Agitation similitude — Froude, Reynolds, and power number:\nDuring liquid agitation in baffled tanks, which set of statements about dimensionless groups and power correlations is correct?

Introduction / Context:
Mixing scale-up relies on dimensionless groups: Reynolds number (inertial/viscous), Froude number (inertial/gravity), and the power number (P/(rho*N^3*D^5)) that captures impeller loading. Understanding when each group matters avoids scale-up surprises like unexpected power draw or vortex formation in unbaffled tanks.

Given Data / Assumptions:

• Baffled, Newtonian liquid systems.
• Standard impeller types (e.g., Rushton, pitched-blade) in tanks with typical baffle configurations.
• Large Reynolds number regime implies fully turbulent flow.

Concept / Approach:
For baffled, fully turbulent systems, the power number becomes essentially independent of Reynolds number; it plateaus to a constant that depends on impeller geometry and clearance. Froude number is invoked when a free surface is present because gravity and surface deformation (vortex depth) influence power draw and aeration; hence Fr is used to correlate surface effects alongside Po. The phrasing in (a) notes that, in power vs. Reynolds plots for baffled tanks, Fr is not the varying axis but a separate parameter in surface-effect correlations; (b) is the classic asymptotic behavior; (c) is the recognized use of Fr for vortex effects.

Step-by-Step Solution:

Verification / Alternative check:
Power number charts show Po plateau at Re > 10^4–10^5; correlations with free surfaces employ Fr to predict vortex depth and associated power penalties.

Why Other Options Are Wrong:

• (e) is incorrect because each listed statement reflects standard mixing theory.

Common Pitfalls:
Using Re-only correlations for unbaffled or free-surface cases; neglecting Fr yields underpredicted power with deep vortices.

Final Answer:
All (a), (b) and (c).