Divergence of mass current density

AI Thread Summary
The expression involving the divergence of mass current density, represented as δt · div(j_m(r,t)), relates to the mass produced or annihilated in a volume element dV around the position vector r during a short time interval δt. The mass current density j_m is defined as the product of mass density ρ_m and velocity v. The discussion seeks clarification on whether this expression accurately reflects the changes in mass within the specified volume over time. Understanding this concept is crucial for analyzing mass transport phenomena in fluid dynamics and related fields. The inquiry emphasizes the importance of precise interpretation in the context of mass conservation principles.
saunderson
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Hi,

i thought a while about the meaning of the following expression


\delta t \, \cdot \, \mathrm{div} \, \vec j_m(\vec r,t) \qquad \mathrm{with} \qquad \vec j_m(\vec r,t) = \rho_m(\vec r,t) \cdot \vec v(\vec r, t)​
Does it indicates the mass, which is produced / annihilated in the Volume \mathrm{d}V located around the position vector \vec r in the short time interval \delta t!?

I'm pretty sure that it was something like this but not entirely.So, thanks for your effort and with best regards...
 
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