Impeller Reynolds number (Rei): What numerical range corresponds to laminar mixing in agitated tanks based on the impeller Reynolds number definition?

Introduction / Context:The impeller Reynolds number Rei = ρ * N * D^2 / μ is used to classify flow regimes in mixing: laminar, transitional, or turbulent. Correctly identifying the laminar range helps choose impeller types and predict power and blending times, especially for viscous or polymer-containing fluids.

Given Data / Assumptions:

• Standard definition of Rei with density ρ, speed N, impeller diameter D, and viscosity μ.
• Newtonian fluid assumption for regime boundaries.
• Baffled tank unless otherwise specified.

Concept / Approach:Typical regime cutoffs in mixing practice are: laminar for Rei less than about 10, transitional for roughly 10 to 10^4, and fully turbulent above about 10^4. In the laminar regime, power number varies inversely with Rei and flow is dominated by viscous effects, making axial/radial distinctions less meaningful than in turbulent flow.

Step-by-Step Solution:

Verification / Alternative check:Power-number correlations (Np vs Rei) show linear laminar scaling for Rei < 10; deviations begin as inertia grows in the transitional regime.

Why Other Options Are Wrong:

• 10–10^4: transitional.
• >10^4: turbulent.
• “None”: recognized boundaries exist.
• 100–1000: sits well inside transitional for mixing practice.

Common Pitfalls:Using pipe-flow Reynolds thresholds; mixing thresholds differ because geometry and rotating flow modify transitions.

Final Answer:Rei < 10