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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 does not vary with time. That is if
If a fluid is incompressible the divergence of is zero:
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) which is the ratio between the volume flow rate and the cross sectional area , given by
^Duderstadt, James J.; Martin, William R. (1979). "Chapter 4:The derivation of continuum description from transport equations". In Wiley-Interscience Publications (ed.). Transport theory. New York. p. 218. ISBN978-0471044925.
^Freidberg, Jeffrey P. (2008). "Chapter 10:A self-consistent two-fluid model". In Cambridge University Press (ed.). Plasma Physics and Fusion Energy (1 ed.). Cambridge. p. 225. ISBN978-0521733175.