Streamlines, Streaklines, and Pathlines

Experimentally, one can visualize streamlines using the Particle Image Velocimetry (PIV) technique. In PIV, fluid particles are “tagged”, usually by mixing in very small, neutrally buoyant bits of “paint,” and taking two photographs in rapid succession.
Experimentally a pathline can be visualized by “tagging” a particular fluid particle and taking a long-exposure photograph of the fluid motion.
Experimentally a streakline can be visualized by injecting dye into a fluid flow at a particular point.

Equations for Streamlines, Pathlines, and Streaklines