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When 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 in vessel 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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When is the safe working pressure for a spherical pressure vessel 1.5...
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P = = 1.8 MPa
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When is the safe working pressure for a spherical pressure vessel 1.5...
Given:
- Internal diameter of the spherical pressure vessel = 1.5 m
- Wall thickness of the vessel = 1.5 cm
- Maximum allowable tensile stress in the vessel = 45 MPa

To find:
- Safe working pressure for the spherical pressure vessel

Assumptions:
- The pressure vessel is made of a homogeneous material with uniform properties.
- The vessel is subjected to internal pressure only.
- The vessel is perfectly spherical, without any irregularities or deformations.

Formula:
The formula to calculate the safe working pressure for a spherical pressure vessel is given by the Lame's equation:

P = (2 * S * t) / (D - t)

Where:
P is the safe working pressure
S is the maximum allowable tensile stress
t is the wall thickness of the vessel
D is the internal diameter of the vessel

Solution:
Given:
- Internal diameter (D) = 1.5 m
- Wall thickness (t) = 1.5 cm = 0.015 m
- Maximum allowable tensile stress (S) = 45 MPa

Using the Lame's equation, we can substitute the given values to calculate the safe working pressure (P):

P = (2 * S * t) / (D - t)
= (2 * 45 * 0.015) / (1.5 - 0.015)
= 1.8 MPa

Therefore, the safe working pressure for the spherical pressure vessel with a 1.5 m internal diameter and 1.5 cm wall thickness, with a maximum allowable tensile stress of 45 MPa, is 1.8 MPa. Hence, the correct answer is option 'D' (1.8 MPa).
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