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The Equation of Continuity is the four dimensional derivative of a four dimensional variable set to zero. This is also called the limit equation and the Boundary equation, and the Homeostasis Equation. The Continuity Equation is also called the Invariant Equation or Condition. The most famous equation that is in fact a continuity Equation is Maxwell's Electromagnetic equations.
(d/dR + Del)(Br + Bv) = (dBr/dR -Del.Bv) + (dBv/dR + DelxBv + Del Br) = 0
This gives two equations the real Continuity Equation:
0=(dBr/dR - Del.Bv)
and the vector Continuity Equation:
0=(dBv/dR + Del Br)
This Equation will be more familiar when R=ct and dR=cdt and cB = E then
0=(dBr/dt - Del.Ev) and
0=(dBv/dt + Del Er)
The Continuity Equation says the sum of the derivatives is zero. The four dimensional variable has two parts a real part Br and a vector part Bv. The Continuity Equation is the sum of the real derivatives is zero and the sum of the vector derivatives is zero.
The term DelxBv is zero at Continuity because this term is perpendicular to both the other two terms and makes it impossible geometrically for the vectors to sum to zero unless it is zero.
Only if the DelxBv=0 can the vectors sum to zero. This situation occurs when the other two terms are parallel or anti-parallel. If anti-parallel then dBv/Dr is equal and opposite to Del Br and the vectors sum to zero.
This is Newton's Equal and Opposite statement in his 3rd Law and is a geometrical necessity for the vectors to sum to zero..
Many Equations of Physics have misrepresented the Continuity Equation and others have not recognized the continuity Equation as in Maxwell's Equations.
The Continuity Equation is probably the most important equation in science!
The Four dimensional space of science is a quaternion non-commutative (non-parallel) space defined by William Rowan Hamilton in 1843, (i,j,k and 1), with rules i^2=j^2=k^2=-1.
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How are the continuity equation and bernoulli's equation related?
The continuity equation states that the mass flow rate is constant in an incompressible fluid, while Bernoulli's equation relates the pressure, velocity, and elevation of a fluid in steady flow. Together, they help describe the relationship between fluid velocity, pressure, and flow rate in a system. The continuity equation can be used to derive Bernoulli's equation for incompressible fluids.
What is the physical meaning of the continuity equation?
The continuity equation in fluid dynamics states that the total mass entering a system must equal the total mass leaving the system, accounting for any accumulation within the system. This equation describes the conservation of mass for a fluid flow, showing how the flow velocity and cross-sectional area of the fluid affect the mass flow rate.
What is continuity equation tell us?
The continuity equation states that in a steady flow, the mass entering a system must equal the mass leaving the system. It expresses the principle of conservation of mass and is used to analyze fluid flow in various engineering applications. The equation is often written in the form of mass flow rate or velocity profile to describe how fluid moves through a system.
Continuity equation for time varying field?
The continuity equation for a time-varying field relates the divergence of the field with the rate of change of field strength at any given point. Mathematically, it is expressed as ∇⋅E = -∂ρ/∂t, where ∇ is the divergence operator, E is the field, ρ is the charge density, and ∂/∂t represents the partial derivative with respect to time. This equation ensures that the field and charge distributions are consistent over time, in accordance with the principle of charge conservation.
What is the physical interpretation of continuity equeation of charges?
The continuity equation for charges describes the conservation of electric charge in a given region. It states that the rate of change of charge density in a region is equal to the divergence of the current density. In physical terms, this means that any change in the amount of charge in a region must be balanced by the movement of charge into or out of that region.
How are the continuity equation and bernoulli's equation related?
The continuity equation states that the mass flow rate is constant in an incompressible fluid, while Bernoulli's equation relates the pressure, velocity, and elevation of a fluid in steady flow. Together, they help describe the relationship between fluid velocity, pressure, and flow rate in a system. The continuity equation can be used to derive Bernoulli's equation for incompressible fluids.
What is continuity equation in fluid mechanics?
Area*Velocity=Constant
When is the speed of a fluid maximum in a venturi meter?
from the continuity equation A1v1 = A2v2 according to the continuity equation as the area decreases the velocity of the flow of the liquid increases and hence maximum velocity can be obtained at its throat
What is continuity equation for compressible fluids?
The continuity equation for compressible fluids states that the rate of change of density (ρ) in a fluid is equal to -∇⋅(ρu), where ρ is density, u is velocity, and ∇⋅ is the divergence operator. This equation is derived from the conservation of mass principle in fluid dynamics.
How do jet engines provide a forward thrust for an airplane by using the continuity Equation?
they move
What has the author Ph W Zettler-Seidel written?
Ph. W. Zettler-Seidel has written: 'Nomograms for three ramjet performance equations (continuity equation, pressure equation, combustion equation)'
How equation of continuity applied on rocket?
in rockets the area of crossection for the ejection of smoke is made small, so according to the equation of continuity the speed of gases increases. this leads to raise the speed (and momentum) of the rocket, and chamge in momentum becomes rapid. as change in momentum gives force, the force on the the rocket increases and it flies fast.
What is the physical meaning of the continuity equation?
The continuity equation in fluid dynamics states that the total mass entering a system must equal the total mass leaving the system, accounting for any accumulation within the system. This equation describes the conservation of mass for a fluid flow, showing how the flow velocity and cross-sectional area of the fluid affect the mass flow rate.
How come in a turbojet afterburner the exhaust gas velocity increase and also pressure increase does it have to do with continuity equation and also confused between continuity and Bernoulli's?
the pressure increases because the gas is expanding at a very fast rate.
What is continuity equation tell us?
The continuity equation states that in a steady flow, the mass entering a system must equal the mass leaving the system. It expresses the principle of conservation of mass and is used to analyze fluid flow in various engineering applications. The equation is often written in the form of mass flow rate or velocity profile to describe how fluid moves through a system.
Derivation of continuity equation in cartesian coordinates?
There are basically SEVERAL continuity equations, one for each conserved quantity. The equations themselves are simply statements that matter (in the example of conservation of mass) will not appear out of nothing, or suddenly teleport to a far-away place.
What does a well written SOP provide the Soldier in the absence of leadership?
Continuity
