Chapter 9, Problem 45P

The velocity profile in a turbulent boundary-layer flow at zero pressure gradient is approximated by the $\frac{1}{6}$-power profile expression,

$\begin{array}{cc}\frac{u}{U}={\eta }^{1/6},& \text{where}\eta \text{=}\frac{y}{\delta }\end{array}$

Use the momentum integral equation with this profile to obtain expressions for δ = x and C_f. Compare with results obtained in Section 9.4 for the $\frac{1}{7}$-power profile.