Thin pressure vessel criterion — classify a shell as thin or thick: A pressure vessel is considered a thin shell when the wall-thickness-to-diameter ratio (t/D) is __________ 1/10.

Introduction:Design formulas for thin pressure vessels assume membrane action with negligible through-thickness stress gradient. The classification relies on the ratio t/D (thickness to diameter).Given Data / Assumptions:

• t is wall thickness; D is mean diameter.
• Empirical demarcations separate thin and thick shell theories.

Concept / Approach:When t/D is small, hoop and longitudinal stresses vary little across the wall, so thin-shell formulas are valid. Many textbooks adopt thresholds such as t/D ≤ 1/10 (or more conservatively ≤ 1/20); the key idea is "less than" a small fraction of diameter.Step-by-Step Solution:

Verification / Alternative check:For very small t/D, radial stress is negligible compared to hoop/longitudinal membrane stresses, validating thin-shell equations like σ_hoop = pD/(2t).Why Other Options Are Wrong:

• equal to / approximately equal to: boundary conditions are conservative; equality is not the intended general rule.
• greater than: would indicate a thick shell, invalidating thin formulas.
• not applicable: classification is central to pressure vessel analysis.

Common Pitfalls:Confusing different conservative thresholds (1/10 vs 1/20). The safer interpretation is that t/D must be less than a small fraction of diameter for thin-shell theory to hold.Final Answer: