For cylindrical pressure vessels, which head/closure type is structurally the weakest and therefore requires the greatest thickness for a given pressure?

Introduction / Context:
Cylindrical vessels are closed by various head shapes. Head geometry controls membrane stresses under pressure; more curved shapes distribute stress more efficiently and need less thickness.

Given Data / Assumptions:

• Thin-shell assumptions are applicable.
• Internal pressure loading dominates.

Concept / Approach:
For the same diameter and pressure, required thickness follows the stress efficiency of the head shape. Hemispherical is strongest (lowest thickness), then elliptical, then torispherical; flat plates (or shallow conical/flat closures) are weakest and need the greatest thickness and/or stiffeners.

Step-by-Step Solution:
1) Compare curvature: hemisphere has continuous curvature → best stress distribution.2) Elliptical and torispherical are intermediate; knuckle and crown radii create stress concentrations but still curved.3) Flat/conical plates lack beneficial curvature → higher bending stresses → greater required thickness.

Verification / Alternative check:
Design codes (e.g., common vessel design formulas) assign lower required thickness to hemispherical and higher to flat heads for identical service.

Why Other Options Are Wrong:
Hemispherical, elliptical, and torispherical heads are stronger per unit thickness than flat plates.

Common Pitfalls:
Ignoring external pressure or vacuum, where buckling may reverse some practical choices; forgetting stiffener rings for flat covers.

Final Answer:
Conical or flat plate head