For a boiler shell with a diameter of 200 cm and plate thickness of 1.5 cm under an internal pressure of 1.5 MN/m , what is the resulting hoop stress_________________?
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Answer: C. 100 MN/m2
Explanation
Hoop stress in a thin cylinder is calculated as (P * d) / (2 * t), yielding 100 MN/m² for the given values. Substituting pressure of 1.5 MN/m², diameter of 200 cm, and thickness of 1.5 cm into the formula gives the exact result. Thin cylinder theory assumes uniform stress distribution across the boiler shell wall thickness. Boiler shells operate as pressure vessels subjected to both circumferential hoop stress and longitudinal stress. Hoop stress acts around the circumference of the cylinder and represents the primary tensile load on vessel walls. Consistent unit conversion between centimeters and meters ensures accurate stress calculation outcomes.
A value of 30 MN/m² underestimates the actual hoop stress resulting from these specific boiler operating dimensions. Fifty MN/m² represents half of the correct calculated stress value due to a calculation error in thickness. Values like 200 or 300 MN/m² overestimate the resulting stress, exceeding safe engineering limits for this pressure.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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