An equation in fluid dynamic ~please help me ~

[abcdefg10645]

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 ?

 

[cortiver]

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.

 

[Pythagorean]

Iirc, you can get at it from conservation of mass:

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

 

[abcdefg10645]

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~