流线、脉线和迹线

A streamline is a path always tangent to the fluid's velocity vector at every point in the flow field. The velocity of a fluid particle is always directed along the streamline, ensuring the particle continuously follows the streamline's path. Streamlines provide an instantaneous representation of the flow's velocity field and are particularly useful for visualizing the overall direction of flow in a fluid system.

A streakline traces the position of particles that have passed through a specific point over time, showing a time-integrated history of particle positions. When dye is introduced at a fixed location, it reveals the path fluid particles take as they move through that point. Unlike streamlines, which are instantaneous snapshots, streaklines can differ from streamlines in unsteady flow because they track particles over time.

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. Each pathline shows the unique route that one specific particle follows through the fluid, capturing its complete motion history.

In steady flow, where conditions do not change over time, streamlines, streaklines, and pathlines all coincide because the flow pattern remains constant. Since velocity and flow direction are unchanging, particles follow the same paths, dye traces the same routes, and instantaneous velocity vectors remain aligned. This makes all three representations indistinguishable in steady and unsteady flow conditions.

In unsteady flow, where velocity and flow direction change over time, pathlines diverge from streamlines and streaklines as each particle follows a unique path through the fluid. Streamlines remain instantaneous snapshots of the velocity field at a given moment, while pathlines capture the actual trajectory each particle takes as conditions evolve. This distinction is critical for analyzing fluid motion under varying flow conditions.

A streakline is created by injecting dye at a fixed point in the flow. The dye particles flow through and continuously trace the fluid particles passing through that point, revealing where particles that have passed through that location are positioned at any given moment. This experimental technique effectively shows the time-integrated history of particle positions downstream from the injection point.

Streamlines are useful for visualizing fluid flow because they represent paths always tangent to the fluid's velocity at every point, showing the instantaneous flow direction. In a curved pipe, streamlines reveal how the flow direction changes throughout the system. Since a fluid particle's velocity is always directed along the streamline, these lines provide a clear, intuitive picture of how fluid moves through the system.