The potential flow model for a storm is represented by the superposition of a sink and a vortex. The stream function can be written in the $(r, \theta)$ system as $\psi=-\frac{\Lambda}{2 \pi} \theta+\frac{\Gamma}{2 \pi} \ln r,$ where $\Lambda=\Gamma=100 \mathrm{~m}^{2} / \mathrm{s}$. Assume a constant air density of $1.2 \mathrm{~kg} / \mathrm{m}^{3}$. The gauge pressure at a distance of $100 \mathrm{~m}$ from the storm eye is

(A) -\infty

(B) $-\frac{1.2}{\pi^{2}}$

(C) $-\frac{1.2}{2 \pi^{2}}$

(D) $-\frac{1.2}{4 \pi^{2}}$

The potential flow model for a storm is represented by the superposition of a sink and a vortex. The stream function can be written in the $(r, \theta)$ system as $\psi=-\frac{\Lambda}{2 \pi} \theta+\frac{\Gamma}{2 \pi} \ln r,$ where $\Lambda=\Gamma=100 \mathrm{~m}^{2} / \mathrm{s}$. Assume a constant air density of $1.2 \mathrm{~kg} / \mathrm{m}^{3}$. The gauge pressure at a distance of $100 \mathrm{~m}$ from the storm eye is

(A) -\infty

(B) $-\frac{1.2}{\pi^{2}}$

(C) $-\frac{1.2}{2 \pi^{2}}$

(D) $-\frac{1.2}{4 \pi^{2}}$

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