Derivation of continuity equation

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Homework Statement



Hi. I have a problem in fluid mechanics that is asking me to derive the conservation of mass equation using an infinitesimal control volume.


My problem is I do not know if I should be treating this problem as a fixed element or if the element is a parcel and its particles are tracked through together in time (a Langrangian method). Which would you assume?

I can solve the former, but if there is supposed to be such a thing for the latter I am not sure how to go about it. Would it be similar to a langangrian finite control volume?
 

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