For mixing in the laminar regime (very low Reynolds number), how does the power number Po scale with the Reynolds number Re for a stirred tank (Po = P / (ρ N^3 D^5), Re = ρ N D^2 / μ)?

Introduction / Context:
In mixing, dimensional analysis yields power number–Reynolds number correlations. In laminar flow, viscous forces dominate and inertial effects vanish from the power requirement.

Given Data / Assumptions:

• Definitions: Po = P/(ρ N^3 D^5), Re = ρ N D^2/μ.
• Low Re (creeping flow) limit.

Concept / Approach:
For laminar mixing, P ∝ μ N^2 D^3, so substituting into Po gives Po ∝ (μ N^2 D^3) / (ρ N^3 D^5) = (μ / ρ N D^2) = 1/Re. Therefore, Po scales inversely with Re in the viscous regime.

Step-by-Step Solution:
Use laminar mixing power correlation P ∝ μ N^2 D^3.Form Po and simplify.Obtain Po ∝ Re^-1.

Verification / Alternative check:
Standard impeller correlations display a Po·Re = constant plateau in laminar flow, equivalent to Po ∝ 1/Re.

Why Other Options Are Wrong:
Zero/positive exponents imply inertia influence, contrary to laminar limit.

Common Pitfalls:
Extending turbulent correlations into laminar ranges.

Final Answer:
Po ∝ Re^-1.0