Chapter 9 : Laminar Boundary Layers
Lecture 28 :

Boundary Layer Coordinates

  • The boundary layer equations derived are in Cartesian coordinates.
  • The Velocity components u and v represent x and y direction velocities respectively.
  • For objects with small curvature, these equations can be used with -
      • x coordinate : streamwise direction
      • y coordinate : normal component
  • They are called Boundary Layer Coordinates.

Application of Boundary Layer Theory

  • The Boundary-Layer Theory is not valid beyond the point of separation.
  • At the point of separation, boundary layer thickness becomes quite large for the thin layer approximation to be valid.
  • It is important to note that boundary layer theory can be used to locate the point of seperation itself.
  • In applying the boundary layer theory although U is the free-stream velocity at the outer edge of the boundary layer, it is interpreted as the fluid velocity at the wall calculated from inviscid flow considerations ( known as Potential Wall Velocity)
  • Mathematically, application of the boundary - layer theory converts the character of governing Navier-Stroke equations from elliptic to parabolic
  • This allows the marching in flow direction, as the solution at any location is independent of the conditions farther downstream.