- #1

joshmccraney

Gold Member

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Can someone help me understand why, when writing the continuity equation we write: $$\frac{\partial}{\partial t} \iiint_v \rho \, dv$$ instead of $$ \iiint_v \frac{\partial}{\partial t} \rho \, dv$$

I understand the two are not necessarily the same, but why derive it the first way rather than the second?

Intuitively, the first seems to be saying "add up all the mass and then see how it changes in time" where as the second seems to say "see how density changes in time at each location and then add it all up".

I'm just having trouble understanding the second integral.

Thanks!

Josh