In flow visualization, the curve whose tangent at every point gives the instantaneous direction of the fluid velocity is called what?

Introduction / Context:
Several distinct curves are used to visualize flows: streamlines, path lines, streak lines, and timelines. Textbook definitions differ subtly but matter for unsteady flows and for interpreting flow-visualization experiments (smoke lines, dye injection, or PIV tracers).

Given Data / Assumptions:

• Instantaneous velocity field V(x, y, z, t) is known at a given time t.
• We seek the curve whose tangent aligns with V at each point at that same instant.

Concept / Approach:

A streamline is defined such that at a fixed instant, its tangent vector is exactly the local velocity direction. In steady flow, streamlines, path lines (particle trajectories), and streak lines coincide. In unsteady flows they differ: a path line is the actual path of one particle over time; a streak line traces all particles that have passed through a particular point; a timeline connects multiple particles released simultaneously.

Step-by-Step Solution:

Verification / Alternative check:

In numerical CFD post-processing, streamlines are seeded to show direction fields; they match analytical definitions by construction.

Why Other Options Are Wrong:

Path line and streak line depend on particle history, not the instantaneous field. “Potential line” is a line of constant velocity potential, orthogonal to streamlines in potential flow, not aligned with the velocity direction.

Common Pitfalls:

Assuming all three coincide even in unsteady flows; this is only true for steady conditions.

Final Answer:

Streamline