Continuity Equation using Reynolds Transport Theorem

Reynolds Transport Theorem for a steady flow

$$\frac{d}{dt}(B_{\text{sys}})={\int }_{\text{CS}}\beta \rho (\vec{v}\cdot \vec{n})dA$$

Where, $B$ is a property and  $\beta$ is the property per infinitesimal mass  $dm$ The property we are looking for is mass (Continuity = Conservation of Mass)
Plug $B=dm$ above equation becomes

$$\boxed{0={\int }_{\text{CS}}\rho (\vec{v}\cdot \vec{n})dA}$$