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- Stream_function abstract "The stream function is defined for incompressible (divergence-free) flows in two dimensions – as well as in three dimensions with axisymmetry. The flow velocity components can then be expressed as the derivatives of the scalar stream function. The stream function can be used to plot streamlines, which represent the trajectories of particles in a steady flow. The two-dimensional Lagrange stream function was introduced by Joseph Louis Lagrange in 1781. The Stokes stream function is for axisymmetrical three-dimensional flow, and is named after George Gabriel Stokes.Considering the particular case of fluid dynamics, the difference between the stream function values at any two points gives the volumetric flow rate (or volumetric flux) through a line connecting the two points.Since streamlines are tangent to the flow velocity vector of the flow, the value of the stream function must be constant along a streamline. The usefulness of the stream function lies in the fact that the flow velocity components in the x- and y- directions at a given point are given by the partial derivatives of the stream function at that point. A stream function may be defined for any flow of dimensions greater than or equal to two, however the two-dimensional case is generally the easiest to visualize and derive.For two-dimensional potential flow, streamlines are perpendicular to equipotential lines. Taken together with the velocity potential, the stream function may be used to derive a complex potential. In other words, the stream function accounts for the solenoidal part of a two-dimensional Helmholtz decomposition, while the velocity potential accounts for the irrotational part.".
- Stream_function thumbnail Potential_cylinder.svg?width=300.
- Stream_function wikiPageExternalLink Streamfunction.
- Stream_function wikiPageID "218091".
- Stream_function wikiPageLength "12521".
- Stream_function wikiPageOutDegree "50".
- Stream_function wikiPageRevisionID "693565266".
- Stream_function wikiPageWikiLink American_Meteorological_Society.
- Stream_function wikiPageWikiLink Cartesian_coordinate_system.
- Stream_function wikiPageWikiLink Category:Continuum_mechanics.
- Stream_function wikiPageWikiLink Category:Fluid_dynamics.
- Stream_function wikiPageWikiLink Complex_number.
- Stream_function wikiPageWikiLink Conservative_vector_field.
- Stream_function wikiPageWikiLink Continuity_equation.
- Stream_function wikiPageWikiLink Curl_(mathematics).
- Stream_function wikiPageWikiLink Derivative.
- Stream_function wikiPageWikiLink Divergence.
- Stream_function wikiPageWikiLink Dot_product.
- Stream_function wikiPageWikiLink Equipotential.
- Stream_function wikiPageWikiLink Exact_differential.
- Stream_function wikiPageWikiLink Flow_velocity.
- Stream_function wikiPageWikiLink Fluid_dynamics.
- Stream_function wikiPageWikiLink Flux.
- Stream_function wikiPageWikiLink George_Batchelor.
- Stream_function wikiPageWikiLink Helmholtz_decomposition.
- Stream_function wikiPageWikiLink Horace_Lamb.
- Stream_function wikiPageWikiLink Incompressible_flow.
- Stream_function wikiPageWikiLink Infinitesimal.
- Stream_function wikiPageWikiLink Joseph-Louis_Lagrange.
- Stream_function wikiPageWikiLink Meteorology.
- Stream_function wikiPageWikiLink Normal_(geometry).
- Stream_function wikiPageWikiLink Oceanography.
- Stream_function wikiPageWikiLink Partial_derivative.
- Stream_function wikiPageWikiLink Poissons_equation.
- Stream_function wikiPageWikiLink Potential_flow.
- Stream_function wikiPageWikiLink Rotational_symmetry.
- Stream_function wikiPageWikiLink Scalar_field.
- Stream_function wikiPageWikiLink Sir_George_Stokes,_1st_Baronet.
- Stream_function wikiPageWikiLink Solenoidal_vector_field.
- Stream_function wikiPageWikiLink Stokes_stream_function.
- Stream_function wikiPageWikiLink Streamlines,_streaklines,_and_pathlines.
- Stream_function wikiPageWikiLink Tangent.
- Stream_function wikiPageWikiLink Vector_calculus_identities.
- Stream_function wikiPageWikiLink Vector_potential.
- Stream_function wikiPageWikiLink Velocity_potential.
- Stream_function wikiPageWikiLink Volumetric_flux.
- Stream_function wikiPageWikiLink Vorticity.
- Stream_function wikiPageWikiLink File:Potential_cylinder.svg.
- Stream_function wikiPageWikiLink File:Stream_function_definition.svg.
- Stream_function wikiPageWikiLinkText "Stream function".
- Stream_function wikiPageWikiLinkText "stream function".
- Stream_function wikiPageWikiLinkText "streamline function".
- Stream_function wikiPageUsesTemplate Template:Citation.
- Stream_function wikiPageUsesTemplate Template:For.
- Stream_function wikiPageUsesTemplate Template:Pad.
- Stream_function wikiPageUsesTemplate Template:Refbegin.
- Stream_function wikiPageUsesTemplate Template:Refend.
- Stream_function wikiPageUsesTemplate Template:Reflist.
- Stream_function wikiPageUsesTemplate Template:See_also.
- Stream_function subject Category:Continuum_mechanics.
- Stream_function subject Category:Fluid_dynamics.
- Stream_function type Dynamic.
- Stream_function type Liquid.
- Stream_function type Mechanic.
- Stream_function type Redirect.
- Stream_function type Science.
- Stream_function type Thing.
- Stream_function comment "The stream function is defined for incompressible (divergence-free) flows in two dimensions – as well as in three dimensions with axisymmetry. The flow velocity components can then be expressed as the derivatives of the scalar stream function. The stream function can be used to plot streamlines, which represent the trajectories of particles in a steady flow. The two-dimensional Lagrange stream function was introduced by Joseph Louis Lagrange in 1781.".
- Stream_function label "Stream function".
- Stream_function seeAlso Vorticity.
- Stream_function sameAs Q2029236.
- Stream_function sameAs Stromfunktion.
- Stream_function sameAs Fonction_de_courant.
- Stream_function sameAs 流れ関数.
- Stream_function sameAs Funkcja_prądu.
- Stream_function sameAs m.01fy8r.
- Stream_function sameAs Функция_тока.
- Stream_function sameAs Akım_fonksiyonu.
- Stream_function sameAs Функція_струменю.
- Stream_function sameAs Q2029236.
- Stream_function wasDerivedFrom Stream_function?oldid=693565266.
- Stream_function depiction Potential_cylinder.svg.
- Stream_function isPrimaryTopicOf Stream_function.