Aerodynamics And Fluids 2005
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  • 1. Fluids and Aerodynamics
    • F1
      • Buoyant Forces
    • F2
      • Non-Viscous Fluid Flow
    • F3
      • Viscous Fluids
    • F4
      • Explaining Lift using Newton and Bernoulli
  • 2. Flying
  • 3. F1 Buoyant Forces
    • An upthrust is provided by the fluid displaced by a submerged or floating object.
    • Archimedes’ Principle
      • The upthrust on a body partially or fully submerged in a fluid is equal to the weight of the fluid displaced by the body.
    • The Principle of Flotation
      • A body floating in a liquid always displaces its own weight of the liquid.
    • The upthrust on a floating object acts at the centre of mass of the displaced fluid ( centre of buoyancy )
    • The stability of a floating object is determined by the relative positions of metacentre and the centre of mass of the floating object.
  • 4. F2 Non-Viscous Fluid Flow
    • Motion Of An Ideal Fluid
      • Steady ( laminar , streamline ) flow
    • Streamlines can be used to define a tube of flow.
    • The equation of continuity is Av = constant for the flow of an ideal, incompressible fluid.
    • Appreciate that the equation of continuity is a form of the principle of conservation of mass.
    • The Bernoulli Effect
      • Pressure differences can arise from different rates of flow in a fluid.
  • 5. F2 Non-Viscous Fluid Flow
    • Derive and use Bernoulli equation
      • p 1 + 1/2(  v 1 2 ) = p 2 + 1/2 (  v 2 2 ) = constant where p is the pressure
      •  is the fluid density and
      • v is the velocity of the fluid
    • Appreciate that Bernoulli Equation is a form of conservation of energy
    • Apply Bernoulli effect in
      • Spinning balls in sport
      • atomisers
      • flow of air over an aerofoil
  • 6. F3 Viscous Fluids
    • Viscous forces in a fluid cause retarding force to be exerted on an object moving through a fluid.
    • In viscous flow, different layers of the liquid move with different velocities.
    • Stokes’ Law states that F = Ar  v where A is a dimensionless constant, for the drag force under laminar conditions in a viscous fluid.
    • Use Stokes’ law to explain quantitatively how a body falling through a viscous fluid under laminar conditions attains a terminal velocity.
  • 7. F3 Viscous Fluids
    • At sufficiently high velocity, the flow of viscous fluid undergoes a transition from laminar to turbulent conditions. Under normal conditions, the drag force resisting motion is proportional to the velocity but under turbulent conditions, the drag force resisting motion is proportional to the square of the velocity.
    • The onset of turbulence is determined by the Reynolds’ number R e =  vr / 
      • For fluid flow in a tube or channel
      • For the motion of an object relative to a fluid.
      • Note :
      • if Re < 2000 , the fluid flowing in the tube or channel is steady. If Re > 2000 , the fluid flow in the tube or channel is turbulent
  • 8. F4: The lift on an aerofoil
    • There are two ways to think about the lift on an aerofoil:
    • 1. Using Newton’s Laws
    • 2. Using Bernoulli’s Equation
  • 9. F4: Explaining lift using Newton
  • 10. F4: Explaining lift using Newton
    • The aerofoil acts to redirect the direction of air passing over it.
  • 11. F4: Explaining lift using Newton
    • This results in a net force upwards (of the aerofoil on the air above) which is called lift
  • 12. F4: Explaining lift using Bernoulli
    • The explanation using Bernoulli’s principal involves the fact that the air moves faster over the top of the aerofoil compared to air moving underneath it.
    • This is based on the equal transit time assumption
  • 13. F4: Explaining lift using Bernoulli
    • This difference in velocity means that there is a difference in pressure above and beneath the wing.
    • This results in Lift.
  • 14. End Note
    • The belief that rear spoilers significantly increase car performance by aiding it’s aerodynamicy is dubious at best