Fluid Mechanics-1

1、1.流體性質(zhì) 本章教學(xué)內(nèi)容本章教學(xué)內(nèi)容 1.1 Definition of a fluid 1.2 Units and Conversion 1.3 Fluid Properties 1.4 Perfect Gas 點(diǎn)擊進(jìn)入點(diǎn)擊進(jìn)入 相應(yīng)章節(jié)相應(yīng)章節(jié) 返回本頁(yè)點(diǎn)擊此返回本頁(yè)點(diǎn)擊此 Home Work 返回主目錄點(diǎn)擊此返回主目錄點(diǎn)擊此 1.1 流體定義流體定義 Fluid classification: Liquid or Gas. The intermolecular attraction of fluid is very small and its molecular motion is v

2、ery intense, so the arrangement of its molecules is very loose. The common character of fluid: can not maintain certain shape and has the fluidity(流動(dòng)性). Solid: Withstanding the pressure, tension and shear force. Fluid: can only resist the pressure, and can not resist any small tension and shear forc

3、e. So fluid can not maintain its certain shape. No matter how small the shear force is applied to a fluid, the fluid will deform continuously. There is no static friction in fluid. Liquid: The distance between molecules of liquid is almost equal to the effective diameter of molecule. Liquid is often

4、 called incompressible fluid. Gas: The distance between the molecules is very large, for example, at normal temperature and pressure, the distance between the molecules of air is 3107 centimeter, the order of magnitude of its molecules effective diameter is 108 centimeter. Gas is often called compre

5、ssible fluid. Attention: When the compressibility is not referred, the equations in fluid mechanics are suitable to liquid as well as gas. When the compressibility is involved, the problem of gas and liquid must be dealt with individually. In this book, liquid is mainly discussed. Continuum Hypothes

6、is (連續(xù)性假設(shè)連續(xù)性假設(shè) ) Obviously there are gaps(間隙) between the fluid and all substances molecules. In fluid mechanics, the macrofluid(宏觀(guān)流體) is consisted of a large number of molecules, the physical quantities of macrofluid (such as pressure, velocity and density) is the statistical average of the action

7、and the behavior of most fluid molecules. In 1753, the continuous media was first proposed as macrofluid model by Euler. The real fluid is considered as no-gap continuous media, called the continuity fluid of fluid or the continuum(連續(xù)體，連續(xù)性) of fluid. 1.2 單位及換算單位及換算 International System of Units (SI,

8、 國(guó)際單位制國(guó)際單位制) newton (N) kilogram (kg) meter (m) second (s) The U.S. customary system of units, an Inch units pound (lb) force slug(斯勒格，質(zhì)量單位) mass foot (ft) length second (s) time 2 s m1 kg1N1 (1.1) (1.2) 2 1ft 1 lb1slug s Centimeter-gram-second system ( universal CGS unit 通用物理單位制，厘米通用物理單位制，厘米-克克-秒制秒

9、制) dyne(達(dá)因) force gram (g) mass centimeter (cm) length second (s) time (1.3) 2 s cm1 g1dyne1 Table 1.1 SI unit, U.S. customary system unit, and conversion Abbreviations of SI units are written in lowercase letters (小寫(xiě) 字母) for terms like hours (h), meters (m), and seconds (s). When a unit is named af

10、ter a person, the abbreviation is uppercase; examples are watt (W), pascal (Pa), and newton (N). Table 1.2 Selected prefixes for powers of 10 in SI units Multiple 因數(shù)因數(shù) SI prefix SI制前綴制前綴 Abbreviation 縮寫(xiě)詞縮寫(xiě)詞 Multiple 倍數(shù)倍數(shù) SI prefix SI制前綴制前綴 Abbreviation 縮寫(xiě)詞縮寫(xiě)詞 109giga (千兆千兆)G10 3milli (毫毫)m 106mega (

11、兆兆)M10 6micro (微微) 103kilo (千千)k10 9nano (納納,毫微毫微)n 10-2centi (厘厘)c10 12pico (皮可皮可,微微微微)p 1.3 流體性質(zhì)流體性質(zhì) Mass force acting on the center of mass in a substance is proportional to the mass. m=V (1) Mass forces The fluid is under the action of gravity g (g=9.806m/s2) (1.4) Figure 1.1 Free body in the fl

12、uid mgG The inertia force I is: (1.5) Figure 1.2 A container filled with liquid in a linear motion x maI The centrifugal acceleration (離心加速度) for point A of mass m is 2r and its centrifugal force is (1.6) Figure 1.3 A rotating container rmR 2 The above three kinds of forces are directly proportional

13、 to the mass of fluid m and act on the centre of mass. The total mass force and resultant acceleration are expressed by W and q respectively. 2 (g)() i Wmarmm XiYjZkq (1.7) 2 ()( ) xixx Wm garmmXq (1.8) 2 2 2 (g) (g) (g) x ix y iy z iz W Xar m W Yar m W Zar m (1.9) the components of force If the mas

14、s force is only gravity and inertia force, the components of force per unit mass are： x W Xa m 0 y W Y m z W Zg m (2) Surface Force Surface force is the force acting on the surface, and it is proportional to the area of surface. Surface force is the force acting on the outer and internal surface of

15、the fluid (external and internal force). In fluid, the surface forces are a pair of action and reaction. ApP (1.10) is average force per unit area, or pressure stress(壓應(yīng)力), usually called pressure. p AT (1.11) is mean friction per unit area, or mean shear stress. Figure 1.1 Free body in the fluid (1

16、) Density Density is the ratio of the mass of fluid to its volume. (1.12) specific volume (比容比容) volume occupied by unit mass (1.13) The specific volume is the reciprocal (倒數(shù)) of density. (kg/m3 ) (m3/kg ) V m m V1 (2) Specific Weight 重度重度 weight per unit volume (1.14) in which is the specific weigh

17、t of fluid, N/m3; G is the weight of fluid, N. g(1.14a) Or the product of density and acceleration of gravity g. V G (3) Relative density and specific gravity The relative density (相對(duì)密度) RD of a fluid is the ratio of its density to the density of a given reference material. ref RD The reference mate

18、rial is water at 4C i.e., ref=water. dimensionless quantity無(wú)量綱 (3) Relative density and specific gravity 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)). waterwater G G SG dimensionless quantity無(wú)量綱 (1) Compress

19、ibility（壓縮性）（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 compressibility (體積壓縮系數(shù)) p , a relative variation rate of volume per unit pressure. p VV p d /d (1.15) The bulk modulus of el

20、asticity (體積彈性模量) K is the reciprocal of coefficient of volume compressibility p. VV p K p /d d1 (1.16) Pa Pa 1 Table1.3 The bulk modulus of elasticity of commonly used materials at 20 Example 1.1 A 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

21、bulk modulus of elasticity? )Pa(105 . 1 1000/ )1000998( 101 . 0101 . 3 / 9 66 VV p K Example 1.2 A pressure gauge tester is shown in Fig.1.4. The cylinder is filled with oil, p =4751012Pa1. As the handwheel rotates, the well sealed piston is screwed in and the oil is compressed then the two pressure

22、 gauges reach a desired pressure. The diameter of piston is D=10 mm, the screw pitch (螺距) t=2mm. At the atmospheric pressure the volume of oil in the cylinder including pipeline is V=200cm3. For the reading of 20.0MPa in the pressure gauge, how many revolutions do the handwheel must screw in? Figure

23、 1.4 A pressure gauge tester 1. handwheel; 2. screw; 3. piston; 4. cylinder; 5. oil; 6. pipeline; 7. standard gauge; 8. gauge to be tested The variation of cylinder volume as the handwheel screws in n revolutions is tnDVVV 2 11 4 d When dV1=dV, the desired pressure dp is reached, so pVtnD p d 4 2 Th

24、e desired revolution of screwing in is )rev( 1 .12 102)1010( 102010200104754 4 323 6612 2 tD Vdp n p Solution: From Eq. (1.15), the decrease of volume of oil is pVV p dd (2) Thermal Expansibility(熱膨脹性熱膨脹性) The coefficient of cubical expansion (體積熱膨脹系數(shù)) t is the relative variation rate of volume per

25、unit temperature change. t VV t d /d (1.17) C 1 (1) Cause of viscosity Viscosity is a property of fluid by virtue of which it offers resistance to shear force. The viscosity of a gas increases with temperature, the viscosity of a liquid decreases with temperature. The resistance of a fluid to shear

26、force depends on its cohesion(內(nèi)聚力) and its rate of transfer of molecular momentum(分子動(dòng)量交換). Predominant cause: Cohesion is the predominant cause of viscosity of liquid. Transfer of molecular momentum is predominant cause the of viscosity of gas. When fluid is at rest, there is no layer moves relative

27、 to adjacent fluid layer, so no shear forces can be generated. The study of static fluid is greatly simplified because any free body of fluid has only gravity forces and normal surface forces acting on it. (2) Newtons law of viscosity and Newtonian fluid Figure 1.5 Deformation resulting from applica

28、tion of constant shear force In Fig.1.5, a substance is filled to the space between two closely spaced parallel plates. The lower plate is fixed, the upper plate moves with a constant velocity V, a force F is applied to the upper plate. Experiment shows that F is directly proportional to A and to V

29、and is inversely proportional to thickness h. h AV F (1.18) If the shear stress is =F/A, it can be expressed as h V (1.19) The angular velocity may also be written as du/dz, so Newtons law of viscosity is The proportionality factor is called the viscosity coefficient. Fluids may be classified as New

30、tonian or non-Newtonian. Newtonian fluid: is constant. (gases and thin liquids) Non-Newtonian fluid: is not constant. (thick, long-chained hydrocarbons) A thixotropic (觸變作用) substance: such as printers ink, has a viscosity and deformation when at rest. dz du (3) Dynamic viscosity and Kinematic visco

31、sity The dynamic viscosity is also called absolute viscosity. kg/ms or Ns/m2 CGS unit Poise (P, 泊)： 1P=100cP(厘泊厘泊) 1P=0.1Pa s(帕帕 秒秒) du/dz (3) Dynamic viscosity and Kinematic viscosity The kinematic viscosity is the ratio of dynamic viscosity to density. (1.20) SI unit of is m2/s, the U.S. customary

32、 unit ft2/s, and CGS unit Stokes (St, 斯) or centistokes (cSt, 厘斯). 1cm2/s=1St 1mm2/s=1cSt Liquid usually contains some dissolved air. The amout of air dissolved in liquid is proportional to the absolute pressure. While pressure is below atmospheric pressure, the air dissolved in liquid at atmospheri

33、c pressure be in a state of over-saturation (過(guò) 飽和), and the air will separate from the liquid and become bubble, this pressure is called air apart pressure (空氣分離壓) . The solubility of a gas depends on temperature, the partial pressures of the gases over the liquid, and the properties of the liquid a

34、nd gas. The concentration of dissolved gas depends on the partial pressure of gas. The partial pressure of gas determines the number of gas molecule colliding with the surface solution. Liquids evaporate because of molecules escaping from the liquid surface. The vapor molecules exert a partial press

35、ure in the space, known as vapor pressure(汽化壓). The vapor pressure of liquid depends on temperature and increases with temperature. When the pressure on the surface of a liquid equals the vapor pressure of the liquid, boiling occurs. Boiling of water, for example, may occur at room temperature if th

36、e pressure is reduced . At 20C, water has a vapor pressure of 2.447 kPa. In many situations involving the flow of liquids, a very low pressure may occur. When the pressure is below the air apart pressure or even the vapor pressure, the air will separate out or even the liquid flashes into vapor. Thi

37、s is called cavitation. A rapidly expanding cavity enters area where the pressure is greater than vapor pressure, the cavity in liquid collapses. The vapor pressure is much lower than the air apart pressure, so in hydraulic technique whether the absolute pressure is lower than the air apart pressure

38、 is being used as a criterion for cavitation. Real fluid is viscous. So while fluid moves, the inner friction is produced. Taking into account the fluid inner friction, it is extremely complex in researching fluid motion. In convenient for the analysis, the fluid is considered as nonviscous, and cal

39、led ideal fluid. So viscosity and shear stress are always zero no matter how the fluid moves. 1.4 完全氣體完全氣體 From physics theorems, the physical quantities relationship between the pressure, temperature and the volume of gas obey the state equation of perfect gas. RTp(1.21) in which: p is absolute pressure, N/m2; the specific volume, m3/kg; T the absolute temperatu