An equation in fluid dynamic ~ me ~

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Discussion Overview

The discussion revolves around a challenging equation encountered in fluid dynamics, with participants exploring potential proofs and relationships to established theorems, such as Gauss's Divergence Theorem. The conversation includes requests for clarification and assistance in understanding the equation and its implications.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant expresses uncertainty about proving a complex fluid dynamics equation and suggests a possible connection to Gauss's Divergence Theorem.
  • Another participant proposes that the equation can be approached by analyzing each vector component separately and applying the divergence theorem.
  • A different participant references the conservation of mass as a potential starting point for understanding the equation, mentioning the product rule in their explanation.
  • A follow-up request for clarification is made regarding the term "etc." and a desire for a more explicit solution to the problem.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to prove the equation, and multiple viewpoints and methods are presented without resolution.

Contextual Notes

Some assumptions and definitions related to the equation and theorems are not fully articulated, which may affect the clarity of the discussion.

abcdefg10645
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When I studied the fluid dynamic , I saw a quite hard equation (typed in attached file) ,

I don't know how to prove it , maybe there's a somehow relationship between this eq with Gauss's Divergence Theorem ...

Can anyone help me ?
 

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abcdefg10645 said:
When I studied the fluid dynamic , I saw a quite hard equation (typed in attached file) ,

I don't know how to prove it , maybe there's a somehow relationship between this eq with Gauss's Divergence Theorem ...

Can anyone help me ?

Your equation is a relation between vectors, but you can prove it by considering each vector component separately and applying the divergence theorem.
 
Iirc, you can get at it from conservation of mass:

dm=o
d(pV) =0
(product rule)
etc...
 
Pythagorean said:
Iirc, you can get at it from conservation of mass:

dm=o
d(pV) =0
(product rule)
etc...

Well,I cannot fully understand what the term "etc" mean , could you be more explicit , or can you just type the solution to this annoying question ?


Thanks again if I get any reply~
 

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