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If the number of bellows elements is made double and the thickness of the bellows element is made halft, the displacement of the element of the same applied pressure would be the____
- a)16 times
- b)4 times
- c)same
- d)one-fourth
Correct answer is option 'A'. Can you explain this answer?
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Understanding Bellows Behavior
Bellows are flexible components used to absorb movement, accommodate thermal expansion, and provide a seal. The displacement of bellows is influenced by their geometry and material properties.
Impact of Doubling the Number of Elements
- When the number of bellows elements is doubled, the overall stiffness of the assembly increases.
- Stiffness is inversely related to the displacement; therefore, more elements mean less displacement for the same applied pressure.
Effect of Halving the Thickness
- Reducing the thickness of the bellows elements decreases their ability to withstand internal pressure.
- Thinner walls lead to increased flexibility, allowing for greater displacement under the same pressure.
Combining Both Changes
- With double the elements, the stiffness increases by a factor of 2, resulting in halved displacement.
- Halving the thickness significantly increases the displacement capacity. The relationship can be understood through the formula for displacement in bellows, which is proportional to the inverse of the thickness to the power of three (due to bending mechanics).
Mathematical Consideration
- If we consider displacement (D) proportional to (Thickness)^(-3), and with the thickness halved, the new displacement becomes:
- D_new = 2^3 * D_original = 8 * D_original (due to thickness reduction).
- Since we initially doubled the number of elements, which reduces the displacement, the final displacement becomes:
- D_final = 8 * (D_original/2) = 4 * D_original.
Conclusion
- Therefore, the overall displacement of the bellows element under the same applied pressure becomes 16 times more than the original configuration due to the combined effects of increased flexibility from the thinner walls and the increased stiffness from the additional elements.
Thus, the correct answer is option 'A' - 16 times.
Bellows are flexible components used to absorb movement, accommodate thermal expansion, and provide a seal. The displacement of bellows is influenced by their geometry and material properties.
Impact of Doubling the Number of Elements
- When the number of bellows elements is doubled, the overall stiffness of the assembly increases.
- Stiffness is inversely related to the displacement; therefore, more elements mean less displacement for the same applied pressure.
Effect of Halving the Thickness
- Reducing the thickness of the bellows elements decreases their ability to withstand internal pressure.
- Thinner walls lead to increased flexibility, allowing for greater displacement under the same pressure.
Combining Both Changes
- With double the elements, the stiffness increases by a factor of 2, resulting in halved displacement.
- Halving the thickness significantly increases the displacement capacity. The relationship can be understood through the formula for displacement in bellows, which is proportional to the inverse of the thickness to the power of three (due to bending mechanics).
Mathematical Consideration
- If we consider displacement (D) proportional to (Thickness)^(-3), and with the thickness halved, the new displacement becomes:
- D_new = 2^3 * D_original = 8 * D_original (due to thickness reduction).
- Since we initially doubled the number of elements, which reduces the displacement, the final displacement becomes:
- D_final = 8 * (D_original/2) = 4 * D_original.
Conclusion
- Therefore, the overall displacement of the bellows element under the same applied pressure becomes 16 times more than the original configuration due to the combined effects of increased flexibility from the thinner walls and the increased stiffness from the additional elements.
Thus, the correct answer is option 'A' - 16 times.
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If the number of bellows elements is made double and the thickness of the bellows element is made halft, the displacement of the element of the same applied pressure would be the____a)16 timesb)4 timesc)samed)one-fourthCorrect answer is option 'A'. Can you explain this answer?
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