Onset of flow separation (boundary layer concept): “The separation of flow occurs when the hydrodynamic boundary-layer thickness is reduced to zero.” State whether this is correct.

Introduction / Context:
Flow separation is a key phenomenon in external aerodynamics and internal flows with adverse pressure gradients. It changes drag, lift, and pressure recovery dramatically. A clear understanding of the boundary-layer behavior at separation avoids common misconceptions stated in the prompt.

Given Data / Assumptions:

• Viscous flow over a wall with possible adverse pressure gradient.
• Boundary layer defined by significant velocity gradient near the wall.
• No special assumption on laminar/turbulent beyond applicability.

Concept / Approach:
Separation is characterized by the wall shear stress falling to zero and then becoming negative as the near-wall flow reverses. The boundary layer does not shrink to zero thickness; rather, it thickens markedly approaching separation. The velocity profile develops an inflection and near-wall backflow forms; the locus of zero wall shear marks the separation point.

Step-by-Step Solution:

Verification / Alternative check:
Classical measurements on airfoils and diffusers show rising shape factor H and growing δ before separation. Surface oil-flow and tuft visualizations confirm flow reversal at the wall where τ_w = 0.

Why Other Options Are Wrong:

• Agree: Contradicts boundary-layer theory and experiments.
• Only true at high Re / only for laminar: Separation criterion is τ_w = 0, not δ = 0, in both laminar and turbulent contexts.

Common Pitfalls:
Confusing “thin boundary layer” with “no boundary layer”; believing separation is a thinning event rather than a detachment triggered by adverse pressure gradient.

Final Answer:
Disagree