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1、1.2 Fluid Flow Phenomena Newtons Law and ViscositylIdeal fluid Ideal fluid has zero viscosity. The flow of such an ideal fluid is called potential flow.(1) neither circulations nor eddies can form within the stream, so that potential flow is also called irrotational flow.Potential flow has two impor
2、tant characteristics: (2) friction cannot develop, so that there is no dissipation of mechanical energy into heat.lBoundary layer the effect of the solid boundary on the flow is confined to a layer of the fluid immediately adjacent to the solid wall. Shear and shear forces are confined to this part
3、of the fluid.Outside the boundary layer, potential flow survives.l lThe velocity field If the wall is at rest in the reference frame, the velocity of the fluid at the interface between the fluid and solid is zero, away from the solid the velocity must vary from point to point in the flowing stream.S
4、teady flowVelocity field is invariant with time, and the velocity at each location is constant. The flow is said to be steady.l lOne-dimensional flow Only one velocity component is required in the flowing stream. The situation is called one-dimensional flow.An example is steady flow through straight
5、 pipe.The following discussion is based on the assumptions of steady one-dimensional flow.l lLaminar flow Fluid flows without lateral mixing, and there are neither cross-currents and eddies. Velocity gradient and rate of shear Consider the steady one-dimensional laminar flow along a solid plane surf
6、ace.yuDistance from wall y0ydu/dy At y=0,u=0, and u increases with distance from the wall but at a decrease rate. Definite the velocity gradient at y, du/dy, byThe velocity gradient is clearly the reciprocal of the slope of the velocity profile of Fig.The local velocity gradient is also called the s
7、hear stress or time of rate of shear.1.2-1 The shear stressIn one-dimensional flow the shear force acts parallel to the plane of the shear.The force per unit area of the shear plane is called the shear stress and denoted by Newtonian fluidthe shear stress is proportional to the shear rate( velocity
8、gradient)1.2-3 the proportionality constant is called the viscosity1.2.1 Newtons Law and Viscosity of FluidsGases The viscosity of a gas increases with temperature, as predicted by kinetic theory, and is almost independent of pressure.liquids liquid viscosities usually increases with molecular weigh
9、t and decrease significantly when the temperature is raised. l Kinematic viscosity The ratio of the absolute viscosity to the density of a fluid, / is often useful.For liquid kinematic viscosities vary with temperature over a narrower range than absolute viscosities.For gases kinematic viscosities i
10、ncrease more rapidly with temperature than does the absolute viscosity.Newtonian fluidsThe curve is plots of shear stress vs. rate of shear. NewtonianFigure 2 Shear stress versus velocity gradient For Newtonian odu/dyThe simplest behavior is a straight line passing through the origin.Fluids followin
11、g this simple linearity are called Newtonian fluids.non-Newtonian fluidsplots of shear stressvs. rate of shear arenot a straight linepassing through theorigin. Binghom plasticodu/dyFigure 3 Shear stress versus velocity gradient for non-Newtonian fluids.The rheological behavior of liquids called non-
12、Newtonian. pseudo-plastic fluid and dilatantPseudo-plasticdu/dyFigure 4 Shear stress versus velocity gradient for non-Newtonian fluids.oThe curve for pseudo- plastic fluid passes through the origin, is concave downward at low shear.The curve for dilatant fluid passes through the origin, is concave u
13、pward at low shear.DilatantTurbulenceIt has long been known that a fluid can flow through a pipe or conduit in two different ways.vAt low flow rates the pressure drop in the fluid increase directly with the fluid velocity.vAt high rates it increases much more rapidly, roughly as the square of the ve
14、locity.1.2.3 Types of Fluid Flow and Reynolds NumberlIn this section we first discuss the two types of fluid flow that can occur: laminar flow and turbulent flow. lAlso, the Reynolds number used to characterize the regimes of flow is considered. Laminar and turbulent flow The distinction between the
15、 two types of flow was first demonstrated by O Reynolds in 1883.The flow is laminar flow when the fluid flows in parallel straight lines. Fluid flows without lateral mixing, and there are neither cross-currents and eddies. The fluid moves erratically in form of crosscurrents and eddies. This type of
16、 motion is turbulent flow. Reynolds Number lStudies have shown that the transition from laminar to turbulent flow in tubes is not only a function of velocity but also of density and viscosity of the fluid and the tube diameter. These variables are combined into the Reynolds number, which is dimensio
17、nless The type of flow depends on four quantities:v the diameter of tubev the viscosityvdensity and average velocity of fluid.Reynolds number defined by1.2-9 It is a dimensionless group of variables.The magnitude of the Reynolds number is independent of the units used, provided the units are consist
18、ent.Additional observation have shown that the transition from laminar to turbulent flow actually may occur over a wide range of Reynolds number. Re4000, flow is turbulenceThe fluids flow in a pipe or tubeBetween 2100 and 4000 a transition region is found where the flow may be either laminar or turb
19、ulent flow.3Nature of turbulence Turbulence can result either from contact of the flowing stream with solid boundaries or from contact between two layers of fluid moving at different velocities.Turbulent flow consists of a mass of eddies of various sizes coexisting in the flowing stream. Large eddie
20、s are continually formed in the turbulence. They break down into smaller eddies, which in turn evolve still smaller ones.Finally, the smallest eddies disappear. Any eddy possesses amount of mechanical energy, and pass energy of rotation along a continuous series of smaller eddies. This mechanical en
21、ergy is finally converted to heat when the smallest eddies are obliterated by viscous action. Deviating velocities in turbulence flow A typical picture of the variations in the instantaneous velocity at a given point in the turbulent flow field is shown in Figure.The components of the velocity vary
22、rapidly in magnitude and direction.Also, the instantaneous pressure at the same point fluctuates rapidly and simultaneously with the fluctuations of velocity.Velocity utimeDeviation velocity is the instantaneous fluctuation of the component around the mean.The deviating velocities are all about zero
23、 as an average.but, the time averages of fluctuating components of velocity and pressure vanish when averaged over a time period. Although at first sight turbulence seems to be structureless and randomized.Eddy viscosityBy analogy with Eq.(1.2-3), the relationship between shear stress and velocity g
24、radient in turbulent stream is used to define an eddy viscosity EvThe eddy viscosity Ev is not just properties ofthe fluid but depends on the fluid velocityand the geometry of the system.Although Ev is analogous to , there is a basic difference between the two kinds of quantities.A viscosity is true
25、 properties of the fluid and is the macroscopic result of averaging motions and momenta of myriad molecules.Flow in boundary layersA boundary layer is defined as that part of a moving fluid in which the fluid motion is influenced by the presence of a solid boundary.OLZx, thickness of boundary layer
26、at distance x; u, local velocity; abc, velocity-versus distance-from-wall curves at points c, c, c; OL, outer limit of boundary layerZxabZxaubZxaucccxx, distance from leading edge;u,velocity of undisturbed streamubLaminar and turbulent flow in boundary layers The velocities close to the solid surfac
27、e are small.Flow in this part of the boundary layer very near the surface therefore is essentially laminarActually it is laminar most of time, but occasionally eddies. They can have a large effect on the heat and mass transfer. A turbulent boundary layer is considered to consist of three zones:v the
28、 viscous sublayerv the buffer layerv the turbulent zoneOnset ofturbulenceBuffer layerViscous sublayerLaminar flow inboundary layerTurbulent flow inboundary layerBoundary-layer thicknessDistance from leading edge,xFigure Development of turbulent boundary layer on a flat plate.Development of turbulent
29、 boundary layer on aflat plate is shown in Figure.In some cases the boundary layer may be entirely laminar, but in most cases of engineering interest it is part laminar, part turbulent.Boundary-layer formation in straight tubes Consider a straight tube with fluid entering it at a uniform velocity. A
30、s shown in Fig.Boundary layerFigure Development of boundary-layer flow in pipe.A boundary layer begins to form at the entrance to the tube.As the stream moves farther down the tube, the boundary layer occupies an increasing portion of the crossing section.Finally, at a point well downstream from ent
31、rance, the boundary layer reaches the center of the tube.The length of the entrance region of the tubenecessary for the boundary layer to reach thecenter of the tube and for fully developed flowto be established is called the transition length . For laminar flowSuch flow with an unchanging velocityd
32、istribution is called fully developed flow.problemlIn a Newtonian fluid ，the relationship between the shear stress and shear rate is（ ）lKeeping the pressure constant，the viscosity of a gas will （ ）as the temperature rising, and the viscosity of a liquid will （ ）as the temperature risinglPotential fl
33、ow has two important characteristics: ( ),( )lthe effect of the solid boundary on the flow is confined to a layer of the fluid immediately adjacent to （ ） lAt low flow rates the pressure drop in the fluid is proportional to the ( ); at high rates it increases as the ( ). lMechanical energy is finally converted to ( ) when eddies in fluid are obliterated by viscous action, which may lead to a large ( ) loss in the fluid.
