工程流体力学英文版第三章pdf_.pdf

1、Chapter 3Concepts and Basic Equation of Fluids in motion(one dimension,ideal fluids)?Contents1.Methods to Study Fluids in Motion2.Flow Classification3.Pathline(?)and Streamline(?)4.Streamtube(?)and Discharge(?)5.Continuity Equation for Steady Flow in a Conduit 6.Motion Differential Equation for Idea

2、l 1-D Flow&The Bernoulli Equation Along a StreamlineContents7.Differential Equation for Ideal Flow along Normal Line8.The Bernoulli Equation for 1-D pipe flow9.Application of The Bernoulli Equation10.The Linear-Momentum(?)Equation and Moment-of-Momentum (?)Equation for Ideal Flow?3.1 Methods to Stud

3、y Fluids in Motion1.Lagrangian Approach(?)2.Eulerian Approach(?)3.System and Control Volume4.Eulerian AccelerationAAB Bviewpoints:a individual fluid particleb certain point in spaceLagrangian Description of Motion is the description that every fluid partide in flow field is observed as a function of

4、 time.Space coordinates?=),(),(),(tcbazztcbayytcbaxx1.Lagrangian ApproachAAB BEuler Approach is the description that the motion factors of every space point in flow field are observed as a function of time.flow field description.Flow field motion factors are the continuous functions of time and spac

5、e?x,y,z?Eulerian Description is utilized widely in engineering.2.Eulerian Approach(x,y,z)-Eulerian Variables()()(),xyztpp xyztVV xyzt?=?=?=?3.System(?and Control Volume?Definition of a SystemA system refers to a specific mass of fluid within the boundaries defined by a closed surface.Shape may chang

6、emass no changeA control volume refers to a fixed region in space,which does not move or change shape.The surface surrounding the control volume is called control surface3.System(?and Control Volume?Shape no changemass may changeDefinition of a Control Volume1?1?2?2?.Eulerian cceleration(),V x y z t

7、?t :position:?x,y,z?tt+:position:velocity:(),xx yy zz+(),tV xx yy zz t+?velocity:y?x?z?0?t?(x,y,z)?()()()()000,lim1lim,limxtttu xx yy zz ttu x y z tatuuuuu x y z txyztu x y z ttxyztutuxuyuzttxtytzt+=?=+?=+?000lim,lim,limtttyxzuvwttt=y?x?z?0?t?(x,y,z)?so?ddxuuuuuauvwttxyz=+and?ddddddxyzuuuuuauvwttxyz

8、vvvvvauvwttxyzwwwwwauvwttxyz?=+?=+?=+?or:()VaVVt=+?ijkxyz=+?Similarly?Acceleration of particles is composed of two parts?1?Local Acceleration the change of velocity at every point with time.?2?Convective Acceleration the change of velocity with positionddpppppuvwttxyz=+dduvwttxyz=+For density and pr

9、essure:General form:ddVtt=+?.The Total Derivativeexample3.1 velocity is:2232Vx yiy jz k=+?(m/s),What is the acceleration of point(3,1,2).solution:2220(2)(3)027xuuuuauvwx yxyyxm stxyz=+=+=22200(3)(3)209yvvvvauvwx yyzm stxyz=+=+=22200(3)02464zwwwwauvwx yyzzm stxyz=+=+=So,the acceleration of point(3,1,

10、2):27964aijk=+?3.2 Classification of Fluid FlowClassification of Fluid FlowBased on the Characteristic of Fluid Based on the State of FlowBased on the Number of Space Variables1.Based on the Characteristics of FluidIdeal flow and Viscous flow 0or=Incompressible flow and compressible flow orconst=2.B

11、ased on the State of FlowSteady flow and unsteady flow 0ort=Rotational(?)flow and irrotational(?)flow Laminar flow(?)and turbulent flow(?)Subsonic flow(?)?Transonic flow(?)and supersonic flow(?)Uniform flow and non-uniform flow 0Vors=?3.Based on the Number of Space VariablesOne dimensional flow(?)Tw

12、o dimensional flow(?)Three dimensional flow(?)4.Steady flow and unsteady flowis the flow whose motion factors dont change with time.That is:Steady Flow(),VV xyz=?0Vt=?H=C?Unsteady flow is the flow that at least one of its motion factors changes with time.That isunsteady Flow(),VV xyzt=?0Vt?H?H?H?5 1

13、-D,2-D and 3-D FlowOne-dimensional Flow:(2)cross-sectional average valuesSfluid motion factors are function of a space coordinate.(1)Ideal flow.(3)motion factors are functions of curved coordinates s.(,)x t=(,)x t=(,)s t=(,)s t=Two-dimensional Flow:fluid motion factors are function of two space coor

14、dinates.(Not only limited to rectangular coordinates).Fluid flows motion factors are functions of three space coordinates.For example:Water flow in a natural river whose cross section shape and magnitude change along the direction of flow;water flows around the ship.Three-dimensional Flow:A pathline

15、 is the trace after a single particle travels in a field of flow over a period of time.(1).DefinitionKinescope1Kinescope2?3.3Pathline(?)and Streamline(?)1.Pathline(2)?Equation of Pathlineu?v?w are functions of both time t and space(x?y?z).Here t is an independent variabledydxdzuvwdt=A Streamline is

16、a curve that show the direction of a number of particles at the at the same instant of time.The curve indicates the velocity vectors of any points occupying on the streamline.Kinescope2.Streamline1.DefinitionaV?bV?cV?dV?eV?2?Equation of StreamlineSelect point A in streamline,ds is a differential arc length,u is the velocity at point Adsdxidyjdzk=+?dsuAVuivjwk=+?Directional cosine between velocity vector and coordinatescos(,)vV yV=?cos(,)uV xV=?cos(,)wV zV=?Directional cosine between dsand coordi