4. Consider a model of a tornado* composed of superposition of a sink, $v_r = -Q/(2\pi r)$, $v_\theta = 0$, $Q > 0$, with a vortex $v_r = 0$, $v_\theta = \Gamma/(2\pi r)$, $\Gamma > 0$.
(a) Determine the streamfunction for this flow¹.
(b) Determine the equation of the streamline, $r(\theta)$, passing through the point
(given in polar coordinates) $(r, \theta) = (R, 0)$.
(c) Sketch the streamlines.
(d) Use Bernoulli's equation to compute the pressure, $p(r)$, throughout the flow
given that the pressure far away from the tornado center is $p(r \to \infty) = P_\infty$ and sketch $p(r)$.