Agitated vertical cylindrical vessel design: Pick the single WRONG statement about geometry and agitation performance.

Introduction:
Mixing vessel geometry strongly influences hydrodynamics, power demand, gas–liquid mass transfer, and solids suspension. This question asks you to identify the single incorrect statement about common vessel shapes and the typical height-to-diameter filling ratios used in agitated vertical cylindrical reactors.

Given Data / Assumptions:

• Standard baffled cylindrical tanks with top-entering impellers are considered.
• “Filling ratio” refers to liquid depth/diameter (H/T).
• Goal scenarios include gas dispersion and heavy-solids suspension.

Concept / Approach:
Typical general-purpose mixing uses H/T ≈ 1 for balanced performance. For gas dispersion, taller liquid depths (H/T ≈ 2) are common to increase gas residence time and the interfacial contact path. Vessel bottoms matter: flat bottoms are prone to dead zones for solids; dished bottoms help flow re-entry and reduce stagnant zones; conical bottoms generally aid solids collection and can help suspension when the impeller is positioned and clearance is optimized.

Step-by-Step Solution:
Evaluate (a): H/T ≈ 1 is a widely used standard for many liquid–liquid and liquid–solid duties → true.Evaluate (b): For gas dispersion, taller columns (H/T around 2) are common to enhance gas holdup/time → true.Evaluate (c): Statement claims both flat and conical bottoms give low efficiency for suspending heavy solids. Flat bottoms can be problematic, but conical bottoms often improve draw-off and can help solids recirculation if impeller clearance is set correctly → false.Evaluate (d): Dished bottoms can increase power needs in some configurations due to altered flow patterns, though they improve flow re-entry; the statement is qualitatively acceptable.

Verification / Alternative check:
Mixing handbooks and vendor guidelines recommend H/T ≈ 1 for general service and higher aspect ratios for gas dispersion; they also note benefits of dished/conical bottoms for reducing dead zones with proper impeller placement.

Why Other Options Are Wrong:

• (a) and (b) reflect standard practice.
• (d) can be observed depending on geometry and impeller type.
• (e) is a practical note, not incorrect.

Common Pitfalls:
Overgeneralizing that all non-flat bottoms are “bad.” In reality, conical and dished bottoms are frequently preferred for solids handling.

Final Answer:
Flat-bottom and conical-bottom vessels have low agitation efficiency for suspending heavy solids in liquids.