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	Continuity equation - Wikipedia, the free encyclopedia
		Continuity equations are the (stronger) local form of conservation laws.
		In electromagnetic theory, the continuity equation is derived from two of Maxwell's equations.
		In fluid dynamics, a continuity equation is an equation of conservation of mass.
	en.wikipedia.org /wiki/Continuity_equation (228 words)

	PlanetMath: continuity equation
		In the former case we apply equations governing the gross behavior of the flow through an integral formulation which is usually easier to treat analytically.
		Since the mentioned disciplines deal with the formulation of the basic laws in terms of finite systems, such formulations are the basis for deriving the control volume equations, concept that we shall develop to continuation.
		This is version 5 of continuity equation, born on 2006-05-31, modified 2006-09-04.
	planetmath.org /encyclopedia/ContinuityEquation.html (1039 words)

	The Omega Equation for Estimating Vertical Flow (Site not responding. Last check: 2007-10-12)
		The problem with using the estimate of ω based upon the continuity equation is that the divergence term depends upon the imperfectly known ageostrophic wind in as much as the divergence of the geostrophic wind is necessarily zero.
		The ω equation which is derived from both the continuity equation and the thermodynamic equation is consistent with both.
		The problem in using the ω equation is that the equation gives a partial differential equation for ω which must be solved to obtain the values of ω.
	www.applet-magic.com /omega.htm (286 words)

	Theory - Kinematic Flood Routing
		The continuity equation is simply a statement that the difference between inflow and outflow must equal the rate of change of storage in the reach being considered.
		This equation is applied around a 'nucleus' of the space-time element which is off-centre and defined by the weighting factors a and b which are applied to the x and t dimensions respectively as shown in Figure 8.4.
		Equation [8.31] is in the form of a diffusion equation where D is the coefficient of diffusion.
	www.alanasmith.com /theory-Kinematic-Flood-Routing.htm (1602 words)

	Aeronautics - Fluid Dynamics - Level 3 (Flow Equations)
		In situations where the fluid may be treated as incompressible and temperature differences are small, the continuity and momentum equations are sufficient to specify the velocities and pressure (that is, four equations [continuity+3 momentum] and four unknown quantities [u,v,w and p]).
		This equation is obtained by replacing the momentum term (density times velocity) by the energy term (density times the sum of the internal and kinetic energies).
		This equation demonstrates that, per unit volume, the change in energy of the fluid moving through a control volume is equal to the rate of heat transferred into the control volume plus the rate of work done by surface forces plus the rate of work done by gravity.
	www.allstar.fiu.edu /aero/Flow2.htm (2444 words)

	6.2 Density Equations
		This partial differential equation is the analog of the Fokker-Planck equation (6.21) for the membrane potential density of integrate-and-fire neurons.
		Equation (6.43) can be rewritten in form of an integral equation for the population activity.
		Integral equations of the form (6.44) are the starting point for a formal theory of population activity; cf.
	diwww.epfl.ch /~gerstner/SPNM/node46.html (3341 words)

	Differential equations of fluid mechanics
		This is known as the equation of continuity, and basically reflects the law of conservation of mass.
		For a monatomic molecule, the factor of 5 in the total energy term on the left side of equation (15) would be replaced by 3, and the factor of 7 on the right-hand side of the equation would be replaced by 5.
		This equation reflects the law of conservation of energy, and also implicitly defines adiabatic behavior, since no energy is added to or subtracted from the system as a whole.
	www.silcom.com /~aludwig/Physics/Main/Differential_equations.html (521 words)

	Euler Equations
		The equations are named in honor of Leonard Euler, who was a student with Daniel Bernoulli, and studied various fluid dynamics problems in the mid-1700's.
		The Euler equations neglect the effects of the viscosity of the fluid which are included in the Navier-Stokes equations.
		The mass flow rate equation developed on the conservation of mass web page is a one dimensional solution of the continuity equation shown here.
	www.grc.nasa.gov /WWW/K-12/airplane/eulereqs.html (659 words)

	Fluid dynamics and Bernoulli's equation
		The equation of continuity states that for an incompressible fluid flowing in a tube of varying cross-section, the mass flow rate is the same everywhere in the tube.
		If the equation was multiplied through by the volume, the density could be replaced by mass, and the pressure could be replaced by force x distance, which is work.
		By applying the continuity equation, the velocity of the fluid is greater in the narrow section.
	physics.bu.edu /~duffy/py105/Bernoulli.html (1199 words)

	Bernoulli Equation
		Both elements in the equation have the unit of pressure and it's common to refer the flow velocity component as the dynamic pressure of the fluid flow (5).
		equation of continuity can be expressed as (e3), it's possible to transform (e1) to (e4).
		Equation of Continuity The Equation of Continuity is a statement of mass conservation
	www.engineeringtoolbox.com /bernouilli-equation-d_183.html (828 words)

	CHAPTER 5 (1/12/98)
		The use of such equations of continuity, then, require you to consider the part of the universe you are interested in, and to construct a closed set of borders around which you will perform a mathematical balance of mass, energy or momentum.
		From this example it should be clear that the problems associated with equations of continuity mainly involve your view of the problem including definition of terms and construction of a box.
		The Navier-Stokes Equation is the equation of continuity for Newtonian fluids of constant viscosity and constant density,
	www.eng.uc.edu /~gbeaucag/Classes/Processing/Chapter2html/Chapter2.html (1592 words)

	Reynolds averaged continuity equation (Site not responding. Last check: 2007-10-12)
		Equation 4.14 is the time accurate continuity equation.
		Equation 4.17 is the Reynolds averaged continuity equation.
		4.14 the continuity equation for turbulence is obtained
	www.le.ac.uk /engineering/ar45/eg7029/eg7029w/node47.html (64 words)

	Equation of Continuity
		The Equation of Continuity is a statement of mass conservation
		Common application where the Equation of Continuity can be used are pipes, tubes and ducts with flowing fluids and gases, rivers, overall processes as power plants, diaries, logistics in general, roads, computer networks and semiconductor technology and more.
		Bernoulli Equation A statement of the conservation of energy in a form useful for solving problems involving fluids.
	www.engineeringtoolbox.com /equation-continuity-d_180.html (526 words)

	Continuity Equation (Site not responding. Last check: 2007-10-12)
		This is a statement of the principle of mass conservation for a steady, one-dimensional flow, with one inlet and one outlet.
		This equation is called the continuity equation for steady one-dimensional flow.
		To continue the freeway analogy, it is the line made up of the lights on all the vehicles that passed through the same toll booth.
	www.princeton.edu /~asmits/Bicycle_web/continuity.html (523 words)

	Example 11.4-1
		These are the steady-state equation of continuity and the x-component of the equation of motion.
		The x-component of the equation of motion is in terms of x and y.
		In a first step towards eliminating y, the equation of energy is integrated from y=0 to y=delta(x)*Delta where Delta is the ratio of the thickness of the thermal boundary layer to the thickness of the velocity boundary layer.
	www.owlnet.rice.edu /~chbe402/ed1projects/proj00/harris/feature2.html (749 words)

	Continuity equation
		The continuity equation describes a basic concept, namely that a change in carrier density over time is due to the difference between the incoming and outgoing flux of carriers plus the generation and minus the recombination.
		This then yields two partial differential equations as a function of the electron density, the hole density and the electric field.
		The diffusion equation will be used to calculate the diffusion current in p-n junctions and bipolar transistors.
	ece-www.colorado.edu /~bart/ecen3320/newbook/chapter2/ch2_9.htm (326 words)

	Bernoulli
		The equation that would relate pressure to velocities (actually one of the most useful equation in engineering) is called Bernoulli's equation and is given as:
		Bernoulli's equation is only valid if one assumes the following: incompressible fluid (fluid velocity less than one third the speed of sound) and inviscid flow (this just means that the point in question along the flow is going to be away from where the flow and the object come into contact).
		This equation basically tells us that, as the flow progresses from one point to another, an increase in speed will be accompanied by a decrease in pressure.
	www.allstar.fiu.edu /aerojava/bernoulli.htm (1116 words)

	The Continuity Equation and Divergence (Site not responding. Last check: 2007-10-12)
		The Continuity Equation is a restatement of the principle of Conservation of Mass applied to the atmosphere.
		In fact, its basic mathematical definition can be traced to the philosophical question...if the top of (a thunderstorm, or a water column) expands from an initial area to a larger area in two hours, what was the percentage (or fractional) change in area over that time interval.
		This equation essentially provides the answer to the question: How do pressure changes (in this context) at sea-level occur (of course, the general expression relates to the bottom of an air column no matter where the base of the air column is found).
	tornado.sfsu.edu /Geosciences/classes/m201/Continuity/Continuity.htm (1309 words)

	The Continuity Equation
		A discussion of the equations governing the flow of ice must begin with an evaluation of the conservation of mass.
		in the continuity equation incorporates the physics of the flow and sliding laws into the problem, since its form depends on the form of the flow and sliding law.
		With the continuity equation determined, all that remains for a complete description of the problem is a discussion of boundary conditions.
	www.umcs.maine.edu /~shamis/papers/theory/node11.html (861 words)

	Continuity Equation
		One of the fundamental principles used in the analysis of uniform flow is known as the Continuity of Flow.
		This principle is derived from the fact that mass is always conserved in fluid systems regardless of the pipeline complexity or direction of flow.
		Once flow and depth are know the continuity equation is used to calculate velocity in the culvert.
	www.fsl.orst.edu /geowater/FX3/help/8_Hydraulic_Reference/Continuity_Equation.htm (200 words)

	Continuity and Conservation of Mass
		This is the form of the continuity equation most often used.
		By the continuity principle, the mass flow rate must be the same at each section - the mass going into the pipe is equal to the mass going out of the pipe.
		Another example of the use of the continuity principle is to determine the velocities in pipes coming from a junction.
	www.efm.leeds.ac.uk /CIVE/CIVE1400/Section3/continuity.htm (964 words)

	88.06.04: The Continuity Equation, the Reynolds Number, the Froude Number
		AV = k where A is the cross sectional area at a point in the pipe, V is the average velocity of the water at the same point and k is a constant, the rate of flow of the pipe, in our units cm/sec.
		Since the equation is true for any two points in the pipe we could also write A1V1 = A2V2 where A1 and V1 are the area and velocity at one point in the pipe, and A2 and V2 are the area and velocity at some other second point in the pipe.
		The way I visualize the continuity equation is to think of a paper wrapper of pennies.
	www.yale.edu /ynhti/curriculum/units/1988/6/88.06.04.x.html (4165 words)

	Analysis of the Effect of Flow Rate on the Doppler Continuity Equation for Stenotic Orifice Area Calculations : A ...
		Nonetheless, the assumption that the Doppler continuity equation
		the Doppler continuity equation to continue to underestimate
		Effects of dobutamine on Gorlin and continuity equation valve areas and valve resistance in valvular aortic stenosis.
	circ.ahajournals.org /cgi/content/full/97/16/1597 (5738 words)

	Continuity Equation
		Satisfying the continuity equation via the Fourier completeness relation (7.117) relies upon the special properties of the (artificial) Brillouin zone created by the q-discretization.
		The derivation of the continuity equation in the continuum case relies on no such property; it follows directly from the antisymmetry of the potential kernel
		In a finite model, however, we must cut off the sequence of k's at some value, and this will remove some terms which would need to be present in the summations of the second term of (7.115) in order to make this term exactly vanish by antisymmetry.
	www.utdallas.edu /~frensley/technical/opensyst/node24.html (428 words)

	No Title
		Because the area is being cut in half as the fluid flows from Region 1 into Region 2, the velocity of the fluid must be increasing, ultimately by a factor of 2 (the relative sizes of the two regions).
		term in Equation 2 must increase, so for the overall equation to stay constant, the pressure must be reduced.
		We can see from Bernoulli's equation that the two factors affecting the pressure that vary between the regions are the height (y) and the velocity (v).
	www.emory.edu /PHYSICS/Faculty/Benson/141/141-99/mcat7sol/mcat7sol.html (328 words)

	The equation of continuity (Site not responding. Last check: 2007-10-12)
		The equation of continuity expresses the conservation of matter--if matter flows away from a point, there must be a decrease in the quantity remaining.
		Since the volume is arbitrary, the continuity equation,
		The hydrodynamic equations are often closely analogous to the electrodynamic equations, but electrodynamics is much easier than hydrodynamics.
	grus.berkeley.edu /~jrg/ay202/node10.html (187 words)

	species continuity (Site not responding. Last check: 2007-10-12)
		The differential equations for the conservation of species A (of a binary mixture of A and B) is obtained by applying the integral equations to the infinitesimal volume at P.
		All properties are continuous, and linear terms in the Taylor's expansion are used to describe properties at adjacent point.
		After our struggle with the energy equation, developing the species continuity equation in vector form should be a piece of cake:
	www.rit.edu /~pnveme/EMEM851n/naturallaws/species_continuity.html (165 words)

	The momentum equation for flow through a nozzle (Site not responding. Last check: 2007-10-12)
		Assume that the inlet is connected to a high pressure tank and that the flow can leave the outlet freely, e.g., into a vacuum.
		then these two equations would be identical and so the velocity flow through the pipe would be exactly the same as the flow through the wind.
		This difference is due to the fact that the velocity does not vary proportional to density for a compressible gas in a flow pipe.
	grus.berkeley.edu /~jrg/ay202/node108.html (663 words)

	seminar "Evolution equations in probability spaces and the continuity equation" (Site not responding. Last check: 2007-10-12)
		It is the aim of the seminar to study Chapters 5 through 8 of [1], which are dedicated to this topic.
		Philippe Clément and I are going to study Chapters 5 through 8 of [1] by means of a weekly seminar during the Spring semester 2006.
		Our goal is to understand gradient flows in metric spaces, optimal transportation of measures, the Wasserstein metric on a space of probability measures, and how they can be used to solve the continuity equation and give a probabilistic interpretation of the solution.
	www.math.leidenuniv.nl /~vangaans/seminarEEPSCE.html (339 words)

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