Cochran boiler shell geometry The hemispherical shell (dome) of a Cochran boiler is provided primarily ________.

Introduction / Context:
The Cochran boiler is a vertical, multi-tubular, fire-tube boiler widely used for small capacities. Its distinctive feature is the hemispherical (or domed) shell and furnace crown. This geometry is not merely aesthetic; it provides structural and functional advantages under internal pressure.

Given Data / Assumptions:

• Thin-walled pressure vessel behavior.
• Hemispherical or domed surfaces under internal steam pressure.
• Space and circulation considerations inside the shell.

Concept / Approach:
A hemisphere has uniform curvature in all directions, distributing membrane stresses more evenly than flat plates and requiring less thickness for the same allowable stress. The dome also offers generous steam space and disengagement volume, reducing priming and carryover, thereby improving steam quality.

Step-by-Step Solution:
Internal pressure acts normal to the shell; curved shapes carry it efficiently as membrane stress.Hemispherical geometry minimizes bending stresses compared to flat heads.Larger steam space above the waterline smooths load changes and reduces moisture in steam.

Verification / Alternative check:
Pressure vessel design rules favor torispherical/hemispherical heads for higher pressures; operational reports show better steam dryness with adequate dome space.

Why Other Options Are Wrong:
Choosing only (a) or only (b) omits part of the motivation; “none” and “appearance only” ignore core engineering reasons.

Common Pitfalls:
Assuming flat plates are equivalent; neglecting the role of steam space in reducing priming.

Final Answer:
both (a) and (b)