1、 22022-3-25 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 fluidDefinition of a fluid 32022-3-25(1) Density （密度）（密度）Density is the ratio of the mass of flu
2、id 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 )Vm mV1 42022-3-25(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 wei
3、ght of fluid, N. g(1.14a) Or the product of density and acceleration of gravity g. VG 52022-3-25(3) Relative density and specific gravity The relative density (相对密度相对密度) RD of a fluid is the ratio of its density to the density of a given reference material. refRD The reference material is water at 4
4、C i.e., ref=water.=1000kg/m3dimensionless quantity无量纲 The specific gravity (比重比重) SG of a fluid is the ratio of its weight to the weight of an equal volume of water at standard conditions(标准状态). waterwaterGGSGdimensionless quantity无量纲 62022-3-25(4) Compressibility（压缩性）（压缩性） The volume of fluid chang
5、es under different pressure. As the temperature is constant, the magnitude of compressibility is expressed by coefficient of volume compressibility (体积压缩系数体积压缩系数) p , a relative variation rate（相对变化率） of volume per unit pressure. pVVpd/d(1.15) The bulk modulus of elasticity (体积弹性模量体积弹性模量) K is the re
6、ciprocal of coefficient of volume compressibility p. VVpKp/dd1(1.16) （Pa）（Pa 1） 72022-3-25 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? 669/3.1 100.1 10(998 1000)/10001.5 10 (Pa)pKV V Example 1.1Solution:So
7、lution: 82022-3-25Predominant Cause: p Cohesion is the cause of 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
8、flow and may be thought as a measure of fluid friction. The resistance of a fluid to shear depends upon its cohesion(内聚力内聚力) and its rate of transfer of molecular momentum(分子动量交换分子动量交换). 92022-3-25Newtons law of viscosityFigure 1.5 Deformation resulting from application of constant shear force In Fi
9、g.1.5, a substance 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. 102022-3-25 Experiment shows that F is directly proportional to A and to V and is
10、 inversely proportional （反比）to thickness h.hAVF (1.18) If the shear stress is =F/A, it can be expressed as hV The ratio V/h is the angular velocity of line ab, or it is the rate of angular deformation of the fluid. 112022-3-25(1.19) The angular velocity may also be written as du/dz, so Newtons law o
11、f 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-Newtonian fluid: is not constant. (thick稠的, long- chained hydrocarbons长
12、链碳氢化合物) dudz 122022-3-25 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：dynes/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) du / dz The kinematic viscosi
13、ty （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) 第二章第二章 流体静力学流体静力学 142022-3-25Gravity G (G=mg) is the only mass force acting on the liquid fx=0，fy=0，fz= gFigure 2.4 A vessel containing liquid
14、 at rest 0gdpdzrewritinggdzdpFrom (2.5)c is the constant of integration (积分常数积分常数) determined by the boundary condition. cgpzintegrating(2.7) 152022-3-25gpzgpz2211)(2112zzgppFor the two points 1 and 2 in the static fluid For the two points 0 and 1 )(1001zzgppFigure 2.4 A vessel containing liquid at
15、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 liquid. 162022-3-25Physical 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
16、unit 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
17、of fluid can be also expressed in terms of the length of column of liquid (液柱液柱), and called the head (水头水头). 172022-3-25 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 ghppaabs gauge pressure (表压表压, 计示压强计示压强) = relative pressure vacuum pressure (真空压强真空压强, 真空度真空度) pv ,
18、or suction pressure (吸入压强吸入压强) , also called negative pressure (负压强负压强) absavppprelative pressure (相对压强相对压强) p absapppgh 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.gppgphaabsvv 182022-3-25Local atmospheric pressure p=paComp
19、lete vacuum pabs=0Absolute pressureVacuumpressureGaugepressure Figure 2.6 absolute pressure, gauge pressure and vacuum pressure p Absolute pressure2 ppa O 192022-3-25 To avoid any confusion, the convention is adopted throughout this text that a pressure is in gauge pressure unless specifically marke
20、d abs, with the exception of a gas, which is absolute pressure unit. Attention: 202022-3-25 used to measure the differences in pressure for two containers or two points in a container. )()(1211hhgghppBA Structure：Measurement principle： Figure 2.10 Differential manometer2A ApA1 A, B hh1B BpBh2)(12hhg
21、ghghppABBAghppBAA= B= 1For two same air, A= B= 0 212022-3-25 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 RDoil=0.92, the relative density of mercury is RDHg=13.6, a
22、nd the 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 apparatuspistonpa 222022-3-25 The pressure on the piston under the weight Pa)(15590035. 04154152
23、2dp From the isobaric surface 1-1 the equilibrium equation ishgghpHgoilsolving for h )m(164. 070. 06 .1392. 0806. 91360015590HgoilHghgph 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 242022-3-25 The space pervaded (弥漫,充满) the flowing fluid is called flow field (流场).l velocity u, l acceleration a, l density , l pr
24、essure p, l temperature T, l viscosity force Fv , and so on. Motion parameters: 252022-3-25 Steady flow and unsteady flow For steady flow (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 un
25、steady flow (非定常流). 0t0tu0tp0tT u=u(x, y, z, t) p=p(x, y, z, t) 262022-3-25 A path line (迹线, 轨迹线) is the trajectory of an individual fluid particle in flow field during a period of time. Streamline (流线流线) is a continuous line (many different fluid particles) drawn within fluid flied at a certain ins
26、tant, 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 lineStreamline 272022-3-25 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
27、section is normal to mini-stream tube or streamline. The flow section is a curved surface（曲面）（曲面）. 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 section 282022-3-25 The amount of fluid passing through a cross section in unit interval is
28、called flow rate or discharge. ) s /m()kg/s()N/s(3GMQQMgQGweight flow ratevolumetric flow ratemass flow rateAudAQ (3.7)For a total flow 2. Flow rate (流量流量) 292022-3-25 3. Average velocity (平均速度平均速度)umaxVFigure 3.6 Distribution of velocity over cross sectionAudAQVAA The velocity u takes the maximum u
29、max on the pipe axle 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, 302022-3-25 Control volume (cv, 控制体控制体) is
30、 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 can not change with time. 2) it is stationary in the coordin
31、ate system. (in this book)3) there may be the exchange of mass and energy on the cs. 312022-3-25NameDefinitionCharactersMethodSystem a collection of fluid matter of fixed identity (i.e. always the same fluid particle) that will move, flow, and interact with its surroundings. (closed)l its shape, vol
32、ume and boundary can change with time; l it can move; l has the exchanges of energy, but no mass. LagrangianControl Volume(cv) a geometrically defined volume in space through which fluid particles may flow in or out of the control volume. Hence it will contain different fluid particles at different
33、points in time. (opened)l its shape, volume and boundary can not change;l it is fixed; l has the exchanges of mass and energy.EulerianSystem vs Control Volume 322022-3-25dA1u1dA2u2A1A2Figure 3.8 One-dimensional stream tubeThe net mass inflow dM=(lu1dA12u2dA2) dtFor compressible steady flow dM=0 lu1d
34、A1=2u2dA2If incompressible, l =2= u1dA1= u2dA2The formula is the continuity equation for incompressible fluid, steady flow along with mini-stream tube.(3.23) 332022-3-2521222111AAdAudAulmV1A1=2mV2A2 (3.24)For incompressible fluid flow, is a constant. Q1=Q2 or V1A1=V2A2dA1u1dA2u2A1A2Figure 3.8 One-di
35、mensional 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. 342022-3-25 Eq.(3.8) is used for ideal fluid flows along a streamline in steady. can be obtained with an inte
36、gral along a streamline :Cgzpu22(m2/s2) (3.29) This is an energy equation per unit 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
37、) shows that the total mechanical energy per unit mass of fluid remains constant at any position along the flow path. 352022-3-25 The Bernoullis equation per unit volume is (N/m2) (3.30) 122Cgzpu Because the dimension of u2/2 is the same as that of pressure, it is called dynamic pressure (动压强). The
38、Bernoullis equation per unit weight is 222Czgpgu(mN/N, or, m) (3.31) For arbitrary two points 1 and 2 along a streamline, 2211221222upupzzgggg(3.32) 362022-3-25 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 fro
39、m 1-1 to 2-2, the Bernoullis equation for a total flow is Let hs be the shaft work per unit weight of fluid, the Bernoullis equation for a real system iswshzgpVhzgpV22221121g2g2 (3.45)zgpegV22whzgpVzgpV22221121g2g2(3.44) 2u 372022-3-25011dhe0Figure 3.20 Pumping water A centrifugal water pump (离心式水泵)
40、 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. Determine the utmost elevation (最大提升) he from the pump shaft to the water s
41、urface on the pond.EXAMPLE 3.6 382022-3-25SolutionSolution 1) two cross sections and the datum plane are selected. 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 secti
42、on 0-0 is taken as the datum plane, z0=0.10w1121100200g2g2hzgpVzgpV 392022-3-252) the parameters in the equation are determined. The pressure p0 and p1 are expressed in relative pressure (gauge pressure).0g0pO)mH(8 . 6gg2v1pp，and So,V0=0. 120.031.7(m/s)0.15 / 4QVALet =1 hw0-1=1 mH2O 0g0p，and ，and 40
43、2022-3-253) 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., 10wv212000hhgpgVe10w21vg2hVgphe The values of pv/(g) and V1 are substituted into above formula and it gives6.80.15 1.05.65(m)eh namely, 4120
44、22-3-25In the actual flow the velocity over a plane cross section(横截平面) is not uniform dAVuAA2)(1AVdAuA22orIf the un-uniform in velocity over the section is taken into account, Eq. (3.48) may be rewritten as)(1122VVFQ is momentum correction factor (动量修正系数). = 4/3 in laminar flow for a straight round
45、 tube. = 1.021.05 in turbulent flow and it could be taken as 1. AVdAuA22ordAVuAA2)(1AVdAuA22or (3.49) (3.50) 4. 流体阻力流体阻力 432022-3-25mlhhhwhw 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 cons
46、tant cross section, the energy loss increases linearly in the direction of flow and the loss is called friction loss. 2. Minor loss (次要损失次要损失) or Local loss (局部损失局部损失) hm 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
47、velocity for the flow. The change results in energy loss, which is called minor loss or local loss. 442022-3-25Reynolds number Re is used to describe the characteristic of flow.VDVDRe 452022-3-25 The discharge（流量） passing through a fixed cross section is3001Rectanglar section ():()212baAUapQudAdzudy
48、bal矩形截面23001Annular section ():2()212aAUapQudArdudyral环形截面312dapQl 462022-3-2524231283232RelQV llpddd It can be written as Suppose the diameter of circular tube is d. Substituting known conditions above to the discharge equation, the discharge of circular tube is lpdQ1284Hagen-Poiseuille (哈根哈根-泊肃叶泊肃
49、叶) equation. So the average velocity of laminar flow in the circular tube is232pdVl 472022-3-25 Fluid flows in a 3-mm-ID horizontal tube. Find the pressure drop per meter. =60 cP, RD=0.83, at Re=200. Example 4.2Solution: 482022-3-25In the Fig. 4.7, p is friction loss of laminar flow in the tube betw
50、een sections 1-1 and 2-2. 2223264642Re2lllpVVVVdddd Re64Let the coefficient of friction loss (沿程摩擦系数，沿程损失系数) 22VdlpobtainsDarcy-Weisbch (达西-韦斯巴赫) Equation 4.3.3 Frictional loss for laminar flow in horizontal circular tube It is used to calculate the frictional pressure drop for laminar flow or turbu
