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What is the safe working pressure for a spherical pressure vessel 1.5 m internal diameter and 1.5 cm wall thickness if the maximum allowable tensile stress is 45 MPa?
- a)0.9 MPa
- b)3.6 MPa
- c)2.7 MPa
- d)1.8 MPa
Correct answer is option 'D'. Can you explain this answer?
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What is the safe working pressure for a spherical pressure vessel 1.5...
For thin spherical vessel:
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For a thin spherical pressure vessel, both longitudinal and hoop stress is the same and given as
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What is the safe working pressure for a spherical pressure vessel 1.5...
Calculation of Safe Working Pressure for a Spherical Pressure Vessel:
1. Given Data:
- Internal diameter of the spherical pressure vessel (D) = 1.5 m
- Wall thickness of the vessel (t) = 1.5 cm = 0.015 m
- Maximum allowable tensile stress (σ) = 45 MPa = 45 N/mm² = 45 * 10^6 Pa
2. Calculation of Radius:
- Radius (r) of the spherical vessel = D/2 = 1.5/2 = 0.75 m
3. Calculation of Hoop Stress:
- Hoop stress (σh) in a spherical pressure vessel = P * r / t
- Where P is the internal pressure
- For safe working, maximum allowable tensile stress (σ) should be greater than or equal to hoop stress (σh)
4. Substitute Values and Solve for Pressure:
- 45 * 10^6 ≥ P * 0.75 / 0.015
- P ≤ 45 * 10^6 * 0.015 / 0.75
- P ≤ 9 * 10^5 Pa = 0.9 MPa
Therefore, the safe working pressure for the given spherical pressure vessel is 0.9 MPa. Hence, option 'a)' is the correct answer.
1. Given Data:
- Internal diameter of the spherical pressure vessel (D) = 1.5 m
- Wall thickness of the vessel (t) = 1.5 cm = 0.015 m
- Maximum allowable tensile stress (σ) = 45 MPa = 45 N/mm² = 45 * 10^6 Pa
2. Calculation of Radius:
- Radius (r) of the spherical vessel = D/2 = 1.5/2 = 0.75 m
3. Calculation of Hoop Stress:
- Hoop stress (σh) in a spherical pressure vessel = P * r / t
- Where P is the internal pressure
- For safe working, maximum allowable tensile stress (σ) should be greater than or equal to hoop stress (σh)
4. Substitute Values and Solve for Pressure:
- 45 * 10^6 ≥ P * 0.75 / 0.015
- P ≤ 45 * 10^6 * 0.015 / 0.75
- P ≤ 9 * 10^5 Pa = 0.9 MPa
Therefore, the safe working pressure for the given spherical pressure vessel is 0.9 MPa. Hence, option 'a)' is the correct answer.
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What is the safe working pressure for a spherical pressure vessel 1.5 m internal diameter and 1.5 cm wall thickness if the maximum allowable tensile stress is 45 MPa?a)0.9 MPab)3.6 MPac)2.7 MPad)1.8 MPaCorrect answer is option 'D'. Can you explain this answer?
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