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Friction velocity

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Dimensional analysis shows that at a wall a charateristic velocity, called the friction velocity, u_*, can be defined in the following way:

u_* \equiv \sqrt{\frac{\tau_w}{\rho}}

Where \tau_w is the wall shear stress and \rho is the fluid density at the wall.

The friction velocity can also be computed from the Darcy friction factor:

u_{\star} = U \cdot \sqrt{\frac{f}{8}}

Where U is the average velocity and f is the Darcy friction factor.

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