IEVref:102-05-20ID:
Language:enStatus: backup
Term: divergence
Synonym1:
Synonym2:
Synonym3:
Symbol:
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 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 The divergence of the vector field U is denoted div U or ∇ ⋅ U.


Publication date:2007-08
Source
Replaces:
Internal notes:
CO remarks:
TC/SC remarks:
VT remarks:
Domain1:
Domain2:
Domain3:
Domain4:
Domain5: