Head geometry terminology: In a formed head, the crown radius and knuckle radius refer respectively to which sections?

Introduction / Context:
Pressure vessel heads combine multiple geometric regions: a central dish, a toroidal knuckle, and sometimes a straight flange. Accurate terminology is vital for fabrication drawings and code calculations.

Given Data / Assumptions:

• A formed head consists of a central dished portion and a surrounding toroidal knuckle transitioning to the shell or flange.
• Standard head types include elliptical, torispherical, and hemispherical.

Concept / Approach:
The crown radius R_c describes the radius of curvature of the central dished region. The knuckle radius r_k is the toroidal corner radius that blends the dish into the shell/straight flange. This language is consistent across head drawings and specifications.

Step-by-Step Solution:

Verification / Alternative check:
Vendor catalogs and code sketches (e.g., torispherical heads) label R for crown and r for knuckle consistently.

Why Other Options Are Wrong:

• Options (b), (c), and (d) misassign the radii to the wrong regions or to the straight flange, which does not define a curvature radius in the same sense.

Common Pitfalls:
Confusing the knuckle with a small fillet; the knuckle is a toroidal segment characterized by its own radius.

Final Answer:
Central dished section and corner torus section.