269:
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:
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Duderstadt, James J.; Martin, William R. (1979). "Chapter 4:The derivation of continuum description from transport equations". In Wiley-Interscience
Publications (ed.).
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Freidberg, Jeffrey P. (2008). "Chapter 10:A self-consistent two-fluid model". In
Cambridge University Press (ed.).
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1220:. Applied mathematical sciences (5th ed.). Springer-Verlag New York Inc. pp.
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938:(with the usual dimension of length per time), defined as the quotient between the
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Vector field which is used to mathematically describe the motion of a continuum
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970:(with dimension of cubed length per time) and the cross sectional area
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is not known in every point and the only accessible velocity is the
159:
351:{\displaystyle {\frac {\partial \mathbf {u} }{\partial t}}=0.}
715:, of a flow can be defined in terms of its flow velocity by
148:{\displaystyle \mathbf {u} =\mathbf {u} (\mathbf {x} ,t),}
877:
In many engineering applications the local flow velocity
645:
If the flow is both irrotational and incompressible, the
66:. The length of the flow velocity vector is scalar, the
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831:{\displaystyle \mathbf {u} =\nabla \mathbf {\phi } .}
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If the vorticity is zero, the flow is irrotational.
748:{\displaystyle \omega =\nabla \times \mathbf {u} .}
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1035:{\displaystyle {\bar {u}}={\frac {\dot {V}}{A}}}
62:used to mathematically describe the motion of a
538:{\displaystyle \nabla \times \mathbf {u} =0.}
581:which is irrotational can be described as a
428:{\displaystyle \nabla \cdot \mathbf {u} =0.}
245:
237:
1192:: CS1 maint: location missing publisher (
1153:: CS1 maint: location missing publisher (
638:{\displaystyle \mathbf {u} =\nabla \Phi .}
221:is the length of the flow velocity vector
761:
204:
180:
649:of the velocity potential must be zero:
14:
1252:
1172:(1 ed.). Cambridge. p. 225.
361:
310:does not vary with time. That is if
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990:(with dimension of square length):
772:If an irrotational flow occupies a
24:
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284:The flow of a fluid is said to be
251:{\displaystyle q=\|\mathbf {u} \|}
25:
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776:fluid region then there exists a
372:If a fluid is incompressible the
1170:Plasma Physics and Fusion Energy
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1217:Supersonic Flow and Shock Waves
671:{\displaystyle \Delta \Phi =0.}
1200:
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1054:Displacement field (mechanics)
1006:
922:
273:
184:{\displaystyle \mathbf {x} \,}
139:
125:
13:
1:
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102:of a fluid is a vector field
91:
892:{\displaystyle \mathbf {u} }
680:
563:{\displaystyle \mathbf {u} }
501:{\displaystyle \mathbf {u} }
453:{\displaystyle \mathbf {u} }
391:{\displaystyle \mathbf {u} }
303:{\displaystyle \mathbf {u} }
7:
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10:
1301:
1285:Vector physical quantities
963:{\displaystyle {\dot {V}}}
931:{\displaystyle {\bar {u}}}
765:
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471:
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277:
1133:. New York. p. 218.
867:Irrotational vector field
572:irrotational vector field
76:; when evaluated along a
708:{\displaystyle \omega }
585:, through the use of a
579:simply-connected domain
462:solenoidal vector field
264:
261:and is a scalar field.
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762:The velocity potential
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604:{\displaystyle \Phi ,}
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908:average flow velocity
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856:
854:{\displaystyle \phi }
833:
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792:{\displaystyle \phi }
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48:statistical mechanics
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208:{\displaystyle t.\,}
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109:
72:. It is also called
44:macroscopic velocity
1265:Continuum mechanics
865:for the flow. (See
368:Incompressible flow
362:Incompressible flow
32:continuum mechanics
1099:Velocity potential
1089:Strain-rate tensor
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863:velocity potential
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96:The flow velocity
1079:Pressure gradient
1074:Particle velocity
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1009:
983:{\displaystyle A}
957:
925:
841:The scalar field
474:Irrotational flow
468:Irrotational flow
340:
80:, it is called a
16:(Redirected from
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1280:Spatial gradient
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1212:Friedrichs, K.O.
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165:element of fluid
158:which gives the
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82:velocity profile
56:electromagnetism
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1270:Vector calculus
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1094:Stream function
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217:The flow speed
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1260:Fluid dynamics
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1179:978-0521733175
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1069:Group velocity
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1059:Drift velocity
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861:is called the
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768:Potential flow
766:Main article:
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685:Main article:
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583:potential flow
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472:Main article:
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366:Main article:
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278:Main article:
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168:at a position
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84:(as in, e.g.,
74:velocity field
52:drift velocity
40:fluid dynamics
26:
18:Fluid velocity
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1125:
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1110:
1109:Wind velocity
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941:
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905:
904:bulk velocity
901:
873:Bulk velocity
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37:
36:flow velocity
33:
19:
1216:
1202:
1169:
1163:
1130:
1124:
907:
903:
900:vector field
876:
840:
778:scalar field
771:
757:
692:
690:
577:A flow in a
576:
548:That is, if
547:
480:irrotational
479:
477:
438:That is, if
437:
371:
285:
283:
268:
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163:
157:
98:
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81:
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60:vector field
51:
43:
35:
29:
1208:Courant, R.
1084:Strain rate
280:Steady flow
274:Steady flow
1254:Categories
1231:0387902325
1116:References
799:such that
478:A flow is
374:divergence
92:Definition
69:flow speed
1214:(1999) .
1188:cite book
1149:cite book
1104:Vorticity
1064:Enstrophy
1023:˙
1007:¯
955:˙
923:¯
849:ϕ
822:ϕ
818:∇
787:ϕ
735:×
732:∇
726:ω
703:ω
693:vorticity
687:Vorticity
681:Vorticity
660:Φ
657:Δ
647:Laplacian
630:Φ
627:∇
596:Φ
522:×
519:∇
508:is zero:
412:⋅
409:∇
398:is zero:
334:∂
324:∂
246:‖
238:‖
191:and time
64:continuum
1275:Velocity
1240:44071435
1047:See also
160:velocity
482:if the
58:, is a
42:, also
1238:
1228:
1176:
1137:
570:is an
286:steady
162:of an
611:with
460:is a
50:, or
1236:OCLC
1226:ISBN
1194:link
1174:ISBN
1155:link
1135:ISBN
691:The
484:curl
265:Uses
78:line
34:the
906:or
869:.)
486:of
376:of
288:if
88:).
54:in
46:in
38:in
30:In
1256::
1234:.
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1186:{{
1151:}}
1147:{{
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666:0.
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423:0.
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1242:.
1196:)
1182:.
1157:)
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1042:.
1028:A
1020:V
1013:=
1004:u
978:A
952:V
920:u
886:u
826:.
815:=
811:u
743:.
739:u
729:=
663:=
633:.
624:=
620:u
599:,
557:u
530:=
526:u
495:u
447:u
420:=
416:u
385:u
343:=
337:t
328:u
297:u
242:u
235:=
232:q
219:q
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199:t
177:x
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137:t
134:,
130:x
126:(
122:u
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114:u
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20:)
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