Cylindrical pressure vessel sizing: a vessel of internal volume 6π m³ (length/diameter = 3) must withstand 10 atm internal pressure. Using allowable stress 125 N/mm² and 2 mm corrosion allowance, estimate the required wall thickness.

Introduction / Context:This is a classic thin-cylinder design estimate for a welded cylindrical pressure vessel. Given the internal volume, the length-to-diameter ratio, the design pressure, and the allowable stress, we can quickly approximate the shell thickness and then add corrosion allowance. Such back-of-the-envelope checks are common in preliminary mechanical design before detailed code calculations.

Given Data / Assumptions:

• Internal volume V = 6π m³.
• Length/diameter ratio L/D = 3 (cylindrical shell only).
• Maximum internal pressure P ≈ 10 atm ≈ 1.013 MPa.
• Allowable design stress σ_allow = 125 N/mm² = 125 MPa.
• Corrosion allowance CA = 2 mm.
• Joint efficiency and other factors assumed unity for this estimate (preliminary sizing).

Concept / Approach:First determine cylinder diameter D from the volume and L/D relation, then apply the thin-cylinder hoop-stress relation t = (P * D) / (2 * σ_allow) for a first-pass thickness. Finally, add corrosion allowance to obtain nominal thickness.

Step-by-Step Solution:

Verification / Alternative check:If we included joint efficiency less than 1, thickness would increase. For a quick sizing, 10 mm aligns with expectations for this pressure, diameter, and allowable stress.

Why Other Options Are Wrong:

• 5 or 6 mm: Too thin; violates hoop stress criterion.
• 8 mm: Roughly the net thickness before corrosion; does not include the 2 mm allowance.

Common Pitfalls:Confusing absolute and gauge pressure; forgetting to add corrosion allowance; ignoring longitudinal stress check (typically smaller) and code-required minimums.

Final Answer:10 mm