IX. 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 δ: This is defined as the y- location where u/ue reaches 0.99%, that is the
u- velocity becomes 99% of the edge velocity.
2. Displacement Thickness δ* : 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
δ*=1−ρu
ρeue
0
∞
∫dy
where the subscript 'e' refers to the conditions at the boundary layer edge. This quantity is usually
computed by numerical integration.
3. Momentum Thickness θ: 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
θ = ρu
ρ
e
u
e
0
∞
∫1−u
u
e
dy
and may be found by numerical integration of the velocity profile.
4. Shape Factor H : This quantity is defined as the ratio δ*/θ . 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,
τwall = τw= µ ∂u
∂y
wall
6. Skin friction Coefficient cf:The derivative of u is computed numerically. This quantity is usually
non-dimensionalized by the dynamic pressure at the boundary layer edge, giving the skin friction
coefficient cf as
cf=τw
1
2ρeue
2
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=
τ
w
dx
Over En tire Su rface
∫
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