Elliptical (2:1) dished heads on pressure vessels: select the correct combined statements about strength and recommended use.

Introduction / Context:Head geometry affects pressure containment, fabrication ease, and cost. The 2:1 elliptical (ellipsoidal) head is a widely used compromise between the strongest hemisphere and the more economical torispherical head. This item reviews practical design-level comparisons recognized in vessel practice.

Given Data / Assumptions:

• Comparisons are qualitative/typical for identical shell thickness and diameter.
• Materials, joint efficiencies, and code details are assumed comparable.

Concept / Approach:Hemispherical heads have the best stress distribution and highest pressure rating for a given thickness and diameter. Elliptical 2:1 heads are slightly weaker but still strong and compact, frequently specified for moderate-to-high pressures. They can be considered similar in strength to a matching seamless cylindrical shell section under analogous code formulae, acknowledging practical approximations.

Step-by-Step Solution:

Verification / Alternative check:Code design equations (e.g., thin-shell formulas) and vendor charts show required thickness relationships that align with the indicated qualitative comparisons.

Why Other Options Are Wrong:

• Each separate statement is broadly accepted in vessel practice; the combined option reflects conventional guidance.

Common Pitfalls:Over-interpreting approximate ratios as exact; always use governing pressure vessel codes and material allowables for final design thickness.

Final Answer:All (a), (b) and (c).