Questions: Streamlines, Pathlines, and Flow Visualization

Question 1

Dye is continuously released from a fixed point in an unsteady flow. A photograph of the dye pattern is taken at a single instant. Does the dye pattern trace the current streamlines?

• A. Yes — dye always follows streamlines because it moves with the fluid
• B. No — the photograph shows a streakline, which differs from instantaneous streamlines in unsteady flow
• C. Yes — in any flow, streamlines and dye traces coincide at a given instant
• D. No — dye traces pathlines, which only equal streamlines in steady flow

Answer: (B)

The dye pattern from a fixed injection point is a streakline — the locus of all particles that have passed through that point up to the current moment. In unsteady flow, the velocity field shifts over time, so particles injected at different past times followed different instantaneous streamlines. The resulting streakline reflects this history and does not match the current instantaneous streamline pattern. In steady flow, streaklines, streamlines, and pathlines all coincide, which is why this distinction is easy to miss initially.

Question 2

In a steady flow, where streamlines converge (the spacing between adjacent streamlines decreases), what happens to velocity and pressure?

• A. Velocity decreases and pressure increases — converging flow slows down
• B. Velocity increases and pressure decreases — consistent with Bernoulli's equation
• C. Velocity increases and pressure increases — more fluid is packed into a smaller region
• D. Neither velocity nor pressure changes — converging streamlines are just a visual artifact

Answer: (B)

By continuity, fluid must speed up where streamlines converge because the same mass flux passes through a smaller cross-sectional area. Bernoulli's equation then requires that this increased velocity be accompanied by a pressure drop. Converging streamlines → higher speed → lower pressure. The reverse holds where streamlines diverge. This is why streamline patterns directly encode pressure information and are so valuable for understanding aerodynamic forces.

Question 3

Two streamlines in a steady, single-valued velocity field can never cross each other.

• T. True
• F. False

Answer: True

A streamline at any point is tangent to the local velocity vector. If two streamlines crossed at a point, there would need to be two different velocity directions at that single point — a contradiction in a single-valued velocity field. The velocity at any point has exactly one direction, so exactly one streamline passes through it. Near stagnation points where velocity goes to zero, streamlines appear to 'meet,' but this is a degenerate special case where the definition requires careful treatment.

Question 4

In an unsteady flow, the pathline of a fluid particle and the streamline passing through the particle's initial position are the same curve.

• T. True
• F. False

Answer: False

Pathlines and streamlines coincide only in steady flow. A pathline traces where a specific particle actually travels as time advances, following the evolving velocity field. A streamline is an instantaneous snapshot — the curve tangent to velocities at one frozen moment. In unsteady flow, the velocity vectors change over time, so a particle's actual trajectory diverges from the streamline that existed at the moment of release. Recognizing whether a flow is steady is the essential first step before interpreting any flow visualization.

Question 5

Why do streamlines and pathlines coincide in steady flow but diverge in unsteady flow?

Model answer: In steady flow, the velocity field does not change with time, so the 'arrows' guiding a particle are fixed. A particle released at a point always follows the same unchanging velocity directions — the very directions that define the streamline through that point. In unsteady flow, the velocity field evolves, so the arrows a particle follows at later times differ from those that defined the streamline at the release instant, causing the actual trajectory (pathline) to deviate from the initial streamline.

The key is that a streamline is defined by the instantaneous velocity field at one moment, while a pathline is defined by the velocity field integrated over time. When these are the same function (steady flow), the two curves are identical. When the velocity field changes (unsteady flow), a particle following the evolving field traces a different path than the frozen snapshot would suggest. This is why asking 'is this flow steady?' is the first habit to develop when interpreting flow visualizations.