Streamlines, Streaklines, and Pathlines

Consider water flowing steadily through a curved pipe. The direction of flow inside the pipe can be visualized using streamlines.

A streamline represents a path always tangent to the fluid's velocity at every point.

When a fluid particle moves along the streamline, its velocity at any point is directed along the path of the streamline. This velocity alignment ensures that the particle follows the flow direction defined by the streamline at every moment.

When a dye is injected into the same pipe at one fixed point, the dye particles flow through and continuously trace the fluid particles passing through that point.

This trace forms a streakline, which shows where particles that have passed through a particular point are located at any moment.

A pathline shows the actual path that a single fluid particle takes over time.

Consider a leaf floating along a river, following its unique path. The path taken by the leaf as it moves downstream represents a pathline.

In steady flow, pathlines align with streamlines and streaklines. However, in unsteady flow, pathlines differ as each particle follows its dynamic route.