Aerodynamics

Aerodynamics

1. Angular velocity

   • Fluid element
     • Is the average of the angular velocities of the lines at a 2D plane
       • However at a real fluid, the equation is in 3D (Figure 1)
       • At the beginning it would be a square, then it will be a diamond

2. Circulation

   • It exist in the flow, it simply means that the line integral in equation is finite
     • It does not necessarily mean that the fluid elements are moving around in circles

3. Vorticity

   • Rotational flow
     • ∇ X V ≠ 0
   • Irrotational flow
     • ∇ X V = 0
   • It is known as ξ=2ω
   • Fluid deformation because of the rate of change of the velocity

4. Velocity Potential

   • The velocity can be defined by the gradient of a scalar field
     • Cylindrical Coordinates
     • Spherical COordinates
     • 3D Flow

5. Pathlines

   • It is the movement line that will follow a particle
     • Each particle is different

6. Streamline

   • It is a curve whose tangent at any point is in the direction of the velocity vector at that point

7. Stream Function

   • It is a powerful tool
     • Streamline can be derivaded
       • dl x v = 0
     • ψ(x,y) = C ► Constant
   • For incompressible Flow
     • Coordinates rectangular
     • Coordinates polar
     • Z axis ξ = - ∇^2 * ψ
     • 0 = - ∇^2 * ψ

8. Laplace's equation

   • Incompressible Flow
     • (Dρ/ Dt) = 0
   • ∇^2 * ϕ = 0

9. Steady Flow

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