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Fluid Mechanics

5.3 Streamlines, Pathlines, and Streaklines

3 min readLast Updated on July 19, 2024

Fluid particle trajectories are crucial for understanding fluid flow behavior. Streamlines, pathlines, and streaklines provide different perspectives on fluid motion, helping engineers visualize and analyze complex flow patterns.

In steady flow, these trajectories align, but they diverge in unsteady conditions. By examining these paths, we can gain insights into fluid mixing, dispersion, and important flow features like vortices and stagnation points.

Fluid Particle Trajectories

Streamlines, pathlines, and streaklines

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  • Streamlines represent a family of curves instantaneously tangent to the velocity vector of the flow at each point (e.g., streamlines in a pipe flow)
    • Show the direction a fluid element will travel at any given instant
  • Pathlines trace the actual path traversed by an individual fluid particle over a specified period of time (e.g., the trajectory of a dye particle in a river)
    • Represent the historical trajectory of a fluid particle
  • Streaklines form the locus of fluid particles that have passed continuously through a particular spatial point in the past (e.g., the path of smoke from a chimney)
    • Created by injecting and tracking a continuous stream of dye or smoke into the fluid at a fixed point

Visualization of fluid flow

  • In steady flow, streamlines, pathlines, and streaklines are identical and do not change over time (e.g., laminar flow in a straight pipe)
  • For unsteady flow, streamlines change with time and are different at each instant (e.g., flow around a bluff body)
    • Pathlines and streaklines differ from streamlines and each other in unsteady flow
  • To sketch streamlines, draw curves tangent to velocity vectors at each point
  • Pathlines can be visualized by tracking the trajectory of individual fluid particles released from a point (e.g., a puff of smoke in the wind)
  • Streaklines are observed by tracking the current positions of fluid particles continuously released from a point in the past (e.g., a stream of dye in a water tank)

Streamlines and velocity fields

  • Streamlines are everywhere tangent to the local velocity vector (e.g., streamlines in a converging nozzle)
  • The velocity vector at any point in the flow is tangent to the streamline at that point
  • In steady flow, streamlines are parallel to the velocity vectors at every point
  • Streamline patterns can reveal important flow features
    • Sources and sinks: streamlines diverge from or converge to a point (e.g., flow into a drain)
    • Vortices: streamlines form closed circular or spiral patterns (e.g., a tornado)

Fluid particle behavior analysis

  • Pathlines represent the trajectory of a single fluid particle over time
    • Obtained by integrating the velocity vector field with respect to time (x(t)=t0tv(x(t),t)dt\vec{x}(t) = \int_{t_0}^t \vec{v}(\vec{x}(t'), t') dt')
    • In unsteady flow, pathlines can cross streamlines (e.g., a particle in a vortex street)
  • Streaklines form by the current positions of fluid particles released continuously from a fixed point in the past
    • Reflect the time-varying nature of the flow
    • In steady flow, streaklines coincide with streamlines and pathlines
  • Analyzing pathlines and streaklines provides insight into
    1. Mixing and dispersion of fluid particles (e.g., pollutant dispersion in the atmosphere)
    2. Residence time distribution in a system (e.g., chemical reactor design)
    3. Identification of recirculation zones or stagnation points (e.g., flow separation behind an obstacle)
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© 2025 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

© 2025 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.