# Consider a compressible flow where an elemental volume of the fluid is $\delta \vartheta,$ moving with velocity $\vec{V}$. Which one of the following expressions is TRUE? (A) $\nabla \cdot \vec{V}=\frac{1}{\delta \vartheta} \frac{D \delta \vartheta}{D t}$ (B) $\nabla \cdot(\nabla \times \vec{V})=\frac{1}{\delta \vartheta} \frac{D \delta \vartheta}{D t}$ (C) $\nabla \cdot \frac{D \vec{V}}{D t}=\frac{1}{\delta \vartheta} \frac{D \delta \vartheta}{D t}$ (D) $\vec{V} \cdot(\nabla \times \vec{V})=\frac{1}{\delta \vartheta} \frac{D \delta \vartheta}{D t}$

## Question ID - 156006 | Toppr Answer Consider a compressible flow where an elemental volume of the fluid is $\delta \vartheta,$ moving with velocity $\vec{V}$. Which one of the following expressions is TRUE? (A) $\nabla \cdot \vec{V}=\frac{1}{\delta \vartheta} \frac{D \delta \vartheta}{D t}$ (B) $\nabla \cdot(\nabla \times \vec{V})=\frac{1}{\delta \vartheta} \frac{D \delta \vartheta}{D t}$ (C) $\nabla \cdot \frac{D \vec{V}}{D t}=\frac{1}{\delta \vartheta} \frac{D \delta \vartheta}{D t}$ (D) $\vec{V} \cdot(\nabla \times \vec{V})=\frac{1}{\delta \vartheta} \frac{D \delta \vartheta}{D t}$

(A) $\nabla \cdot \vec{V}=\frac{1}{\delta \vartheta} \frac{D \delta \vartheta}{D t}$