Shear velocity
Encyclopedia
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:
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.
Where
is the shear stress in an arbitrary layer of fluid and 
is the density
of the fluid.
Typically, for sediment transport applications, the shear velocity is evaluated at the lower boundary of an open channel:
Where
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).
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
may be re-written in units of velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
. It is useful as a method in fluid mechanics
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
to compare true velocities, such as the velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
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:
- DiffusionDiffusionMolecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
and dispersionDispersion (water waves)In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, and forced by gravity and surface tension...
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.
Where
is the shear stress in an arbitrary layer of fluid and is the densityDensity
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
of the fluid.
Typically, for sediment transport applications, the shear velocity is evaluated at the lower boundary of an open channel:
Where
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).