Transition in Internal Flow – Definition of Critical Velocity The critical velocity is the characteristic mean velocity at which internal flow in a duct shifts from laminar to turbulent, commonly identified using a threshold Reynolds number.

Introduction:
Internal flow regimes are classified using Reynolds number Re = (rho * V * D) / mu. The velocity associated with the onset of turbulence is often referred to as the critical velocity, important for selecting correlations for head loss and heat transfer.

Given Data / Assumptions:

• Newtonian fluid in a circular pipe under steady conditions.
• Onset of transition defined by empirical threshold of Re (about 2000 for smooth pipes).
• Mean bulk velocity V relates to Re at given diameter and properties.

Concept / Approach:

For specified fluid properties and pipe diameter, the velocity at which Re reaches the threshold is calculated and termed critical velocity. Below it, viscous forces dominate (laminar). Above it, inertial instabilities amplify, leading to turbulence.

Step-by-Step Solution:

Verification / Alternative check:

Laboratory pipe-flow experiments show parabolic velocity profiles and Hagen-Poiseuille law validity below the critical value, with breakdown to flatter turbulent profiles above it.

Why Other Options Are Wrong:

Velocity of approach: Used in weir and orifice corrections, not regime transition. Sub-sonic and super-sonic velocities concern compressible gas dynamics, not laminar-turbulent transition in incompressible internal flow. Drift velocity: Not a standard fluid mechanics term for this context.

Common Pitfalls:

Treating the critical value as universal and exact; neglecting roughness, inlet disturbances, and measurement uncertainty that shift the transition range.

Final Answer:

critical velocity