2dA1dA2Figure 3.5 Flow section2023/5/2 28篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 The amount of fluid passing through a cross section in unit interval is called flow rate or discharge
32、.weight flow ratevolumetric flow ratemass flow rate (3.7)For a total flow 2.Flow rate(流量流量)2023/5/2 29篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 3.Average velocity(平均速度平均速度)umaxVFigure 3.6 Distribution of velocity over cross section The velocity u takes the maximum umax on the pipe axle
33、and the zero 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(截面平均速度截面平均速度).According to the equivalency of flow rate,VA=A udA=Q,therewith,2023/5/2 30篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 3.3.
34、2 Control volume 3.3.2 Control volume Control volume(cv,控控制制体体)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 volume is called control surface(cs,控制面控制面).For a cv:1)its shape,volume and its cs c
35、an 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.2023/5/2 31篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统System vs Control Volume2023/5/2 32篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 3.4.1
36、Steady flow continuity equation of 1D mini stream tube 3.4.1 Steady flow continuity equation of 1D mini stream tubedA1u1dA2u2A1A2Figure 3.8 One-dimensional stream tubeThe net mass inflow dM=(lu1dA12u2dA2)dtFor compressible steady flow dM=0 lu1dA1=2u2dA2If incompressible,l=2=u1dA1=u2dA2The formula is
37、 the continuity equation for incompressible fluid,steady flow along with mini-stream tube.(3.23)2023/5/2 33篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 3.4.2 Total flow continuity equation for 1D steady flow 3.4.2 Total flow continuity equation for 1D steady flowlmV1A1=2mV2A2 (3.24)For inc
38、ompressible fluid flow,is a constant.Q1=Q2 or V1A1=V2A2dA1u1dA2u2A1A2Figure 3.8 One-dimensional stream tubeMaking integrals at both sides of Eq.(3.23)Integrating it average density average velocityThe total flow continuity equation for the incompressible fluid in steady flow.2023/5/2 34篮球比赛是根据运动队在规定
39、的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 3.5.2 Bernoullis equation 3.5.2 Bernoullis equation Eq.(3.8)is used for ideal fluid flows along a streamline in steady.Bernoullis equationBernoullis equation can be obtained with an integral along a streamline:(m2/s2)(3.29)This is an energy equation per unit
40、 mass.It has the dimensions(L/T)2 because mN/kg=(mkgm/s2)/kg=m2/s2.The meanings u2/2 the kinetic energy per unit mass(mu2/2)/m.p/the pressure energy per unit 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 posi
41、tion along the flow path.2023/5/2 35篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 The Bernoullis equation per unit volume is(N/m2)(3.30)Because the dimension of u2/2 is the same as that of pressure,it is called dynamic pressure(动压强).The Bernoullis equation per unit weight is(mN/N,or,m)(3.31
42、)For arbitrary two points 1 and 2 along a streamline,(3.32)2023/5/2 36篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统 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,the Bernoullis equation
43、 for a total flow is Let hs be the shaft work per unit weight of fluid,the Bernoullis equation for a real system is (3.45)(3.44)3.7.2 The Bernoullis equation for the real-fluid total flow 3.7.2 The Bernoullis equation for the real-fluid total flow 2023/5/2 37篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计
44、分系统是一种得分类型的系统011dhe0Figure 3.20 Pumping water A centrifugal water pump(离心式水泵)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 all head losses in the suction pipe hw=1mH2O.Determi
45、ne the utmost elevation(最大提升)he from the pump shaft to the water surface on the pond.EXAMPLE 3.62023/5/2 38篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统Solution 1)two cross sections and the datum plane are selected.The sections should be on the gradually varied flow,the two cross sections h
46、ere 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 plane,z0=0.2023/5/2 39篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统2)the parameters in the equation are determined.The pressure p0 and p1 are expressed in relat
47、ive pressure(gauge pressure).，and So,V0=0.Let=1 hw0-1=1 mH2O，and，and 2023/5/2 40篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统3)calculation for the unknown parameter is carried out.By substituting V0=0，p0=0，z0=0，p1=pv，z1=he，1=1 and V1=1.7 into the Bernoullis equation,i.e.,The values of pv/(g
48、)and V1 are substituted into above formula and it givesnamely,2023/5/2 41篮球比赛是根据运动队在规定的比赛时间里得分多少来决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统In the actual flow the velocity over a plane cross section(横截平面)is not uniform orIf the un-uniform in velocity over the section is taken into account,Eq.(3.48)may be rewritt
49、en as is momentum correction factor(动量修正系数).=4/3 in laminar flow for a straight round tube.=1.021.05 in turbulent flow and it could be taken as 1.oror(3.49)(3.50)3.8 THE LINEAR-MOMENTUM EQUATION 3.8 THE LINEAR-MOMENTUM EQUATION 2023/5/2Chapter 4.FLUID RESISTANCE 4.流体阻力流体阻力 43篮球比赛是根据运动队在规定的比赛时间里得分多少来
50、决定胜负的，因此，篮球比赛的计时计分系统是一种得分类型的系统hw head losses(水头损失水头损失)comprises of friction losses and minor losses.1.Friction loss(沿程损失沿程损失,摩擦水头损失摩擦水头损失)hl 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 los