The stream wise velocity component of a steady, incompressible, laminar, flat plate boundary layer of boundary layer thickness δ is approximated by the sine wave profile of Prob. 10–114. Generate expressions for displacement thickness and momentum thickness as functions of δ, based on this sine wave approximation. Compare the approximate values of δ*/δ and u/δ to the values of δ*/δ and θ/δ obtained from the Blasius solution.

Data from problem 114.

The Blasius boundary layer profile is an exact solution of the boundary layer equations for flow over a flat plate. However, the results are somewhat cumbersome to use, since the data appear in tabular form (the solution is numerical). Thus, a simple sine wave approximation (Fig. P10–114) is often used in place of the Blasius solution, namely

for y ≪ δ, where δ is the boundary layer thickness. Plot the Blasius profile and the sine wave approximation on the same plot, in non dimensional form (u/U versus y/δ), and compare. Is the sine wave profile a reasonable approximation?

FIGURE P10–114

Transcribed Image Text:

u(y) = Usin пу 28 for y< 8, and u = U