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- Q2029236 subject Q7138878.
- Q2029236 subject Q7731439.
- Q2029236 abstract "Template:ForThe 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.".
- Q2029236 thumbnail Potential_cylinder.svg?width=300.
- Q2029236 wikiPageExternalLink Streamfunction.
- Q2029236 wikiPageWikiLink Q1066266.
- Q2029236 wikiPageWikiLink Q1143513.
- Q2029236 wikiPageWikiLink Q1153588.
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- Q2029236 wikiPageWikiLink Q7138878.
- Q2029236 wikiPageWikiLink Q7731439.
- Q2029236 wikiPageWikiLink Q80222.
- Q2029236 wikiPageWikiLink Q827688.
- Q2029236 type Thing.
- Q2029236 comment "Template:ForThe 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.".
- Q2029236 label "Stream function".
- Q2029236 seeAlso Q1143513.
- Q2029236 depiction Potential_cylinder.svg.
