Velocity field

In continuum mechanics the macroscopic velocity, also flow velocity in fluid dynamics or drift velocity in electromagnetism, is a vector field which is used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar.

The flow velocity u of a fluid is a vector field

which gives the velocity of an element of fluid at a position ${\displaystyle \mathbf {x} \,}$ and time ${\displaystyle t.\,}$

The flow speed q is the length of the flow velocity vector

and is a scalar field.

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:

The flow of a fluid is said to be steady if ${\displaystyle \mathbf {u} }$ does not vary with time. That is if

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