Continuity Equation

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continuity equation

[‚känt·ən′ü·əd·ē i′kwā·zhən]
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 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.


References in periodicals archive ?
As per continuity equation, the mass flow rate (product of fluid density, tube's cross-sectional area, and the fluid velocity) remains constant throughout the capillary tube.
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Equation (3) is the continuity equation expressing the conservation of mass.
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Pressure-velocity coupling is achieved by discretisation of the continuity equation to derive an equation for pressure from the discrete continuity equation.
To derive the continuity equation of a phase, the Boltzmann equation is multiplied by the characteristic mass of the phase and is integrated over the velocity space.
The terms responsible for the gravity wave speed are the pressure gradient term in the momentum equation, g[nabla][zeta], and the divergence term in the continuity equation [nabla].
Redefining the gravitational energy density and the gravitational pressure density, the continuity equation has been satisfied.
The corresponding continuity equation of an incompressible fluid is

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