Shear velocity

This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (September 2014) (Learn how and when to remove this message)

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 between 5% and 10% of the mean flow velocity.

For river base case, the shear velocity can be calculated by Manning's equation.

${\displaystyle u^{*}=\langle u\rangle {\frac {n}{a}}(gR_{h}^{-1/3})^{0.5}}$

• n is the Gauckler–Manning coefficient. Units for values of n are often left off, however it is not dimensionless, having units of: (T/[L^1/3]; s/[ft^1/3]; s/[m^1/3]).
• R_h is the hydraulic radius (L; ft, m);
• the role of a is a dimension correction factor. Thus a= 1 m^1/3/s = 1.49 ft^1/3/s.

Instead of finding ${\displaystyle n}$ and ${\displaystyle R_{h}}$ for the specific river of interest, the range of possible values can be examined; for most rivers, ${\displaystyle u^{*}}$ is between 5% and 10% of ${\displaystyle \langle u\rangle }$:

For general case

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

where τ is the shear stress in an arbitrary layer of fluid and ρ is the density of the fluid.

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

${\displaystyle u_{\star }={\sqrt {\frac {\tau _{b}}{\rho }}}}$

where τ_b is the shear stress given at the boundary.

Shear velocity is linked to the Darcy friction factor by equating wall shear stress, giving:

${\displaystyle u_{\star }={\langle u\rangle }{\sqrt {\frac {f_{\mathrm {D} }}{8}}}}$

where f_D is the friction factor.^[1]

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).