Agitation system guideline: for general mixing service, the approximate operating liquid depth (working height) in a stirred tank is typically what proportion of the tank diameter d?

Introduction / Context:
Preliminary sizing rules for mixing tanks help process engineers make quick, consistent decisions before detailed mechanical design. One frequently used rule is the relationship between working liquid height and vessel diameter, which affects power number scaling, impeller placement, and baffle design.

Given Data / Assumptions:

• Cylindrical, baffled mixing tank with flat or dished bottom.
• General-purpose liquid–liquid or solid–liquid mixing (not specialized tall reactors).
• Seeking a widely used preliminary proportion, not a strict code requirement.

Concept / Approach:
A common heuristic is to select the working liquid height approximately equal to the tank diameter (H ≈ d). This ratio balances mixing performance, structural practicality, and headroom for gas disengagement or foam. It also simplifies impeller submergence and multiple-impeller spacing when required.

Step-by-Step Solution:

Verification / Alternative check:
Many vendor guides and handbooks suggest H/d in the 0.8–1.2 range; choosing H = d is a standard baseline.

Why Other Options Are Wrong:

• 0.5 d or 0.75 d: short tanks can limit circulation and may require special impeller placement.
• 2 d or 1.25 d: tall tanks are used for special duties; not the general baseline.

Common Pitfalls:
Applying H = d to gas–liquid mass transfer systems with foaming; ignoring headspace required for vapor disengagement in exothermic reactions.

Final Answer:
d