The velocity field of a two-dimensional unsteady flow is given by:
$u = y + t$, $v = -x$
a) Sketch the velocity vector fields at $t = 0$, $t = \frac{\pi}{4}$ and $t = \frac{\pi}{2}$.
b) Determine the streamlines.
c) Sketch a few streamlines at $t = \frac{\pi}{2}$.
d) Determine the pathline for a particle with initial position $(0, 0)$. Sketch this pathline for