Chapter 2, Problem 27P

Tiny hydrogen bubbles are being used as tracers to visualize a flow. All the bubbles are generated at the origin (x = 0, y = 0). The velocity field is unsteady and obeys the equations:

$\begin{array}{lll}u=1\text{m}/s\hfill & \upsilon =2\text{m}/\text{s}\hfill & 0\le t<2\text{s}\hfill \\ u=0\hfill & \upsilon =-1\text{m}/\text{s}\hfill & 0\le t\le 4\text{s}\hfill \end{array}$

Plot the pathlines of bubbles that leave the origin at t = 0, 1, 2, 3, and 4 s. Mark the locations of these five bubbles at t = 4 s. Use a dashed line to indicate the position of a streakline at t = 4 s.