# Continuity Equation

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## continuity equation

[‚känt·ən′ü·əd·ē i′kwā·zhən] (physics)

An equation obeyed by any conserved, indestructible quantity such as mass, electric charge, thermal energy, electrical energy, or quantum-mechanical probability, which is essentially a statement that the rate of increase of the quantity in any region equals the total current flowing into the region. Also known as equation of continuity.

## Continuity Equation

one of the equations of hydrodynamics that expresses the law of the conservation of mass for any volume of moving liquid or gas. In Euler variables the continuity equation has the form

where ρ is the density of the fluid, v is its velocity at a given point, and v_{x}, v_{y}, and v_{z} are the components of the velocity along the coordinate axes. If the fluid is incompressible (ρ = const), then the continuity equation takes the form

For steady, one-dimensional flow in a pipe or channel with a cross-sectional area *S*, the continuity equation gives the law of constancy of the flow rate ρ*S _{v}* = const.

S. M. TARG