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A thin walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed is
- a)14 MPa
- b)1.4 MPa
- c)0.14 MPa
- d)0.014 MPa
Correct answer is option 'A'. Can you explain this answer?
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Understanding the Problem
To find the hoop stress in a thin-walled cylindrical pressure vessel, we can use the formula for hoop stress (σ_h):
σ_h = (P * r) / t
Where:
- P = Internal Pressure
- r = Radius of the cylinder
- t = Wall Thickness
Given values:
- P = 700 kPa = 700,000 Pa
- r = 0.5 m = 500 mm
- t = 25 mm = 0.025 m
Calculating the Hoop Stress
1. Convert Units:
- Ensure all dimensions are in meters for consistency:
- P = 700,000 Pa
- r = 0.5 m
- t = 0.025 m
2. Substitute Values into the Formula:
- σ_h = (700,000 * 0.5) / 0.025
3. Perform the Calculation:
- σ_h = (350,000) / 0.025
- σ_h = 14,000,000 Pa
Final Result
- Convert the stress into MPa for easier interpretation:
- 14,000,000 Pa = 14 MPa
Thus, the hoop stress developed in the thin-walled cylindrical pressure vessel is:
Answer: 14 MPa (Option A)
Conclusion
- This result indicates a significant amount of stress in the vessel's walls due to the internal pressure.
- Understanding hoop stress is essential in designing safe pressure vessels to prevent failure.
To find the hoop stress in a thin-walled cylindrical pressure vessel, we can use the formula for hoop stress (σ_h):
σ_h = (P * r) / t
Where:
- P = Internal Pressure
- r = Radius of the cylinder
- t = Wall Thickness
Given values:
- P = 700 kPa = 700,000 Pa
- r = 0.5 m = 500 mm
- t = 25 mm = 0.025 m
Calculating the Hoop Stress
1. Convert Units:
- Ensure all dimensions are in meters for consistency:
- P = 700,000 Pa
- r = 0.5 m
- t = 0.025 m
2. Substitute Values into the Formula:
- σ_h = (700,000 * 0.5) / 0.025
3. Perform the Calculation:
- σ_h = (350,000) / 0.025
- σ_h = 14,000,000 Pa
Final Result
- Convert the stress into MPa for easier interpretation:
- 14,000,000 Pa = 14 MPa
Thus, the hoop stress developed in the thin-walled cylindrical pressure vessel is:
Answer: 14 MPa (Option A)
Conclusion
- This result indicates a significant amount of stress in the vessel's walls due to the internal pressure.
- Understanding hoop stress is essential in designing safe pressure vessels to prevent failure.
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A thin walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed isa)14 MPab)1.4 MPac)0.14 MPad)0.014 MPaCorrect answer is option 'A'. Can you explain this answer?
Question Description
A thin walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed isa)14 MPab)1.4 MPac)0.14 MPad)0.014 MPaCorrect answer is option 'A'. 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 having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed isa)14 MPab)1.4 MPac)0.14 MPad)0.014 MPaCorrect answer is option 'A'. 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 having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed isa)14 MPab)1.4 MPac)0.14 MPad)0.014 MPaCorrect answer is option 'A'. Can you explain this answer?.
A thin walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed isa)14 MPab)1.4 MPac)0.14 MPad)0.014 MPaCorrect answer is option 'A'. 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 having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed isa)14 MPab)1.4 MPac)0.14 MPad)0.014 MPaCorrect answer is option 'A'. 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 having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed isa)14 MPab)1.4 MPac)0.14 MPad)0.014 MPaCorrect answer is option 'A'. Can you explain this answer?.
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