# Continuity equation

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The **continuity equation** expresses the conservation of mass. It is a direct consequence of Gauss theorem.

If the mass enclosed in a region is , by definition of mass density :

The net loss of matter in this region must be caused by an outward flow across its boundary:

According to Gauss theorem,

Since the region is a general one, and it does not change with time, the resulting equation is

As a direct consequence an incompressible fluid, with constant , implies a solenoidal velocity field: .