These three regions are labeled in fig 68 in the

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Unformatted text preview: a in the wall layer. These experimental facts enable us to use a crude but very effective model for the velocity distribution u(y) across a turbulent wall layer. The Logarithmic-Overlap Law We have seen in Fig. 6.8 that there are three regions in turbulent flow near a wall: 1. Wall layer: Viscous shear dominates. 2. Outer layer: Turbulent shear dominates. 3. Overlap layer: Both types of shear are important. From now on let us agree to drop the overbar from velocity u. Let w be the wall shear stress, and let and U represent the thickness and velocity at the edge of the outer layer, y . For the wall layer, Prandtl deduced in 1930 that u must be independent of the shearlayer thickness u f( , w, , y) | v v By dimensional analysis, this is equivalent to | e-Text Main Menu | Textbook Table of Contents | Study Guide (6.17) Chapter 6 Viscous Flow in Ducts u u* u F yu* w u* 1/2 (6.18) Equation (6.18) is called the law of the wall, and the quantity u* is termed the friction velocity because it has dimensions {LT 1}, although it is not actually...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.

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