1 / 16

F (x, y) = <x, y>

F (x, y) = <y, -x>. F (x, y) = <x, y>. Div F = 0. Div F = 2 > 0. The divergence of a vector field at a point (x, y, z) corresponds to the net flow Of fluid out of a small box centered at (x, y, z). If Div F > 0, more fluid exits the

piper
Télécharger la présentation

F (x, y) = <x, y>

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. F (x, y) = <y, -x> F (x, y) = <x, y> Div F = 0 Div F = 2 > 0 The divergence of a vector field at a point (x, y, z) corresponds to the net flow Of fluid out of a small box centered at (x, y, z). If Div F > 0, more fluid exits the Box than enters (as in the figure on the left) and we call the point a source. If Div F <0, more fluid enters the box than exits and we call the point a sink. If Div F = 0, throughout some region D, then we say that the vector field F is Source-free or incompressible.

  2. F (x, y, z) = <x, y, 0> Curl F = <0, 0, 0> F (x, y, z) = <y, -x, 0> Curl F = <0, 0, -2> The curl of a vector filed at a point measures the rotation of the fluid at the point. The direction of the vector Curl F is determined by the right hand rule (curl the Fingers of your right hand along the flow lines with your fingertips pointing in the Direction of the flow, your thumb will point to the direction that is parallel to Curl F. If Curl F = zero vector, then the vector field F is irrotational (as in the figure on the Left).

More Related