Kinematics: Types of Fluid Flow, Streamline, Pathline, and Streakline

Definition

Fluid Kinematics is the study of fluid motion without considering the forces (pressure or gravity) that cause the motion. It focuses on describing the velocity, acceleration, and position of fluid particles as they move through space and time.

Main Content

1. Streamline

A streamline is an imaginary line drawn in a flow field such that the tangent at any point on the line represents the direction of the velocity vector at that instant.
Because the velocity vector is tangent to the streamline, no fluid can cross a streamline; therefore, the flow between two streamlines is constant.

Flow Direction (V)
    ------> (A) ------> (B) ------>
Streamline is the path representing velocity vectors at a specific instant.

2. Pathline

A pathline is the actual trajectory or path traced by a single fluid particle over a period of time.
It is a "Lagrangian" concept because it tracks the history of one specific particle as it moves through the flow field.

Particle P movement over time (t1 to t4):
(t1) . ---> (t2) . ---> (t3) . ---> (t4) .
The pathline records the exact position of one particle at different times.

3. Streakline

A streakline is the locus of all fluid particles that have passed through a specific fixed point in space at some earlier time.
It is often observed experimentally by injecting a dye or smoke into a flow from a fixed point.

Fixed Point (S)
      |
      V
    (P3) . (P2) . (P1) .
Particles that passed through point S at different times form the streakline.

Working / Process

1. Visualization of Flow Fields

To analyze flow, engineers use tracer particles (like neutrally buoyant beads or hydrogen bubbles).
By taking time-exposure photographs of these tracers, one can map out the flow structure.

2. Mathematical Determination

For a velocity field $\vec{V} = u\hat{i} + v\hat{j} + w\hat{k}$, the equation for a streamline is defined by: $dx/u = dy/v = dz/w$
By integrating this differential equation, you can derive the equation of the streamline curve.

3. Experimental Mapping

Inject a continuous stream of dye into a moving fluid at a steady rate.
Observe the line formed by the dye particles; this represents the instantaneous streakline of the flow at the injection point.

Advantages / Applications

Aerodynamics: Used to study airflow over airplane wings to identify areas of flow separation or turbulence.
Hydraulic Engineering: Helps in designing channels and pipelines to prevent stagnation zones and ensure smooth flow.
Meteorology: Essential for tracking the movement of air masses, pollutants, or clouds in the atmosphere.

Summary

Fluid kinematics describes motion through streamlines (instantaneous velocity direction), pathlines (trajectory of one particle), and streaklines (locus of particles passing a fixed point). In steady flow, these three lines are identical.
Key terms: Lagrangian (particle-tracking) vs. Eulerian (field-tracking), Velocity vector, and Flow visualization.