Identify the mixing regime for an agitated vessel based on the impeller Reynolds number (Rei). Which range corresponds to fully turbulent flow for typical stirred-tank geometries?

Introduction / Context:
Determining whether flow is laminar, transitional, or turbulent in a stirred tank guides the choice of correlations for power, mixing time, and mass transfer. The impeller Reynolds number Rei provides the basis for these regime distinctions.

Given Data / Assumptions:

• Newtonian fluid with consistent properties.
• Standard baffled stirred tanks and common impellers.
• Rei = ρ * N * Di^2 / μ.

Concept / Approach:
Rule-of-thumb thresholds place laminar flow at Rei < 10, transitional between about 10 and 10^4, and fully turbulent at Rei > 10^4. In the turbulent regime, correlations often simplify (e.g., constant Np), enabling straightforward scale-up.

Step-by-Step Solution:
Compute Rei for the process conditions.Compare with thresholds: <10 (laminar), 10–10^4 (transition), >10^4 (turbulent).Select the turbulent range if Rei exceeds 10^4.Apply relevant turbulent correlations thereafter.

Verification / Alternative check:
Plotting Np vs Rei exhibits a 1/Rei trend in laminar, curvature in transition, and a plateau for Rei > 10^4, confirming the threshold utility.

Why Other Options Are Wrong:
Rei < 10: laminar regime.10 < Rei < 10^4: transitional, not fully turbulent.“None of these” is incorrect because a standard turbulent threshold exists.

Common Pitfalls:
Treating thresholds as exact rather than guidelines; neglecting that very high-viscosity media or non-Newtonian behavior shifts practical boundaries.

Final Answer:
Rei > 10^4