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continuity equation[‚känt·ən′ü·əd·ē i′kwā·zhən]
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 vx, vy, and vz 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 ρSv = const.
S. M. TARG