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What is the velocity profile for turbulent boundary layer on a flat surface?

(a) $\frac{u}{u_{\infty }}= sin\left ( \frac{y}{\delta } \right )^{\frac{1}{7}}$

(b) $\frac{u}{u_{\infty }}= \left ( \frac{y}{\delta } \right )^{\frac{1}{7}}$

(c) $\frac{u}{u_{\infty }}= 2\left ( \frac{y}{\delta }-\frac{y}{8} \right )^{\frac{1}{7}}$

(d) $\frac{u}{u_{\infty }}= \frac{3}{2}\left ( \frac{y}{\delta } -\frac{1}{2}\left ( \frac{y}{\delta } \right )^{3}\right )$

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