Divergence theorm example for 28 Nov 12:00

In summary, the conversation revolves around understanding a concept using a word document with complicated characters and using the divergence theorem. The solution attempted involved changing the form of the equations and comparing them, but there was an issue with the left and right hand side. However, the link provided could not be opened due to a missing plug in.
  • #1
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Homework Statement



Hi. I think it will be easiest to understand if I upload a word document as it has some complicated characters. The bold letters stand for vectors.

http://www.sendspace.pl/file/1f830d4ff025d966f71b62c

Homework Equations



Divergence theorm

http://www.math.oregonstate.edu/hom...ulusQuestStudyGuides/vcalc/diverg/diverg.html

The Attempt at a Solution



I tried to change the form of the those two equations to the form stated in divergence theorm and then to compare the u (or F as in link above), but the u (F) on the left hand side is never equal to this on the right.
 
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  • #2
Unfortunately, I am not able to open your links because I "do not have the correct plug in". And most people are very wary of opening links or, certainly, down loading plug ins from unknown sites.
 

1. What is the Divergence Theorem?

The Divergence Theorem is a mathematical theorem that relates the flux of a vector field through a closed surface to the divergence of the field within the volume enclosed by the surface.

2. How is the Divergence Theorem used in science?

The Divergence Theorem is used in various scientific fields, such as physics, engineering, and mathematics, to calculate the flow of vector fields through different surfaces and volumes. It is particularly useful in fluid dynamics and electromagnetism.

3. Can you provide an example of the Divergence Theorem in action?

One example of the Divergence Theorem is calculating the volume flow rate of a fluid through a closed surface, such as a pipe or a nozzle. By knowing the divergence of the fluid velocity field within the volume enclosed by the surface, the flux through the surface can be determined using the Divergence Theorem.

4. What is the significance of the Divergence Theorem in mathematics?

The Divergence Theorem is an important tool in vector calculus and is used to solve many problems in physics and engineering. It also provides a deeper understanding of the relationships between flux, divergence, and the geometry of the surface and volume being considered.

5. Are there any limitations to the Divergence Theorem?

The Divergence Theorem is only applicable to closed surfaces and cannot be used for surfaces with holes or openings. Additionally, it assumes that the vector field is well-behaved and continuous within the enclosed volume.

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