<P> where ρ (\ textstyle \ rho) is the density (mass per unit volume), t (\ textstyle t) is the time, ∇ ⋅ (\ textstyle \ nabla \ cdot) is the divergence, and v (\ textstyle \ mathbf (v)) is the flow velocity field . The interpretation of the continuity equation for mass is the following: For a given closed surface in the system, the change in time of the mass enclosed by the surface is equal to the mass that traverses the surface, positive if matter goes in and negative if matter goes out . For the whole isolated system, this condition implies that the total mass M (\ textstyle M), sum of the masses of all components in the system, does not change in time, i.e. </P> <P> d M d t = d d t ∫ ρ d V = 0 (\ displaystyle (\ frac ((\ text (d)) M) ((\ text (d)) t)) = (\ frac (\ text (d)) ((\ text (d)) t)) \ int \ rho (\ text (d)) V = 0), </P> <P> where d V (\ textstyle (\ text (d)) V) is the differential that defines the integral over the whole volume of the system . </P> <P> The continuity equation for the mass is part of Euler equations of fluid dynamics . Many other convection--diffusion equations describe the conservation and flow of mass and matter in a given system . </P>

Who came up with law of conservation of mass