IEVref:102-05-20ID:
Language:enStatus: Standard
Term: divergence
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Definition: scalar div U associated at each point of a given space region with a vector U, equal to the limit of the flux of the vector which emerges from a closed surface S, divided by the volume of the interior of the surface when all its geometrical dimensions become infinitesimal

divU= lim V→0 1 V ∯ S U⋅ e n dA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiGacsgacaGGPbGaai ODaiaahwfacqGH9aqpdaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGa amOvaiabgkziUkaaicdaaeqaaOWaaSaaaeaacaaIXaaabaGaamOvaa aadaWdwbqaaiaahwfacqGHflY1caWHLbWaaSbaaSqaaiaad6gaaeqa aOGaciizaiaadgeaaSqaaiaabofaaeqaniablkH7slabgUIiYlabgU IiYdaaaa@5082@

where endA is the vector surface element oriented outwards and V is the volume

Note 1 to entry: In orthonormal Cartesian coordinates, the divergence is:

divU= ∂ U x ∂x + ∂ U y ∂y + ∂ U z ∂z MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiGacsgacaGGPbGaai ODaiaahwfacqGH9aqpdaWcaaqaaiabgkGi2kaadwfadaWgaaWcbaGa amiEaaqabaaakeaacqGHciITcaWG4baaaiabgUcaRmaalaaabaGaey OaIyRaamyvamaaBaaaleaacaWG5baabeaaaOqaaiabgkGi2kaadMha aaGaey4kaSYaaSaaaeaacqGHciITcaWGvbWaaSbaaSqaaiaadQhaae qaaaGcbaGaeyOaIyRaamOEaaaaaaa@4D81@

Note 2 to entry: The divergence of the vector field U is denoted div U or ∇ ⋅ U.


Publication date:2017-07
Source
Replaces:102-05-20:2007-08
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