Basic Fluid dynamic - Vicphysics基本的流體動(dòng)力vicphysics

1、.6Nagle CollegeU2 Physics Basic Fluid dynamicDraftThis is a note for some gifted students who want more challenge of the topic.1. Laminar (steady) flowAccelerating force (inertia force)Retarding force (viscous force)· A fluid is sheared when it flows past a surface. The opposition set up by the

2、 fluid to shear is called viscosity.· Viscosity is a kind of internal friction exhibited to some degree by all fluid. It arises in liquids because the forced movement of a molecule relative to its neighbours is opposed by the intermolecular forces between them.· Viscous forces act as soon

3、as fluid flow starts. If the external forces causing the flow are constant, the rate of flow becomes constant steady flow, retarding force (viscous force) = applied force (accelerating force, inertia force). The viscous force stops the flow when the applied force is removed.· Newtonian fluid; T

4、angential stress velocity gradient when temperature = const.2. Coefficient of viscosity · = (tangential stress / velocity gradient) = shear stress / velocity gradientAcceleration force = (F/A) / (v/h)Retarding force AV + vVh3. Bernoullis equationP1 + ½V12 + gh1 = P2 + ½V22 + gh2 = kP1

5、 + ½V12 + gh1 = k = total pressure created by the fluid in a system. P1 is the static pressure, a pressure component, which is normal (90o) to the velocity of the flowing fluid. ½V12 is the dynamic pressure, a pressure component, which created by the velocity of the flowing fluid. gh1 is t

6、he fluid pressure.P1 + ½V12 = k = total pressure created by the moving fluid(V1) in a system. when h1 = 0 m.P1 = static pressure (the only real pressure), ½V12 = dynamic pressure. Pressure (P1) falls when velocity V1 rises and vice versa.4. Under Steady Flow· Poiseuilles Formulae Q =

7、( pr4) / (8L)eg. weepP +pL2r· This formulae will not work when the flow becomes unsteady (turbulent) or with non Newtonian fluid (compressible and viscous), eg. blood flow in vessel.5. Turbulent Flow· A fluid motion in which velocity, pressure, and other flow quantities fluctuates irregula

8、rly in time and space, Eddies current existed. It is called turbulent or non laminar flow.6. Reynolds Number. ReRe = Inertia force / Viscous force Re = (vL)/ = density of a fluidv = velocity of the fluidL = Length of flow or diameter of the pipe = coefficient of viscosity of the fluid· It play

9、a central role in determine the state of fluid motion. When Re increase, the instability of a flow increase.· When Re < 2200 à Steady flow· When Re 2200 à velocity of fluid = Vc = critical velocity, turbulent flow begins.· When Re > 2200 à turbulent flow.7. Stokes

10、 Law. (steady/laminar flow)· F = 6vtr = Viscous retarding force (Drag)F (viscosity of a fluid)F vt (terminal velocity)F r (radius of the ball)· It only works under steady flowF = 6vtrU = (4/3) r3gW = mg = (4/3)r3g· (4/3)r3g = (4/3) r3g + FandF = 6vtrhencevt = 2r2g(-)/9· F v(linea

11、r relation)8. Drag(D) (turbulent flow)· Drag D = (CD AV2) / 2 or for a wing, it has two sides (2A) D = CD AV2Drag Drag V2 (non linear relation) Drag A (Choose different A, total surface area As, wing area Aw, or cross sectional area Ac will produce a different coefficient of drag. CD hence diff

12、erent drag. CD will depend on the size, the shape of the tested model, V, , , , compressibility of the fluid and . It will be found out by experiments with wind tunnel. = density of the fluidA = area of a tested objectV velocity of the fluid = angle of attack = viscosityCD = coefficient of drag.Stal

13、lD/N15oAngle of attackFor aircrafts Drag total = skin drag (viscosity and surface smoothness) + form drag (shape, streamline) + induce drag (pressure differences between top and bottom sides foil and angle of attack)CDi = coefficient of induce drag of a plane CDi = CL2 / (es2/A)where A = width of a

14、wing and s = the length of a wing and e is the constant between 0 and 1which depends on the shape of the wing (oval 1). CL = coefficient of lift9. Lift (L)· In a steady flow and angle of attack = 0· Bernoullis equation P + rgh1 + ½ r V1 2 = P + rgh2 + ½ r V2 2 = constant· L

15、= p Awhere p = ½ (V1 2 V2 2)= ½ V2A = span area of a wing· L V2LiftvelocityOr· Lift equation angle of attack 0L = CL (AV2) / 2L V2 L i. L A (area of the span wing)In takeoff and landing, velocity is relative low, Area of the wings will increase by sliding the flaps backwards and shifting the slats forwards.liftareaCL will depend on the shape of the plane, the size, the V, , , and compressibility of the air. It will be determine by experiment data in wind tunnel.ii. Angle of attack L for is small usually < 15oFor larger , the lift and relation is more complicate