From Glossary of Meteorology
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In hydrodynamics, a point, line, or area at which mass or energy is added to a system, either instantaneously or continuously.

Conversely, a sink is a point where mass or energy is removed from the system. An incompressible fluid will possess sources or sinks of mass only at points where the divergence of its velocity vector is nonzero; a source is associated with positive divergence and a sink with negative divergence (convergence). The fluid is usually assumed to pass outward from a source or inward to a sink equally in all directions along radial lines. The strength of a source, for example, the rate of mass flow of fluid of unit density across a curve enclosing the source, is given by
where r is the distance from the source and vn the radial speed.