The flow speed q is the length of the flow velocity vector[3]
and is a scalar field.
Usesedit
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:
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 (with the usual dimension of length per time), defined as the quotient between the volume flow rate (with dimension of cubed length per time) and the cross sectional area (with dimension of square length):
^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.{{cite book}}: CS1 maint: location missing publisher (link)
^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.{{cite book}}: CS1 maint: location missing publisher (link)
^Courant, R.; Friedrichs, K.O. (1999) [unabridged republication of the original edition of 1948]. Supersonic Flow and Shock Waves. Applied mathematical sciences (5th ed.). Springer-Verlag New York Inc. pp. 24. ISBN0387902325. OCLC 44071435.
January 01, 1970
flow, velocity, continuum, mechanics, flow, velocity, fluid, dynamics, also, macroscopic, velocity, statistical, mechanics, drift, velocity, electromagnetism, vector, field, used, mathematically, describe, motion, continuum, length, flow, velocity, vector, sca. In continuum mechanics the flow velocity in fluid dynamics also macroscopic velocity 1 2 in statistical mechanics or drift velocity in electromagnetism is a vector field used to mathematically describe the motion of a continuum The length of the flow velocity vector is scalar the flow speed It is also called velocity field when evaluated along a line it is called a velocity profile as in e g law of the wall Contents 1 Definition 2 Uses 2 1 Steady flow 2 2 Incompressible flow 2 3 Irrotational flow 2 4 Vorticity 3 The velocity potential 4 Bulk velocity 5 See also 6 ReferencesDefinition editThe flow velocity u of a fluid is a vector field u u x t displaystyle mathbf u mathbf u mathbf x t nbsp which gives the velocity of an element of fluid at a position x displaystyle mathbf x nbsp and time t displaystyle t nbsp The flow speed q is the length of the flow velocity vector 3 q u displaystyle q mathbf u nbsp and is a scalar field Uses editThe 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 edit Main article Steady flow The flow of a fluid is said to be steady if u displaystyle mathbf u nbsp does not vary with time That is if u t 0 displaystyle frac partial mathbf u partial t 0 nbsp Incompressible flow edit Main article Incompressible flow If a fluid is incompressible the divergence of u displaystyle mathbf u nbsp is zero u 0 displaystyle nabla cdot mathbf u 0 nbsp That is if u displaystyle mathbf u nbsp is a solenoidal vector field Irrotational flow edit Main article Irrotational flow A flow is irrotational if the curl of u displaystyle mathbf u nbsp is zero u 0 displaystyle nabla times mathbf u 0 nbsp That is if u displaystyle mathbf u nbsp 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 F displaystyle Phi nbsp with u F displaystyle mathbf u nabla Phi nbsp If the flow is both irrotational and incompressible the Laplacian of the velocity potential must be zero D F 0 displaystyle Delta Phi 0 nbsp Vorticity edit Main article Vorticity The vorticity w displaystyle omega nbsp of a flow can be defined in terms of its flow velocity by w u displaystyle omega nabla times mathbf u nbsp If the vorticity is zero the flow is irrotational The velocity potential editMain article Potential flow If an irrotational flow occupies a simply connected fluid region then there exists a scalar field ϕ displaystyle phi nbsp such that u ϕ displaystyle mathbf u nabla mathbf phi nbsp The scalar field ϕ displaystyle phi nbsp is called the velocity potential for the flow See Irrotational vector field Bulk velocity editIn many engineering applications the local flow velocity u displaystyle mathbf u nbsp vector field is not known in every point and the only accessible velocity is the bulk velocity or average flow velocity u displaystyle bar u nbsp with the usual dimension of length per time defined as the quotient between the volume flow rate V displaystyle dot V nbsp with dimension of cubed length per time and the cross sectional area A displaystyle A nbsp with dimension of square length u V A displaystyle bar u frac dot V A nbsp See also editDisplacement field mechanics Drift velocity Enstrophy Group velocity Particle velocity Pressure gradient Strain rate Strain rate tensor Stream function Velocity potential Vorticity Wind velocityReferences edit 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 ISBN 978 0471044925 a href Template Cite book html title Template Cite book cite book a CS1 maint location missing publisher link 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 ISBN 978 0521733175 a href Template Cite book html title Template Cite book cite book a CS1 maint location missing publisher link Courant R Friedrichs K O 1999 unabridged republication of the original edition of 1948 Supersonic Flow and Shock Waves Applied mathematical sciences 5th ed Springer Verlag New York Inc pp 24 ISBN 0387902325 OCLC 44071435 Retrieved from https en wikipedia org w index php title Flow velocity amp oldid 1198171278 Bulk velocity, wikipedia, wiki, book, books, library,