Pressure vessel classification: A vessel is considered “thin-walled” when the ratio of diameter to wall thickness satisfies which condition?

Introduction / Context:
Thin-wall versus thick-wall assumptions determine which stress equations apply for cylinders and spheres under pressure. The thin-wall approximation simplifies analysis by assuming uniform membrane stress and negligible through-thickness stress variation.

Given Data / Assumptions:

• Prismatic cylindrical vessels under internal pressure.
• Elastic behavior within code-allowable stress.

Concept / Approach:
A common rule is that a shell can be treated as thin-walled when the diameter-to-thickness ratio D/t is sufficiently large (or equivalently, when t/D is small). A widely used threshold is D/t > 10 (some texts use > 20 for a more conservative thin-wall assumption). The question asks for the basic condition; hence “> 10” matches standard teaching definitions.

Step-by-Step Solution:

Verification / Alternative check:
Comparisons of Lamé thick-cylinder equations with thin-wall formulas show small error once D/t exceeds ~10–20, supporting the rule of thumb.

Why Other Options Are Wrong:

• < 10 indicates thicker walls where thin-wall formulas may be inaccurate.
• > 20 is more conservative but not the minimal defining threshold commonly taught.
• “30” as a stand-alone number lacks inequality context.

Common Pitfalls:
Using thin-wall stress formulas outside their validity; always check code requirements and joint efficiency.

Final Answer:
> 10