If we denote the density of a fluid media as $\rho$ and $\vec{q}$ as the flow velocity vector, then the equation $$\frac{1}{\rho}\bigg(\frac{\partial \rho}{\partial t}+\vec{q}.\vec{\nabla}\rho\bigg)+\vec{\nabla}.\vec{q}=0$$ is the equation of
$(a)$ conservation of mass.
$(b)$ conservation of angular momentum.
$(c)$ conservation of linear momentum.
$(d)$ conservation of energy.
At the first sight, I was unable to recognize what type of particular equation of fluid motion it is related to, so I took a rather naive approach. We know that the equation of continuity (which is rather an equation of conservation of mass) is given by $$\frac{D\rho}{Dt}+\rho\vec{\nabla}.\vec{q}=0$$ where $\displaystyle{\frac{D}{Dt}}$ is the material derivative operator. Substituting this to the original equation gives us $$\frac{\partial \rho}{\partial t}+\vec{q}.\vec{\nabla}\rho-\frac{D\rho}{Dt}=0 \\ \implies \bigg(\frac{D}{Dt}-\frac{\partial}{\partial t}\bigg)\rho=\vec{q}.\vec{\nabla}\rho$$ which becomes an obvious identity if we break the operator in LHS. That's where I'm stuck as I cannot relate the conservation of momentum or mass or energy in any of the cases. How to approach for this type of problems if the given equations are unknown as in this case? Any help is appreciated.