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What is the safe working pressure for a spherical pressure vessel 1.5m internal diameter and 1.5cm 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...
Hoop stress ≤ Maximum allowable tensile stress (for spherical vessel)
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P ≤ 1.8 MPa For safe working, pressure should be less than 1.8 MPa
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What is the safe working pressure for a spherical pressure vessel 1.5...
To determine the safe working pressure for a spherical pressure vessel, we need to consider the maximum allowable tensile stress and the dimensions of the vessel.
Given:
Internal diameter = 1.5 m
Wall thickness = 1.5 cm
Maximum allowable tensile stress = 45 MPa
Step 1: Convert the wall thickness to meters
1 cm = 0.01 m
Wall thickness = 0.015 m
Step 2: Calculate the radius of the vessel
Radius = internal diameter / 2
Radius = 1.5 m / 2
Radius = 0.75 m
Step 3: Calculate the hoop stress in the vessel
Hoop stress = pressure × radius / wall thickness
We need to find the pressure that will result in a hoop stress equal to the maximum allowable tensile stress.
Step 4: Rearrange the hoop stress formula to solve for pressure
Pressure = hoop stress × wall thickness / radius
Step 5: Substitute the given values into the formula
Pressure = 45 MPa × 0.015 m / 0.75 m
Pressure = 0.9 MPa
Therefore, the safe working pressure for the spherical pressure vessel is 0.9 MPa.
Explanation:
A spherical pressure vessel is subjected to hoop stress, which is given by the formula mentioned in Step 3. We rearrange the formula and substitute the given values to calculate the pressure that will result in the maximum allowable tensile stress of 45 MPa. By solving the equation, we find that the safe working pressure is 0.9 MPa.
Given:
Internal diameter = 1.5 m
Wall thickness = 1.5 cm
Maximum allowable tensile stress = 45 MPa
Step 1: Convert the wall thickness to meters
1 cm = 0.01 m
Wall thickness = 0.015 m
Step 2: Calculate the radius of the vessel
Radius = internal diameter / 2
Radius = 1.5 m / 2
Radius = 0.75 m
Step 3: Calculate the hoop stress in the vessel
Hoop stress = pressure × radius / wall thickness
We need to find the pressure that will result in a hoop stress equal to the maximum allowable tensile stress.
Step 4: Rearrange the hoop stress formula to solve for pressure
Pressure = hoop stress × wall thickness / radius
Step 5: Substitute the given values into the formula
Pressure = 45 MPa × 0.015 m / 0.75 m
Pressure = 0.9 MPa
Therefore, the safe working pressure for the spherical pressure vessel is 0.9 MPa.
Explanation:
A spherical pressure vessel is subjected to hoop stress, which is given by the formula mentioned in Step 3. We rearrange the formula and substitute the given values to calculate the pressure that will result in the maximum allowable tensile stress of 45 MPa. By solving the equation, we find that the safe working pressure is 0.9 MPa.
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