Why is a spherical pressure vessel considered ideal among common shapes for internal pressure? Choose the primary engineering reason.

Introduction / Context:
Pressure vessels are fabricated in cylindrical, spherical, or torispherical forms. The choice impacts stress distribution, material usage, and overall cost. Spheres are often touted as “ideal,” but the engineering basis matters.

Given Data / Assumptions:

• Thin-shell theory applies (uniform internal pressure).
• Comparison among common shapes for stress efficiency.
• Material yield strength and allowable stress are fixed.

Concept / Approach:
In a sphere, membrane stress is equal in all directions and equals p * r / (2t). For a cylinder, hoop stress is p * r / t (twice as large at the same thickness). Therefore, for a given internal pressure and radius, a sphere requires roughly half the thickness of a cylinder to achieve the same stress level, or conversely, can withstand higher pressure at the same thickness.

Step-by-Step Solution:
Spherical membrane stress: σ_s = p * r / (2t).Cylindrical hoop stress: σ_h = p * r / t.At equal t, σ_s is lower → higher allowable p for the sphere.Hence, the key advantage is pressure capacity per unit thickness.

Verification / Alternative check:
Storage spheres for LPG and other volatiles illustrate the efficiency; despite higher fabrication complexity, lifecycle economics can favor spheres at high capacities/pressures.

Why Other Options Are Wrong:
Fabrication and support (b, d): spheres are actually harder to fabricate and support.Wind loads (c): must still be considered; spherical symmetry does not eliminate environmental loads.

Common Pitfalls:
Equating “ideal” with cheapest; overlooking fabrication and erection challenges even when stress efficiency is superior.

Final Answer:
withstand higher pressure for a given metallic shell thickness.