Which of the following is the correct form of the mass divergence form of the continuity equation for a compressible fluid?
[In the given equations, $\rho$ is the density and $\mathbf{V}$ the three dimensional velocity vector of the fluid.]
- $\frac{\partial \rho}{\partial t}+\nabla \times(\rho \mathbf{v})=0$
- $\frac{\partial \rho}{\partial t}+\nabla \cdot(\rho \mathbf{v})=0$
- $\frac{\partial \mathbf{v}}{\partial t}+\rho \cdot \nabla \mathbf{v}=0$
- $\frac{\partial \rho}{\partial t}+\mathbf{v} \cdot \nabla \rho=0$
- $\textsf{(i)}$ and $\textsf{(ii)}$
- $\textsf{(ii)}$
- $\textsf{(i)}$ and $\textsf{(iv)}$
- $\textsf{(iii)}$
