FLUID DYNAMICS

FLUID DYNAMICS

1. STREAMLINES

   • Curved tangent at any point
     • In direction of velocity
       • • Most common to visualize fluid flow
   • On unsteady flow
     • Streamline pattern different at different times
       • Because velocity vectors are changing at all times
   • On steady flows
     • As velocity is fixed at all times
       • Streamline and pathlines are identical
   • Equation given by
     • 3D STEADY FLOW
     • 2D STEADY FLOW

2. PATHLINE

   • Path that fluid traces
   • UNSTEADY FLOW
   • STEADY FLOW
     • Same as streamline

3. ANGULAR VELOCITY

   • An infinitesimal fluid moving along streamline
     • • Displacement given by (takinkg small angles)
         • On X axis
         • On Y axis
         • Derivating and taking average of velocities
           • 2D
           • 3D (Derivatives of Velocity field)
   • The change of angle of a infinitesimal fluid
     • Average of angular veloicites on angles

4. VORTICITY

   • Se define como dos velocidad angular
   • in coordinates
     • • if its not 0
         • Rotational
           • Finite angular velocity
       • If = 0
         • Irrotational
           • No angular velocity
           • Pure translation regarding motion
           • Are described by velocity potential
   • On 2D
   • Most important uses

5. CIRCULATION

   • Movement in a circle
   • Ecuation given by
     • • Negative due to convention on aerodynamics
   • Referring to
     • • If Vorticity is = 0
         • Then the circulation is 0, too

6. Stream Function

   • Having 2D steady flow integrated is:
     • Where stream function is constant
   • Having different streamlines
     • C is equal to the mass flow
       • Final equation separating the components is
         • Compressible flow
           • Rectangular coordinates
           • Polar coodinates
         • Incompressible flow
           • Recrangular coordinates
           • Polar coordinates
     • Also used for vorticity in 2D
       • Irrotational incompressible
       • Rotational

7. Velocity Potential

   • Used for irrotational flows (potential flows)
   • 3D Flows
   • Replacing on irrotational flow equation
   • Obtained differeciating same direction as velocities

8. LaPlace's equation

   • No mass conservation
     • For incompressible and irrotational flow
       • Ecuation is given by
         • • Carteasian coordinates
           • Cylidrincal coordinates
           • Spherical coordinates
     • Stream function
     • Velocity potential
   • Represents a velocity potencial and stream function
   • Is a second order lineal- partial differential equation
   • Different flows are governed by same equation
     • But not to different boundary conditions
       • Infinity boundary conditions
         • Surface is impermeable
         • Inviscid fluid
         • Infinite distance from the body
       • Wall boundary conditions
         • Solid surface
           • Vector tangent to surface
         • On inviscind flow
           • Velocidty at surface is finit

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