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A cylinder of thickness 1.5cm has to withstand maximum internal pressure of 1.5 N/mm2. If the ultimate tensile stress in the material of the cylinder is 300 N/mm2, factor of safety 3.0 and joint efficiency 80%, the diameter of the cylinder is
- a)160 m
- b)160 cm
- c)160 mm
- d)160 km
Correct answer is option 'B'. Can you explain this answer?
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A cylinder of thickness 1.5cm has to withstand maximum internal press...
300/3 =
d = 1600 mm = 160 cm
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A cylinder of thickness 1.5cm has to withstand maximum internal press...
To determine the diameter of the cylinder, we need to consider the maximum internal pressure, ultimate tensile stress, factor of safety, and joint efficiency.
Given:
- Thickness of the cylinder (t) = 1.5 cm
- Maximum internal pressure (P) = 1.5 N/mm^2
- Ultimate tensile stress (UTS) = 300 N/mm^2
- Factor of safety (FoS) = 3.0
- Joint efficiency (JE) = 80%
Let's calculate the hoop stress and then equate it to the ultimate tensile stress to find the diameter.
1. Hoop Stress (σh):
The formula for hoop stress in a cylinder is given by:
σh = P * D / (2 * t)
where σh is the hoop stress, P is the pressure, D is the diameter, and t is the thickness.
2. Equating hoop stress to ultimate tensile stress:
To ensure the cylinder can withstand the pressure, the hoop stress should be less than or equal to the ultimate tensile stress. So, we have:
σh ≤ UTS
3. Solving for diameter (D):
Rearranging the equation from step 1, we get:
D = (2 * σh * t) / P
4. Determining the allowable stress:
The allowable stress is the product of the ultimate tensile stress and the factor of safety:
Allowable stress = UTS / FoS
5. Considering the joint efficiency:
The actual allowable stress is reduced by the joint efficiency:
Actual allowable stress = Allowable stress * JE
6. Substituting values and solving for diameter (D):
D = (2 * σh * t) / P
D = (2 * (Allowable stress * JE) * t) / P
Substituting the given values:
Allowable stress = (UTS / FoS) = (300 N/mm^2 / 3.0) = 100 N/mm^2
Actual allowable stress = (Allowable stress * JE) = (100 N/mm^2 * 0.80) = 80 N/mm^2
D = (2 * 80 N/mm^2 * 1.5 cm) / 1.5 N/mm^2
D = 160 cm
Therefore, the diameter of the cylinder is 160 cm (option B).
Given:
- Thickness of the cylinder (t) = 1.5 cm
- Maximum internal pressure (P) = 1.5 N/mm^2
- Ultimate tensile stress (UTS) = 300 N/mm^2
- Factor of safety (FoS) = 3.0
- Joint efficiency (JE) = 80%
Let's calculate the hoop stress and then equate it to the ultimate tensile stress to find the diameter.
1. Hoop Stress (σh):
The formula for hoop stress in a cylinder is given by:
σh = P * D / (2 * t)
where σh is the hoop stress, P is the pressure, D is the diameter, and t is the thickness.
2. Equating hoop stress to ultimate tensile stress:
To ensure the cylinder can withstand the pressure, the hoop stress should be less than or equal to the ultimate tensile stress. So, we have:
σh ≤ UTS
3. Solving for diameter (D):
Rearranging the equation from step 1, we get:
D = (2 * σh * t) / P
4. Determining the allowable stress:
The allowable stress is the product of the ultimate tensile stress and the factor of safety:
Allowable stress = UTS / FoS
5. Considering the joint efficiency:
The actual allowable stress is reduced by the joint efficiency:
Actual allowable stress = Allowable stress * JE
6. Substituting values and solving for diameter (D):
D = (2 * σh * t) / P
D = (2 * (Allowable stress * JE) * t) / P
Substituting the given values:
Allowable stress = (UTS / FoS) = (300 N/mm^2 / 3.0) = 100 N/mm^2
Actual allowable stress = (Allowable stress * JE) = (100 N/mm^2 * 0.80) = 80 N/mm^2
D = (2 * 80 N/mm^2 * 1.5 cm) / 1.5 N/mm^2
D = 160 cm
Therefore, the diameter of the cylinder is 160 cm (option B).
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A cylinder of thickness 1.5cm has to withstand maximum internal pressure of 1.5 N/mm2. If the ultimate tensile stress in the material of the cylinder is 300 N/mm2, factor of safety 3.0 and joint efficiency 80%, the diameter of the cylinder isa) 160 mb) 160 cmc) 160 mmd) 160 kmCorrect answer is option 'B'. Can you explain this answer?
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