Vortices in fluid mechanics — identifying correct statements Which statement about forced and free vortices, and flow regimes, is correct?

Introduction / Context:
Vortical motion is common in mixers, drains, and atmospheric flows. Distinguishing forced vs. free vortices and recalling basic laminar/turbulent features are foundational for fluid engineers.

Given Data / Assumptions:

• Definitions of forced vortex (solid-body rotation) and free vortex (irrotational swirl).
• Newton's law for Newtonian fluids.
• Characteristics of turbulent flow.

Concept / Approach:
Forced vortex: every fluid element spins with constant angular velocity, like a solid disc (v ∝ r). Free vortex: angular momentum is conserved and tangential speed varies as vθ ∝ 1/r. Newton's law of viscosity holds for Newtonian fluids, including in laminar regimes. Turbulence is replete with eddies and cross-currents.

Step-by-Step Solution:
Evaluate (a): matches definition of a forced vortex → true.Evaluate (b): false; Newton's law defines laminar shear behavior in Newtonian fluids.Evaluate (c): describes forced, not free, vortex → false.Evaluate (d): turbulence is characterized by eddies and fluctuations → false.

Verification / Alternative check:
Plotting vθ vs. r: solid-body linear profile for forced vortex; hyperbolic for free vortex confirms the definitions.

Why Other Options Are Wrong:

• (b) Misstates Newtonian behavior.
• (c) Confuses forced and free vortex characteristics.
• (d) Contradicts the very definition of turbulence.

Common Pitfalls:

• Assuming any rotating flow is a forced vortex; the driving mechanism matters.

Final Answer:
A forced vortex occurs when fluid rotates as a solid about an axis.