Vector field which is used to mathematically describe the motion of a continuum
In
continuum
. The length of the flow velocity vector is scalar, the flow speed.
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 speed q is the length of the flow velocity vector[3]
and is a scalar field.
Uses
The flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity. Some common examples follow:
Steady flow
Main article:
Steady flow
The flow of a fluid is said to be steady if does not vary with time. That is if
simply-connected fluid region then there exists a scalar field
such that
The scalar field is called the
Irrotational vector field
.)
Bulk velocity
In many engineering applications the local flow velocity vector field is not known in every point and the only accessible velocity is the bulk velocity or average 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 (with dimension of square length):