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

1 Answer - 5876 Votes

3537

Answer Key : (A) -

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



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