Difficulty: Easy
Correct Answer: Both (a) & (b)
Explanation:
Introduction / Context:
Cross-sectional shape influences both mechanical integrity and material economy in piping. A sound choice minimizes stress concentration, maximizes resistance to internal pressure, and reduces required wall area per unit flow capacity. Circular pipes dominate industrial practice for these reasons.
Given Data / Assumptions:
Concept / Approach:
For a given internal pressure, a circular cylinder develops uniform hoop stress; other shapes develop bending and stress concentrations at corners. From geometry, a circle encloses the maximum area for a given perimeter, or equivalently, provides the minimum perimeter (surface area) for a given enclosed area. Thus circular pipes achieve both better structural efficiency and material economy.
Step-by-Step Solution:
Verification / Alternative check:
Thin-cylinder stress formulas and isoperimetric inequality underpin these conclusions mathematically and are standard in mechanical design texts.
Why Other Options Are Wrong:
Common Pitfalls:
Ignoring fabrication/connection issues; misapplying to non-pressure structural members where other shapes may be preferred.
Final Answer:
Both (a) & (b)
Discussion & Comments