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 LogarithmicOverlap 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  eText 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.
 Spring '08
 Sakar

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