Geometrical Distinction between Streamline, Pathline, and Streakline

Introduction:
In fluid mechanics, streamline, pathline, and streakline are important concepts used to describe the behavior of fluid flow. While these terms are related to the motion of fluid particles, they have different geometrical distinctions. However, in the case of steady flow, there is no geometrical distinction between them. Let's explore this in detail:

1. Streamline:
- A streamline is an imaginary line that represents the instantaneous direction of the flow at a given point in a fluid.
- It is a curve that is tangent to the velocity vector at every point.
- Streamlines do not intersect each other and provide a visualization of the flow pattern.
- In steady flow, the streamlines remain fixed in space, and there is no change in their shape or position over time.

2. Pathline:
- A pathline is the actual path traced by a fluid particle as it moves through the flow field.
- It represents the trajectory followed by a fluid particle from its initial position to its final position.
- Pathlines can be visualized by tracking the movement of a colored dye or a particle injected into the flow.
- In steady flow, the pathlines coincide with the streamlines because the flow field remains constant over time.

3. Streakline:
- A streakline is formed by connecting all the fluid particles that have passed through a specific point in the flow field over a certain time duration.
- It represents the history of the flow by showing the positions of different fluid particles at different times.
- Streaklines can be visualized by injecting a continuous stream of dye or tracer particles into the flow.
- In steady flow, the streaklines coincide with the streamlines and pathlines because the flow field remains unchanged.

Geometrical Distinction:
- In the case of steady flow, all the fluid particles follow the same streamlines, pathlines, and streaklines.
- Since the flow field does not change over time, the streamlines, pathlines, and streaklines coincide and have the same geometrical representation.
- This means that there is no distinction between these concepts in terms of their shape or position.
- However, in unsteady flow where the flow field changes with time, the geometrical representations of streamlines, pathlines, and streaklines differ from each other.

Conclusion:
In summary, in the case of steady flow, there is no geometrical distinction between the streamline, pathline, and streakline. They all coincide and have the same representation because the flow field remains constant over time. However, in unsteady flow, these concepts have different geometrical characteristics, representing the instantaneous flow direction, particle trajectory, and flow history, respectively.