Flow velocity

Flow velocity

In fluid dynamics the flow velocity, or velocity field, of a fluid is a vector field which is used to mathematically describe the motion of a fluid.

Definition

The flow velocity of a fluid is a vector field

: mathbf{u}=mathbf{u}(mathbf{x},t)

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

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:

teady flow

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

: frac{partial mathbf{u{partial t}=0.

Incompressible flow

A fluid is incompressible if the divergence of mathbf{u} is zero:

: ablacdotmathbf{u}=0.

That is, if mathbf{u} is a solenoidal vector field.

Irrotational flow

A flow is "irrotational" if the curl of mathbf{u} is zero:

: abla imesmathbf{u}=0.

That is, if mathbf{u} is an irrotational vector field.

Vorticity

The "vorticity", omega, of a flow can be defined in terms of its flow velocity by

: omega= abla imesmathbf{u}.

Thus in irrotational flow the vorticity is zero.

The velocity potential

If an irrotational flow occupies a simply-connected fluid region then there exists a scalar field phi such that

: mathbf{u}= ablamathbf{phi}

The scalar field phi is called the velocity potential for the flow. (See Irrotational vector field.)


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • flow velocity — tekėjimo greitis statusas T sritis Standartizacija ir metrologija apibrėžtis Greitis, kuriuo teka skystis arba dujos. atitikmenys: angl. flow velocity; stream velocity vok. Fleißgeschwindigkeit, f; Strömungsgeschwindigkeit, f rus. скорость потока …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

  • flow velocity — tekėjimo greitis statusas T sritis fizika atitikmenys: angl. flow velocity; stream velocity vok. Fleißgeschwindigkeit, f; Strömgeschwindigkeit, f; Strömungsgeschwindigkeit, f rus. скорость потока, f; скорость течения, f pranc. vitesse… …   Fizikos terminų žodynas

  • flow velocity — vandentėkmės greitis statusas T sritis ekologija ir aplinkotyra apibrėžtis Vandens tekėjimo greitis tam tikrame upės ruože. Priklauso nuo upės nuolydžio, vagos grublėtumo ir kitų veiksnių. atitikmenys: angl. flow speed; flow velocity vok.… …   Ekologijos terminų aiškinamasis žodynas

  • flow velocity — vandens srovės greitis statusas Aprobuotas sritis hidrometeorologija apibrėžtis Vandens tekėjimo greitis metrais per sekundę. atitikmenys: angl. flow velocity vok. Strömungsgeschwindigkeit rus. скорость течения šaltinis Vandens debito matavimo… …   Lithuanian dictionary (lietuvių žodynas)

  • flow velocity —    See specific discharge …   Lexicon of Cave and Karst Terminology

  • flow velocity — speed at which a current travels …   English contemporary dictionary

  • Flow measurement — is the quantification of bulk fluid movement. Flow can be measured in a variety of ways. Positive displacement flow meters acumulate a fixed volume of fluid and then count the number of times the volume is filled to measure flow. Other flow… …   Wikipedia

  • Flow-accelerated corrosion — (FAC), also known as flow assisted corrosion, is a corrosion mechanism in which a normally protective oxide layer on a metal surface dissolves in a fast flowing water. The underlying metal corrodes to re create the oxide, and thus the metal loss… …   Wikipedia

  • Velocity potential — A velocity potential is used in fluid dynamics, when a fluid occupies a simply connected region and is irrotational. In such a case,: abla imes mathbf{u} =0,where mathbf{u} denotes the flow velocity of the fluid. As a result, mathbf{u} can be… …   Wikipedia

  • flow speed — vandentėkmės greitis statusas T sritis ekologija ir aplinkotyra apibrėžtis Vandens tekėjimo greitis tam tikrame upės ruože. Priklauso nuo upės nuolydžio, vagos grublėtumo ir kitų veiksnių. atitikmenys: angl. flow speed; flow velocity vok.… …   Ekologijos terminų aiškinamasis žodynas

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”