An equation in fluid dynamic ~ me ~

AI Thread Summary
The discussion revolves around a challenging equation encountered in fluid dynamics, with a potential connection to Gauss's Divergence Theorem. Participants suggest that the equation can be proven by analyzing each vector component and applying the divergence theorem, linking it to the conservation of mass. There is a request for clarification on the explanation provided, particularly regarding the term "etc." and a desire for a more explicit solution. The conversation highlights the complexity of fluid dynamics equations and the need for detailed understanding in proving them. Overall, the thread emphasizes collaboration in solving advanced mathematical problems in fluid dynamics.
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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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