Streamlines for the Case Study

Streamlines are lines tangent to the velocities, hence

     dy/dx = v/u = -x/y

The above equation can be integrated to yield

where c' and c are arbitrary constants (c² = 2c' ). Thus, the obtained streamlines are concentric circles, as shown in the figure.

Since the flow is steady (independent of time), the pathlines and streaklines are identical to the streamlines.