Chapter 4, Problem 4.19P

A proposed incompressible plane flow in polar coordinates is given by

${\text{v}}_{\text{r}}=\text{2rcos}\left(\text{2}\theta \right)$ ; ${\text{v}}_{\theta }=-\text{2r sin}\left(\text{2}\theta \right)$

(a) Determine if this flow satisfies the equation of continuity.

(b) If so, sketch a possible streamline in the first quadrant by finding the velocity vectors at (r, $\theta$) = (1,25, 20°), (1.0, 45°), and (1.25, 70°). (c) Speculate on what this flow might represent.