The velocity profile for the turbulent layer over a flat plate is.

1
\(\frac{u}{{{u_x}}} = \sin \left( {\frac{\pi }{2} - \frac{y}{\delta }} \right)\)
2
\(\frac{u}{{{u_x}}} = {\left( {\frac{y}{\delta }} \right)^{\frac{1}{7}}}\)
3
\(\frac{u}{{{u_x}}} = 2\left( {\frac{y}{\delta }} \right) - {\left( {\frac{y}{\delta }} \right)^{\frac{1}{7}}}\)
4
\(\frac{u}{{{u_x}}} = \frac{3}{2}\left( {\frac{y}{\delta }} \right) - \frac{1}{2}{\left( {\frac{y}{\delta }} \right)^3}\)

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