answersLogoWhite

0

What is the equation of continuity?

Updated: 9/14/2023
User Avatar

Wiki User

15y ago

Best Answer

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.

User Avatar

Wiki User

15y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: What is the equation of continuity?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Continue Learning about Physics
Related questions

How are the continuity equation and bernoulli's equation related?

Continuity equations describe the movement of constant. Bernoulli's equation also relates to movement, the flow of liquids. For some situations, where the liquid flowing is a constant, both a continuity equation and Bernoulli's equation can be applied.


What is continuity equation tell us?

fluid flow.


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


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)'


What are the physical significances of equation of continuity?

it is the mathematical representation of principle of conservation of masses that flow into a controlled volume.


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.


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.


Continuity equation for time varying field?

The Continuity Equation for a time varying field Eris:dEr/cdt = Del.Ev where Ev is the vector field associated with the real time varying field.Er + Ev =E, constitute a quaternion field.Del.Ev is the Divergence of the vector field.The Continuity Equation is a statement that the time variation of the real field is equal to the Divergence of the vector field. or more succinctly, the quaternion field E=Er + Ev is Real invariant.The Vector part of the variation is 0= dEv/cdt + Del Er + DelxEv , this is Vector Invariance of E. This is not the Continuioty Equatin but the Induction Equation. Together they represent the Invariance of the quaternion field E=Er + Ev.Because quaternions are not taught in schools yet, few realize the relationship between Continuity and Induction, they are the Real and Vector parts of Invariance!


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