Definition check — turbulent flow and particle paths A flow in which each liquid particle does not have a definite smooth path and the paths appear to intermix or cross due to eddies is termed turbulent flow. Do you agree?

Introduction / Context:
Turbulence is characterized by irregular, three-dimensional, time-dependent motion with eddies and intense mixing. Unlike laminar flow where particles follow smooth, non-intersecting paths, turbulent motion yields fluctuating velocities and seemingly intersecting tracks when viewed over time.

Given Data / Assumptions:

• Newtonian fluid; discussion in kinematic terms.
• High Reynolds number environment where inertia dominates.
• Qualitative description of particle trajectories (pathlines/streamlines).

Concept / Approach:
In laminar flow, neighboring layers slide smoothly with well-defined streamlines; instantaneous pathlines do not cross each other at the same instant. In turbulent flow, strong fluctuations cause rapid changes in the local velocity direction and magnitude, so over time the observed paths appear to intermix and “cross,” reflecting eddy motion and mixing.

Step-by-Step Solution:

Verification / Alternative check:
Dye injection in a turbulent pipe shows rapid dispersion and irregular streaklines compared to straight streamlines in laminar flow.

Why Other Options Are Wrong:

• “Disagree” or constraints to low Re/compressibility are incorrect: turbulence is high-Re and occurs in liquids and gases.
• Calling it laminar contradicts standard definitions.

Common Pitfalls:
Over-interpreting “crossing” literally at the same instant; in strict kinematics, instantaneous streamlines do not intersect, but the time-evolving paths give the observed intermixing.

Final Answer:
Agree