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AE2020 Handout #6
Boundary layer Profile Properties
To the practicing engineer the velocity profile itself is of very little interest. The following parameters
are more important.
1. Boundary Layer Thickness : This is defined as the y- location where u/u reaches 0.99%, that is the ue
velocity becomes 99% of the edge velocity.
2. Displacement Thickness * : This is a measure of the outward displacement of the streamlines from the
solid surface as a result of the reduced u- velocity within the boundary layer. This quantity is defined as

 u 
*   1
dy
  u 
e e 
0 
where the subscript 'e' refers to the conditions at the boundary layer edge. This quantity is usually computed
by numerical integration.
3. Momentum Thickness : This is a measure of the momentum loss within the boundary layer as a result of
the reduced velocities within the boundary layer. It is defined as

u  u 
1
dy



u
u


e
e
e
0

and may be found by numerical integration of the velocity profile.
*
4. Shape Factor H : This quantity is defined as the ratio  / . For laminar flows H varies between 2 and 3. It
is 3.7 near separation point. Thus excessively large values of H (above 3) indicate that the boundary layer is
about to separate. In turbulent flows, H varies between 1.5 and 2.
5.
Surface Shear Stress: The shear stress at the wall can be found from the definition of shear stress
(See Handout #1). It is given by,
u 
 wal l   w  
y wal l
6. Skin friction Coefficient c :The derivative of u is computed numerically. This quantity is usually
f
non-dimensionalized by the dynamic pressure at the boundary layer edge, giving the skin friction coefficient
c as
f
cf 
w
1  u 2 
2 e e 
7. Skin Friction Drag, D : The shear stress may be numerically integrated over the entire solid surface to give
the skin friction drag force along the x- axis:
D

dx
w
Over Entire Surface
8. Skin Friction Drag Coefficient C
The drag force is usually non-dimensionalized by the freestream
d:
dynamic pressure times the chord of the airfoil c, giving the skin friction drag coefficient along the x- axis, C .
d
Cd 
D
1

  V 2 c 

 2

Important: Note that all of the above definitions hold for laminar and turbulent, compressible and
incompressible boundary layers!