# $\phi(x, y)$ 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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(B) $\nabla \times \vec{V}=0$

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For a quasi-one-dimensional isentropic supersonic flow through a diverging duct, which of the following is true in the direction of the flow?
(A) Both the Mach number and the static temperature increase.
(B) The Mach number increases and the static temperature decreases.
(C) The Mach number decreases and the static temperature increases.
(D) Both the Mach number and the static temperature decrease. 