Blasius Flow Over A Flat Plate

• The classical problem considered by H. Blasius was
  1. Two-dimensional, steady, incompressible flow over a flat plate at zero angle of incidence with respect to the uniform stream of velocity .
  2. The fluid extends to infinity in all directions from the plate. 

The physical problem is already illustrated in Fig. 28.1

• Blasius wanted to determine
  (a) the velocity field solely within the boundary layer,
  (b) the boundary layer thickness ,
  (c) the shear stress distribution on the plate, and
  (d) the drag force on the plate.
  
• The Prandtl boundary layer equations in the case under consideration are

(28.15)

The boundary conditions are

(28.16)

• Note that the substitution of the term in the original boundary layer momentum equation in terms of the free stream velocity produces which is equal to zero.
• Hence the governing Eq. (28.15) does not contain any pressure-gradient term.
• However, the characteristic parameters of this problem are  that is,
  
• This relation has five variables .
• It involves two dimensions, length and time.
  
• Thus it can be reduced to a dimensionless relation in terms of (5-2) =3 quantities ( Buckingham Pi Theorem)
  
• Thus a similarity variables can be used to find the solution
  
• Such flow fields are called self-similar flow field .