In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity[1][2] in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum.
It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall).
The flow velocity u of a fluid is a vector field which gives the velocity of an element of fluid at a position
The flow speed q is the length of the flow velocity vector[3] and is a scalar field.
Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity.
Some common examples follow: The flow of a fluid is said to be steady if
A flow in a simply-connected domain which is irrotational can be described as a potential flow, through the use of a velocity potential
If the flow is both irrotational and incompressible, the Laplacian of the velocity potential must be zero:
If an irrotational flow occupies a simply-connected fluid region then there exists a scalar field
is called the velocity potential for the flow.
In many engineering applications the local flow velocity
(with the usual dimension of length per time), defined as the quotient between the volume flow rate
(with dimension of cubed length per time) and the cross sectional area