Elliptical (2:1) dished heads on pressure vessels: select the correct combined statements about strength and recommended use.
-
ACommon 2:1 heads are used above about 1.5 MN/m^2 and have a 2:1 major-to-minor axis ratio.
-
BThey resist roughly half the pressure rating of a hemispherical head of the same thickness and diameter.
-
CThey are approximately as strong as a seamless cylindrical shell of the same internal and external diameters.
-
DAll (a), (b) and (c).
Answer
Correct Answer: All (a), (b) and (c).
Explanation
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:
Recognize geometry ranking: hemisphere > 2:1 elliptical > torispherical.Note common practice: 2:1 elliptical heads are standard above moderate pressures.Relative strength comparisons support the listed statements as practical rules of thumb.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).