Continuity Equation - A Closed System Approach

We know that the conservation of mass is inherent to the definition of a closed system as Dm/Dt = 0 (where m is the mass of the closed system).

However, the general form of continuity can be derived from the basic equation of mass conservation of a system.

Derivation :-

Let us consider an elemental closed system of volume V and density ρ.

Now  (dilation per unit volume)

In vector notation we can write this as

The above equations are same as that formulated from Control Volume approach