For the sine wave approximation of Prob. 10–114, use the definition of local skin friction coefficient and the Kármán integral equation to generate an expression for δ/x. Compare your result to the Blasius expression for δ/x.

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