Divergence Theorem

From ExoDictionary
Jump to: navigation, search
This definition page has been automatically generated.
You can help ExoDictionary by expanding, updating, or correcting it.

This autostub has not yet had its initial copyediting proof and may contain significant formatting and even factual errors. You can improve Exodictionary by cleaning up the page markup and verifying that the definition is correct and then removing this tag.

This autostub has not yet had its initial categorization proof and may be categorized incorrectly. You can improve Exodictionary by removing inappropriate categories and then removing this tag.

Divergence Theorem

The statement that the volume integral of the divergence of a vector, such as the velocity U, over the volume V is equal to the surface integral of the normal component of U over the surface s of the volume, often called the export through the closed surface, provided U and its derivatives are continuous and single-valued throughout V and s. This may be written

Missing Image:img src="SP7-d_files/84diverg.gif" height="30" width="199"
where n

is a unit vector normal to the element of surface ds, and the symbol Missing Image:img src="SP7-d_files/integralpath.gif" Missing Image:img src="SP7-d_files/integralpath.gif" indicates that the integration is to be carried out over a closed surface. This theorem is sometimes called Green's ''theorem in the plane for the case of two-dimensional flow, and Green's theorem in space for the three-dimensional case described above. Also called Gauss theorem. </dd>
The divergence theorem is used extensively in manipulating the meteorological equations of motion and aerodynamic equations of motion. </dd>


This article is based on NASA's Dictionary of Technical Terms for Aerospace Use