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Difference between revisions of "Continuity equation"

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One of the basic equations in hydrodynamics, expressing the law of conservation of mass for any volume of a moving fluid (or gas). In Euler variables the continuity equation has the form
 
One of the basic equations in hydrodynamics, expressing the law of conservation of mass for any volume of a moving fluid (or gas). In Euler variables the continuity equation has the form
  

Revision as of 17:35, 28 March 2013


One of the basic equations in hydrodynamics, expressing the law of conservation of mass for any volume of a moving fluid (or gas). In Euler variables the continuity equation has the form

where is the density of the fluid, is its velocity at a given point, and are the projections of the velocity on the coordinate axes. If the fluid is incompressible , then the continuity equation takes the form

For a stationary one-dimensional flow in a tube, canal, etc., with cross-sectional area , the continuity equation gives the law for the flow.

How to Cite This Entry:
Continuity equation. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Continuity_equation&oldid=29562
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article