The Steady, Turbulent Boundary Layer on a Flat Plate

5 THE STEADY, TURBULENT BOUNDARY LAYER ON A FLAT PLATE 

There are no known analytical solutions for turbulent boundary layers that are analogous to Blasius solution for the laminar boundary layer on a flat plate. Prandtl, to describe the steady, turbulent boundary layer on a flat plate, made 

The average velocity in the x direction at any point has the same kind of distribution as that found in a pipe and is represented by Prandtl s power rule (Eq. 11.31) in the form 

This presupposes that the velocity profiles at any x are similar to each other this is the kind of assumption made by Blasius when he assumed that the velocity was a function of rj, not of x and y separately. 

Over the Reynolds number range of 3 x 10 to 3 x 10 the friction factor plot for smooth pipes can be approximated (see Prob. 11.13) by 

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