$\phi(x, y)$ represents the velocity potential of a two-dimensional flow with velocity field $\vec{V}=u(x, y) \hat{\imath}+v(x, y) \hat{\jmath},$ where $\hat{\imath}$ and $\hat{\jmath}$ are unit vectors along the $x$ and $y$ axes, respectively. Which of the following is necessarily true?
(A) $\nabla^{2} \phi=0$
(B) $\nabla \times \vec{V}=0$
(C) $\nabla \cdot \vec{V}=0$
$(\mathrm{D}) u=-\partial \phi / \partial y, v=\partial \phi / \partial x$

Question ID - 155435 :-

$\phi(x, y)$ represents the velocity potential of a two-dimensional flow with velocity field $\vec{V}=u(x, y) \hat{\imath}+v(x, y) \hat{\jmath},$ where $\hat{\imath}$ and $\hat{\jmath}$ are unit vectors along the $x$ and $y$ axes, respectively. Which of the following is necessarily true?
(A) $\nabla^{2} \phi=0$
(B) $\nabla \times \vec{V}=0$
(C) $\nabla \cdot \vec{V}=0$
$(\mathrm{D}) u=-\partial \phi / \partial y, v=\partial \phi / \partial x$

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