Boundary-Layer Flow Over a Flat Plate — For laminar flow, the local Reynolds number threshold Re_x should be less than approximately what value?

Introduction:
The transition from laminar to turbulent boundary-layer flow over a smooth flat plate occurs when the local Reynolds number, Re_x = (U * x) / ν, exceeds a critical range. Recognizing the typical threshold helps in heat-mass transfer correlations and drag predictions.

Given Data / Assumptions:

• Smooth flat plate in a low-disturbance free stream.
• Local Reynolds number definition Re_x = U * x / nu, where U is free-stream velocity, x is distance from leading edge, and nu is kinematic viscosity.
• Typical engineering threshold values are used.

Concept / Approach:

For many practical cases, laminar flow persists up to Re_x of the order of 5 × 10^5 (sometimes cited between 3 × 10^5 and 1 × 10^6 depending on surface roughness and freestream turbulence). Below this value, boundary-layer assumptions and laminar correlations apply for skin friction and convection coefficients.

Step-by-Step Solution:

Verification / Alternative check:

Empirical data and classic correlations (e.g., Blasius laminar solutions) are applied up to Re_x around several 10^5 before transition and intermittency effects dominate.

Why Other Options Are Wrong:

A and D: Provide lengths, not Reynolds numbers. B: Far too small; would predict transition almost immediately. E: 5 × 10^3 is too low for typical clean flat-plate transition.

Common Pitfalls:

Confusing local Reynolds number Re_x with global Re based on plate length; also mixing units into a dimensionless parameter.

Final Answer:

5 × 10^5