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For the same internal diameter, wall thickness, material and internal pressure, the ratio of maximum stress, induced in a thin cylindrical and in a thin spherical pressure vessel will be:
- a)2
- b)1/2
- c)4
- d)1/4
Correct answer is option 'A'. Can you explain this answer?
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**Introduction:**
When a thin cylindrical or spherical pressure vessel is subjected to internal pressure, it experiences stress due to the internal pressure. The maximum stress induced in the vessel is an important parameter to consider. In this case, we are comparing the maximum stress in a thin cylindrical pressure vessel with that in a thin spherical pressure vessel.
**Comparison of thin cylindrical and spherical pressure vessels:**
**1. Thin Cylindrical Pressure Vessel:**
A thin cylindrical pressure vessel is characterized by its internal diameter (D), wall thickness (t), material properties, and internal pressure (P). The maximum stress induced in the cylindrical vessel can be calculated using the following formula:
σcylindrical = (PD) / (2t)
**2. Thin Spherical Pressure Vessel:**
A thin spherical pressure vessel is characterized by its internal diameter (D), wall thickness (t), material properties, and internal pressure (P). The maximum stress induced in the spherical vessel can be calculated using the following formula:
σspherical = (PD) / (4t)
**Comparison of maximum stress:**
To compare the maximum stress induced in the two types of vessels, we can calculate their ratio:
Ratio = σcylindrical / σspherical
Substituting the respective formulas, we get:
Ratio = [(PD) / (2t)] / [(PD) / (4t)]
Simplifying the expression, we get:
Ratio = 2 / 1
Therefore, the ratio of maximum stress induced in a thin cylindrical pressure vessel to that in a thin spherical pressure vessel is 2.
**Explanation:**
The ratio of maximum stress in the two types of vessels depends on the geometry of the vessels. The cylindrical vessel has a larger surface area compared to the spherical vessel for the same internal diameter and wall thickness. As a result, the stress is distributed over a larger area in the cylindrical vessel, leading to a lower maximum stress.
On the other hand, the spherical vessel has a smaller surface area compared to the cylindrical vessel for the same internal diameter and wall thickness. Consequently, the stress is concentrated over a smaller area in the spherical vessel, resulting in a higher maximum stress.
Therefore, the ratio of maximum stress in the cylindrical vessel to that in the spherical vessel is 2, indicating that the maximum stress in the cylindrical vessel is twice that in the spherical vessel.
Hence, option 'A' is the correct answer.
When a thin cylindrical or spherical pressure vessel is subjected to internal pressure, it experiences stress due to the internal pressure. The maximum stress induced in the vessel is an important parameter to consider. In this case, we are comparing the maximum stress in a thin cylindrical pressure vessel with that in a thin spherical pressure vessel.
**Comparison of thin cylindrical and spherical pressure vessels:**
**1. Thin Cylindrical Pressure Vessel:**
A thin cylindrical pressure vessel is characterized by its internal diameter (D), wall thickness (t), material properties, and internal pressure (P). The maximum stress induced in the cylindrical vessel can be calculated using the following formula:
σcylindrical = (PD) / (2t)
**2. Thin Spherical Pressure Vessel:**
A thin spherical pressure vessel is characterized by its internal diameter (D), wall thickness (t), material properties, and internal pressure (P). The maximum stress induced in the spherical vessel can be calculated using the following formula:
σspherical = (PD) / (4t)
**Comparison of maximum stress:**
To compare the maximum stress induced in the two types of vessels, we can calculate their ratio:
Ratio = σcylindrical / σspherical
Substituting the respective formulas, we get:
Ratio = [(PD) / (2t)] / [(PD) / (4t)]
Simplifying the expression, we get:
Ratio = 2 / 1
Therefore, the ratio of maximum stress induced in a thin cylindrical pressure vessel to that in a thin spherical pressure vessel is 2.
**Explanation:**
The ratio of maximum stress in the two types of vessels depends on the geometry of the vessels. The cylindrical vessel has a larger surface area compared to the spherical vessel for the same internal diameter and wall thickness. As a result, the stress is distributed over a larger area in the cylindrical vessel, leading to a lower maximum stress.
On the other hand, the spherical vessel has a smaller surface area compared to the cylindrical vessel for the same internal diameter and wall thickness. Consequently, the stress is concentrated over a smaller area in the spherical vessel, resulting in a higher maximum stress.
Therefore, the ratio of maximum stress in the cylindrical vessel to that in the spherical vessel is 2, indicating that the maximum stress in the cylindrical vessel is twice that in the spherical vessel.
Hence, option 'A' is the correct answer.
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For the same internal diameter, wall thickness, material and internal pressure, the ratio of maximum stress, induced in a thin cylindrical and in a thin spherical pressure vessel will be:a)2b)1/2c)4d)1/4Correct answer is option 'A'. Can you explain this answer?
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