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IEVref: | 102-05-20 | ID: | |

Language: | en | Status: Standard | |

Term: | divergence | ||

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Definition: | scalar div 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 infinitesimalU$\mathrm{div}U=\underset{V\to 0}{\mathrm{lim}}\frac{1}{V}{\displaystyle \underset{\text{S}}{\u222f}U\cdot {e}_{n}\mathrm{d}A}$ where Note 1 to entry: In orthonormal Cartesian coordinates, the divergence is: $\mathrm{div}U=\frac{\partial {U}_{x}}{\partial x}+\frac{\partial {U}_{y}}{\partial y}+\frac{\partial {U}_{z}}{\partial z}$ Note 2 to entry: The divergence of the vector field or U∇ ⋅ . U | ||

Publication date: | 2017-07 | ||

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Replaces: | 102-05-20:2007-08 | ||

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$\mathrm{div}U=\underset{V\to 0}{\mathrm{lim}}\frac{1}{V}{\displaystyle \underset{\text{S}}{\u222f}U\cdot {e}_{n}\mathrm{d}A}$

where *e*_{n}d*A* is the vector surface element oriented outwards and *V* is the volume

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

$\mathrm{div}U=\frac{\partial {U}_{x}}{\partial x}+\frac{\partial {U}_{y}}{\partial y}+\frac{\partial {U}_{z}}{\partial z}$

Note 2 to entry: The divergence of the vector field ** U** is denoted div