u
f '
U ∞
=
1
0
Blausius
Laminar flow
5
η =
y Re x
x
u
u
+
u*
=
5
5
Data by Martinelli, Von
Karman for pipe or B. L.
Turbulent wake
(core flow)
20
30
500
1000
Laminar buffer
sublayer zone
Turbulent core
ln y + =
yu*
ν
�
�
�
� �
206
Analytical Heat Transfer
FIGURE 10.5
Analytical universal velocity profile for laminar boundary layer and semiempirical law of wall
velocity profile for turbulent boundary layer.
Consider a laminar sublayer region, very close to the wall region where
viscosity is dominated and turbulence is damped at the wall.
du
τ = ρν
(10.34)
dy
τ w
du �
u
= ν
≈ ν
ρ
dy
y
w
τ w τ w
du
= ν
ρ
ρ
dy
du
∗ ∗
u u = ν dy
Therefore,
∗
u
yu
=
u ∗
ν
f '
U ∞
=
1
0
Blausius
Laminar flow
5
η =
y Re x
x
u
u
+
u*
=
5
5
Data by Martinelli, Von
Karman for pipe or B. L.
Turbulent wake
(core flow)
20
30
500
1000
Laminar buffer
sublayer zone
Turbulent core
ln y + =
yu*
ν
�
�
�
� �
206
Analytical Heat Transfer
FIGURE 10.5
Analytical universal velocity profile for laminar boundary layer and semiempirical law of wall
velocity profile for turbulent boundary layer.
Consider a laminar sublayer region, very close to the wall region where
viscosity is dominated and turbulence is damped at the wall.
du
τ = ρν
(10.34)
dy
τ w
du �
u
= ν
≈ ν
ρ
dy
y
w
τ w τ w
du
= ν
ρ
ρ
dy
du
∗ ∗
u u = ν dy
Therefore,
∗
u
yu
=
u ∗
ν