### Shear velocity

**Shear velocity**, also called **friction velocity**, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a velocity that relates shear between layers of flow.

Shear velocity is used to describe shear-related motion in moving fluids. It is used to describe:

- Diffusion and dispersion of particles, tracers, and contaminants in fluid flows
- The velocity profile near the boundary of a flow (see Law of the wall)
- Transport of sediment in a channel

Shear velocity also helps in thinking about the rate of shear and dispersion in a flow. Shear velocity scales well to rates of dispersion and bedload sediment transport. A general rule is that the shear velocity is about 1/10 of the mean flow velocity.

u_{\star}=\sqrt{\frac{\tau}{\rho}}

Where \tau is the shear stress in an arbitrary layer of fluid and \rho is the density of the fluid.

Typically, for sediment transport applications, the shear velocity is evaluated at the lower boundary of an open channel:

u_{\star}=\sqrt{\frac{\tau_b}{\rho}}

Where \tau_b is the shear stress given at the boundary.

Shear velocity can also be defined in terms of the local velocity and shear stress fields (as opposed to whole-channel values, as given above).

## References

Whipple, K. X (2004), III: Flow Around Bends: Meander Evolution, 12.163 Course Notes, MIT. http://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-163-surface-processes-and-landscape-evolution-fall-2004/lecture-notes/3_flow_around_bends.pdf