Continuity equation

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.