Clutter (radar): Difference between revisions

Revision as of 14:51, 14 January 2014

In continuum mechanics the macroscopic velocity^[1], also flow velocity in fluid dynamics or drift velocity in electromagnetism, of a fluid is a vector field which is used to mathematically describe the motion of a fluid. The length of the flow velocity vector is the flow speed.

Definition

The flow velocity u of a fluid is a vector field

u = u (x, t)

which gives the velocity of an element of fluid at a position $x$ and time $t$ .

The flow speed q is the length of the flow velocity vector^[2]

q = | | u | |

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

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.

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

\frac{\partial u}{\partial t} = 0 .

Incompressible flow

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.

If a fluid is incompressible the divergence of $u$ is zero:

\nabla \cdot u = 0 .

That is, if $u$ is a solenoidal vector field.

Irrotational flow

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.

A flow is irrotational if the curl of $u$ is zero:

\nabla \times u = 0 .

That is, if $u$ is an irrotational vector field.

A flow in a simply-connected domain which is irrotational can be described as a potential flow, through the use of a velocity potential $Φ,$ with $u = \nabla Φ .$ If the flow is both irrotational and incompressible, the Laplacian of the velocity potential must be zero: $Δ Φ = 0 .$

Vorticity

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.

The vorticity, $ω$ , of a flow can be defined in terms of its flow velocity by

ω = \nabla \times u .

Thus in irrotational flow the vorticity is zero.

The velocity potential

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. If an irrotational flow occupies a simply-connected fluid region then there exists a scalar field $ϕ$ such that

u = \nabla ϕ

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

Notes and references

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

↑ Template:Harvnb, Template:Harvnb
↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[1] Template:Harvnb, Template:Harvnb

[2] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[1]

[2]

@@ Line 1: / Line 1: @@
-Nestor is the title my parents gave me but I don't like when individuals use my complete name. Years ago we moved to Kansas. Interviewing is what I do for a living but I strategy on altering it. One of the things I love most is climbing and now I have time to consider on new things.<br><br>Look into my homepage [http://Www.chillister.com/blogs/post/27388 chillister.com]
+In [[continuum mechanics]] the '''macroscopic velocity'''<ref>{{harvnb|Duderstadt|1979|p=218}}, {{harvnb|Freidberg|2008|p=225}}</ref>, also '''flow velocity''' in [[fluid dynamics]] or '''drift velocity''' in [[electromagnetism]], of a fluid is a [[vector field]] which is used to mathematically describe the motion of a fluid. The length of the flow velocity vector is the '''flow speed'''.
+==Definition==
+The flow velocity '''''u''''' of a fluid is a vector field
+:<math> \mathbf{u}=\mathbf{u}(\mathbf{x},t)</math>
+which gives the [[velocity]] of an ''[[fluid parcel|element of fluid]]'' at a position <math>\mathbf{x}\,</math> and time <math> t\, </math>.
+The flow speed ''q'' is the length of the flow velocity vector<ref>{{cite book| first1=R. | last1=Courant | author1-link=Richard Courant | first2=K.O. | last2=Friedrichs | author2-link=Kurt Otto Friedrichs | edition=5th | publisher=Springer | origyear=First published in 1948 | isbn=0387902325 | pages=24 | title=Supersonic Flow and Shock Waves | oclc=44071435 | publisher=Springer-Verlag New York Inc | year=1999 | series=Applied mathematical sciences}}</ref>
+:<math>q = || \mathbf{u} ||</math>
+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|Steady flow}}
+The flow of a fluid is said to be ''steady'' if <math> \mathbf{u}</math> does not vary with time.  That is if
+:<math> \frac{\partial \mathbf{u}}{\partial t}=0.</math>
+===Incompressible flow===
+{{Main|Incompressible flow}}
+If a fluid is incompressible the [[divergence]] of <math>\mathbf{u}</math> is zero:
+:<math> \nabla\cdot\mathbf{u}=0.</math>
+That is, if <math>\mathbf{u}</math> is a [[solenoidal vector field]].
+===Irrotational flow===
+{{main|Irrotational flow}}
+A flow is ''irrotational'' if the [[Curl (mathematics)|curl]] of <math>\mathbf{u}</math> is zero:
+:<math> \nabla\times\mathbf{u}=0. </math>
+That is, if <math>\mathbf{u}</math> is an [[irrotational vector field]].
+A flow in a [[simply-connected domain]] which is irrotational can be described as a [[potential flow]], through the use of a [[velocity potential]] <math>\Phi,</math> with <math>\mathbf{u}=\nabla\Phi.</math> If the flow is both irrotational and incompressible, the [[Laplacian]] of the velocity potential must be zero: <math>\Delta\Phi=0.</math>
+===Vorticity===
+{{Main| Vorticity}}
+The ''vorticity'', <math>\omega</math>, of a flow can be defined in terms of its flow velocity by
+:<math> \omega=\nabla\times\mathbf{u}.</math>
+Thus in irrotational flow the vorticity is zero.
+==The velocity potential==
+{{main|Potential flow}}
+If an irrotational flow occupies a [[simply-connected]] fluid region then there exists a [[scalar field]] <math> \phi </math> such that
+:<math> \mathbf{u}=\nabla\mathbf{\phi} </math>
+The scalar field <math>\phi</math> is called the [[velocity potential]] for the flow. (See [[Irrotational vector field]].)
+==Notes and references==
+{{reflist}}
+==Further reading==
+* {{cite book |author=Duderstadt, James J., Martin, William R.| title= Transport theory | editor=Wiley-Interscience Publications | location= New York| year= 1979 | ed= | ISBN=978-0471044925|chapter=Chapter 4:The derivation of continuum description from trasport equations}}
+* {{cite book | author=Freidberg, Jeffrey P.|title=Plasma Physics and Fusion Energy|edition=1|editor=Cambridge University Press|location=Cambridge|year=2008| ISBN=978-0521733175|chapter=Chapter 10:A self-consistent two-fluid model}}
+[[Category:Fluid dynamics]]
+[[Category:Continuum mechanics]]
+[[Category:Vector calculus]]

Clutter (radar): Difference between revisions

Revision as of 14:51, 14 January 2014

Contents

Definition

Uses

Steady flow

Incompressible flow

Irrotational flow

Vorticity

The velocity potential

Notes and references

Further reading

Navigation menu

Clutter (radar): Difference between revisions

Revision as of 14:51, 14 January 2014

Definition

Uses

Steady flow

Incompressible flow

Irrotational flow

Vorticity

The velocity potential

Notes and references

Further reading

Navigation menu

Search