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A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the cylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (in mm) is________.
(Important - Enter only the numerical value in the answer)
Correct answer is '5'. Can you explain this answer?
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A thin-walled cylindrical pressure vessel of internal diameter 2 m is ...
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A thin-walled cylindrical pressure vessel of internal diameter 2 m is ...
Given information:
- Internal diameter of the cylindrical pressure vessel = 2 m
- Internal pressure of the vessel = 500 kPa (gauge)
- Allowable normal stress at any point within the cylindrical portion of the vessel = 100 MPa
To find: The minimum thickness of the plate of the vessel (in mm)
Assumptions:
- The vessel is thin-walled, which means the thickness of the wall is much smaller compared to the diameter.
- The vessel is subjected to internal pressure only.
Formula:
The formula for calculating the hoop stress in a thin-walled cylindrical vessel is given by:
Stress (σ) = P * r / t
Where,
σ = Hoop stress
P = Internal pressure
r = Internal radius of the vessel
t = Thickness of the vessel wall
Solution:
1. Convert the internal pressure from kPa to MPa:
500 kPa = 500/1000 = 0.5 MPa
2. Calculate the internal radius of the vessel:
Given internal diameter = 2 m
Internal radius = Diameter/2 = 2/2 = 1 m
3. Rearrange the formula for stress to find the thickness of the vessel wall:
t = P * r / σ
4. Substitute the given values into the formula:
t = 0.5 * 1 / 100 = 0.005 m = 5 mm
Conclusion:
The minimum thickness of the plate of the vessel is 5 mm.
- Internal diameter of the cylindrical pressure vessel = 2 m
- Internal pressure of the vessel = 500 kPa (gauge)
- Allowable normal stress at any point within the cylindrical portion of the vessel = 100 MPa
To find: The minimum thickness of the plate of the vessel (in mm)
Assumptions:
- The vessel is thin-walled, which means the thickness of the wall is much smaller compared to the diameter.
- The vessel is subjected to internal pressure only.
Formula:
The formula for calculating the hoop stress in a thin-walled cylindrical vessel is given by:
Stress (σ) = P * r / t
Where,
σ = Hoop stress
P = Internal pressure
r = Internal radius of the vessel
t = Thickness of the vessel wall
Solution:
1. Convert the internal pressure from kPa to MPa:
500 kPa = 500/1000 = 0.5 MPa
2. Calculate the internal radius of the vessel:
Given internal diameter = 2 m
Internal radius = Diameter/2 = 2/2 = 1 m
3. Rearrange the formula for stress to find the thickness of the vessel wall:
t = P * r / σ
4. Substitute the given values into the formula:
t = 0.5 * 1 / 100 = 0.005 m = 5 mm
Conclusion:
The minimum thickness of the plate of the vessel is 5 mm.
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A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand aninternal pressure of 500 kPa (gauge). If the allowable normal stress at any point within thecylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (inmm) is________.(Important - Enter only the numerical value in the answer)Correct answer is '5'. Can you explain this answer?
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A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand aninternal pressure of 500 kPa (gauge). If the allowable normal stress at any point within thecylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (inmm) is________.(Important - Enter only the numerical value in the answer)Correct answer is '5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand aninternal pressure of 500 kPa (gauge). If the allowable normal stress at any point within thecylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (inmm) is________.(Important - Enter only the numerical value in the answer)Correct answer is '5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand aninternal pressure of 500 kPa (gauge). If the allowable normal stress at any point within thecylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (inmm) is________.(Important - Enter only the numerical value in the answer)Correct answer is '5'. Can you explain this answer?.
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