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Unformatted text preview: a flow velocity.
Subsequently, Kármán in 1933 deduced that u in the outer layer is independent of
molecular viscosity, but its deviation from the stream velocity U must depend on the
layer thickness and the other properties
(U u)outer g( , w, , y) (6.19) Again, by dimensional analysis we rewrite this as
U u G u* y (6.20) where u* has the same meaning as in Eq. (6.18). Equation (6.20) is called the
velocitydefect law for the outer layer.
Both the wall law (6.18) and the defect law (6.20) are found to be accurate for a
wide variety of experimental turbulent duct and boundarylayer flows [1 to 3]. They
are different in form, yet they must overlap smoothly in the intermediate layer. In 1937
C. B. Millikan showed that this can be true only if the overlaplayer velocity varies
logarithmically with y:
u
u* 1 ln yu* B overlap layer (6.21) Over the full range of turbulent smooth wall flows, the dimensionless constants and
B are found to have the approximate values
0.41 and B 5.0. Equation (6.21) is...
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 Spring '08
 Sakar

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