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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
velocity-defect 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 boundary-layer 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 overlap-layer velocity varies
logarithmically with y:
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