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.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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 v_x, v_y, and v_z 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 ρS_v = const.

S. M. TARG

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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.

Two-phase VOF model for the refrigerant flow through adiabatic capillary tube

It will be shown that in the far zone, where radiative EM fields prevail, the generalized EM energy-momentum tensor yields the standard continuity equation (Poynting theorem), hence implying equal propagation (retardation) rates for both bound and radiative EM field components.

Propagation of electromagnetic fields in near and far zones: actualized approach with non-zero trace electro-magnetic energy-momentum tensor

Equation (3) is the continuity equation expressing the conservation of mass.

MHD stability of a self-gravitating rotating streaming perfectly conducting compressible fluid medium

A continuity equation is derived for the conserved energetic field quantities averaged over the waveguide cross section.

The real-valued time-domain TE-modes in lossy waveguides

Continuity equation, motion equation and constitutive equation[9] are used as follows:

Stress and deformation of residual oil film in the complex pore

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.

Engineering fluid mechanics, 9th ed

The partial differential equations (pdes) governing fluid flow and heat transfer include the continuity equation, the Navier-Stokes equations and the energy equation (Grigore &Popa, 2009).

Contributions regarding numerical simulation of fluid flow in a plate heat exchanger

Pressure-velocity coupling is achieved by discretisation of the continuity equation to derive an equation for pressure from the discrete continuity equation.

An analysis on the proportional mixing of liquids using venturi jet mixer

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.

An improved LES on dense particle-liquid turbulent flows using integrated Boltzmann equations

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].

An additive Schwarz preconditioner for the spectral element ocean model formulation of the shallow water equations

Redefining the gravitational energy density and the gravitational pressure density, the continuity equation has been satisfied.

Thermodynamics of the FRW Universe at the Event Horizon in Palatini f(R) Gravity