Mixing Reynolds number — The transitional (sometimes called transient) flow range for impeller Reynolds number Re_i in stirred tanks corresponds to which interval?

Introduction:
The impeller Reynolds number Re_i = rho * N * D^2 / mu classifies mixing regimes in stirred tanks. Recognizing the approximate boundaries between laminar, transitional, and turbulent flow is essential for selecting correlations for power number, blending time, and k_La.

Given Data / Assumptions:

• Newtonian fluids in conventional baffled tanks.
• Typical definitions used in mixing literature.
• Order-of-magnitude boundaries rather than sharp transitions.

Concept / Approach:
Standard ranges: laminar for Re_i roughly below 10; transitional between about 10 and 10^4; and fully turbulent above about 10^4. These thresholds guide which empirical correlations apply and whether scale-up should target constant Re_i (laminar) or constant tip speed/ power density (turbulent).

Step-by-Step Solution:
Identify regime boundaries: laminar Re_i <~ 10; turbulent Re_i >~ 10^4.Transitional range lies between these limits.Select the interval 10 < Re_i < 10^4 as transitional.

Verification / Alternative check:
Power number versus Re_i curves flatten at high Re_i, indicating turbulence; at low Re_i, power number scales inversely with Re_i, indicating laminar behavior—bracketing the mid-range as transitional.

Why Other Options Are Wrong:

• (a) Describes laminar regime.
• (c) Describes turbulent regime.
• (d) Incorrect because (b) matches the standard transitional range.
• (e) Creeping flow is a subset of laminar, not the transitional range.

Common Pitfalls:
Treating the boundaries as exact; forgetting non-Newtonian fluids shift effective Reynolds interpretation.

Final Answer:
10 < Re_i < 10^4 (transitional)