17.3 : Streamlines, Streaklines, and Pathlines

A streamline represents the trajectory that is always tangent to the fluid's velocity vector at any given point. The velocity of a fluid particle is always directed along the streamline, ensuring the particle continuously follows the streamline's path. Streamlines are particularly useful for visualizing the overall direction of flow in a fluid system, and they provide an instantaneous representation of the flow's velocity field. In steady flow, where conditions do not change over time, streamlines offer a consistent picture of the flow pattern.

Streaklines, in contrast, trace the position of particles that have passed through a specific point over time. When a dye is introduced at a fixed location in the flow, it reveals the path fluid particles take as they move through that point, effectively showing a time-integrated history of their positions. Streaklines can differ from streamlines in unsteady flow because they track particles over time, whereas streamlines are instantaneous.

A pathline is a single fluid particle's trajectory as it moves through space over time. For example, the path of a leaf floating downstream in a river represents a pathline. Pathlines coincide with streamlines and streaklines in a steady flow, where conditions are constant, making them indistinguishable. However, in unsteady flow, where velocity and flow direction change over time, pathlines can diverge from streamlines and streaklines as each particle follows a unique path through the fluid. These distinctions are important for analyzing fluid motion under varying flow conditions.