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
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
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