Chapt06

18 equation 618 is called the law of the wall and the

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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 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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