Flow visualization – Definition of streamline The imaginary curve drawn in a flowing fluid such that the tangent at any point gives the instantaneous direction of motion at that point is called a what?

Introduction:
Flow visualization uses several kinematic constructs: streamlines, pathlines, and streaklines. Although related, each has a distinct definition and physical interpretation. This question asks for the curve whose tangent everywhere gives the instantaneous flow direction field.

Given Data / Assumptions:

• Steady or unsteady flow field v(x, t).
• We are considering an instantaneous snapshot of the velocity field.
• No specific body forces or boundaries are required to define the kinematics.

Concept / Approach:

A streamline is defined at an instant by the differential relation dy/dx = v_y / v_x in 2D, ensuring its tangent is aligned with the local velocity vector. A pathline is the actual trajectory traced by a single fluid particle over time. A streakline is the locus of all particles that have previously passed through a particular point (e.g., dye injected continuously). In steady flows, all three coincide; in unsteady flows, they differ.

Step-by-Step Solution:

Verification / Alternative check:

Textbook diagrams of steady flow show streamlines coincident with particle paths; in unsteady flows, releasing dye from a point generates a streakline that may not align with streamlines at later times, reinforcing the distinction.

Why Other Options Are Wrong:

Path line: Tracks one particle over time, not the instantaneous field direction at every point.Streak line: Locus of particles that passed through a point, not necessarily tangent to the instantaneous velocity everywhere.Potential line: A contour of velocity potential; tangent is not generally the velocity direction unless specific conditions hold.Vortex line: Curve everywhere tangent to vorticity, not velocity.

Common Pitfalls:

Assuming all three lines are always identical. They coincide only under steady conditions.

Final Answer:

stream line