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I have the following slide, and whilst I understand that the original point is "the rate of density, ρ, in each volume element is equal to the mass flux"....i am totally lost on the mathematics! (And I am meant to be teaching this tomorrow). I do not have any information on what the indivudual symbols refer to, I guess A is area and t is time etc. Can anyone understand this:

-∇(ρv)=[itex]\frac{\partial}{\partial t}[/itex](ρd[itex]\tau[/itex]) where d[itex]\tau[/itex]=Adx

-∇.v = [itex]\frac{\partial}{\partial t}[/itex] (Adx)

-[itex]\frac{\partial v}{\partial x}[/itex] Adx = [itex]\frac{\partial}{\partial t}[/itex](Adx)

-[itex]\frac{\partial v}{\partial x}[/itex]=[itex]\frac{1}{A}[/itex] [itex]\frac{\partial A}{\partial T}[/itex]

Unfortunately I am not sure how to even get from line 1 to 2

and how t combine partial with full!

Argh! Thank you in advance!!!

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# Continuity equation, partial derivative and differential operators

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