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.
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