# 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 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

References in periodicals archive ?
In hydraulics routing used from continuity equation and movement equation and it is based on the nonpermanent streams theory.
The continuity equation of the motion of the fluid [nabla].
Equation (3) is the continuity equation expressing the conservation of mass.
Continuity equation, motion equation and constitutive equation[9] are used as follows:
The topics are fluid properties, fluid statics, flowing fluids and pressure variation, the control volume approach and the continuity equation, momentum equation, the energy equation, dimensional analysis and similitude, surface resistance, flow in conduits, drag and lift, compressible flow, flow measurements, turbomachinery, and flow in open channels.
Each of the mass flow rates satisfies the continuity equation,
Accordingly, only the steady-state part of the solution to the continuity equation is of interest.
0] f([eta]) and using continuity equation together with boundary condition at y = 0, we have
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.
Notice that the divergence operator in the continuity equation has been integrated by parts.
With the flow depth and velocity at the approach and for a computed discharge representing the design discharge, the velocity and flow depth were computed at the contraction of the abutment in the flood plain using Bernoulli's energy equation without elevation terms (11) and Continuity equation (12).

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