Boundary Layer Thickness

• Since , it is customary to select the boundary layer thickness as that point where approaches 0.99.
• From Table 28.1, reaches 0.99 at η= 5.0 and we can write     

  (29.5)

  
  
• However, the aforesaid definition of boundary layer thickness is somewhat arbitrary, a physically more meaningful measure of boundary layer estimation is expressed through displacement thickness .

                         Fig. 29.1   (Displacement thickness)     (b) Momentum thickness

• Displacement thickness : It is defined as the distance by which the external potential flow is displaced outwards due to the decrease in velocity in the boundary layer.

  Therefore,	(29.6)

  
  
• Substituting the values of and from Eqs (28.21a) and (28.19) into Eq.(29.6), we obtain

or,

(29.7)

Following the analogy of the displacement thickness, a momentum thickness may be defined. 

Momentum thickness ( ): It  is defined as the loss of momentum in the boundary layer as compared with that of potential flow. Thus

(29.8)

With the substitution of and from Eg. (28.21a) and (28.19), we can evaluate numerically the value of for a flat plate as

(29.9)

The relationships between have been shown in Fig. 29.1.