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A compound tube is composed of a tube 250 mm internal diameter and 25 mm thick shrunk on a tube of 250 mm external diameter and 25 mm thick. The radial pressure at the junction is 9 N/mm2 . The compound tube is subjected to an internal fluid pressure of 90 N/mm2 . Find the variation of the hoop stress over the wall of the compound tube and sketch the stress distribution diagram. ?
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A compound tube is composed of a tube 250 mm internal diameter and 25 ...
Compound Tube Design Analysis
Given Data:
- Internal diameter of tube = 250 mm
- Thickness of tube = 25 mm
- External diameter of tube = 250 mm
- Radial pressure at the junction = 9 N/mm2
- Internal fluid pressure = 90 N/mm2
Hoops Stress Calculation:
- The compound tube can be treated as a thick cylinder.
- Hoop stress is given by the formula: σh = (pi*di^2*P) / (4*t*do)
- where pi is 3.14, di is the internal diameter, P is the internal fluid pressure, t is the thickness, and do is the external diameter.
- Substituting the given values, σh = (3.14*250^2*90) / (4*25*250) = 283.5 N/mm2.
Stress Distribution:
- The variation of hoop stress over the wall of the compound tube can be calculated using the formula: σh = (P*ro)/(R^2-ro^2) * ((R^2+r^2)/(R^2-r^2))
- where ro is the outer radius, R is the radius of the inner tube, and r is the radius of the compound tube.
- The stress distribution diagram can be plotted using the calculated values of hoop stress for different radii.
Conclusion:
- The compound tube can safely withstand the internal fluid pressure of 90 N/mm2 as the calculated hoop stress is 283.5 N/mm2, which is less than the yield strength of the material.
- The stress distribution diagram shows that the maximum hoop stress occurs at the inner radius of the compound tube and decreases towards the outer radius.
Given Data:
- Internal diameter of tube = 250 mm
- Thickness of tube = 25 mm
- External diameter of tube = 250 mm
- Radial pressure at the junction = 9 N/mm2
- Internal fluid pressure = 90 N/mm2
Hoops Stress Calculation:
- The compound tube can be treated as a thick cylinder.
- Hoop stress is given by the formula: σh = (pi*di^2*P) / (4*t*do)
- where pi is 3.14, di is the internal diameter, P is the internal fluid pressure, t is the thickness, and do is the external diameter.
- Substituting the given values, σh = (3.14*250^2*90) / (4*25*250) = 283.5 N/mm2.
Stress Distribution:
- The variation of hoop stress over the wall of the compound tube can be calculated using the formula: σh = (P*ro)/(R^2-ro^2) * ((R^2+r^2)/(R^2-r^2))
- where ro is the outer radius, R is the radius of the inner tube, and r is the radius of the compound tube.
- The stress distribution diagram can be plotted using the calculated values of hoop stress for different radii.
Conclusion:
- The compound tube can safely withstand the internal fluid pressure of 90 N/mm2 as the calculated hoop stress is 283.5 N/mm2, which is less than the yield strength of the material.
- The stress distribution diagram shows that the maximum hoop stress occurs at the inner radius of the compound tube and decreases towards the outer radius.
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A compound tube is composed of a tube 250 mm internal diameter and 25 mm thick shrunk on a tube of 250 mm external diameter and 25 mm thick. The radial pressure at the junction is 9 N/mm2 . The compound tube is subjected to an internal fluid pressure of 90 N/mm2 . Find the variation of the hoop stress over the wall of the compound tube and sketch the stress distribution diagram. ?
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A compound tube is composed of a tube 250 mm internal diameter and 25 mm thick shrunk on a tube of 250 mm external diameter and 25 mm thick. The radial pressure at the junction is 9 N/mm2 . The compound tube is subjected to an internal fluid pressure of 90 N/mm2 . Find the variation of the hoop stress over the wall of the compound tube and sketch the stress distribution diagram. ? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A compound tube is composed of a tube 250 mm internal diameter and 25 mm thick shrunk on a tube of 250 mm external diameter and 25 mm thick. The radial pressure at the junction is 9 N/mm2 . The compound tube is subjected to an internal fluid pressure of 90 N/mm2 . Find the variation of the hoop stress over the wall of the compound tube and sketch the stress distribution diagram. ? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A compound tube is composed of a tube 250 mm internal diameter and 25 mm thick shrunk on a tube of 250 mm external diameter and 25 mm thick. The radial pressure at the junction is 9 N/mm2 . The compound tube is subjected to an internal fluid pressure of 90 N/mm2 . Find the variation of the hoop stress over the wall of the compound tube and sketch the stress distribution diagram. ?.
A compound tube is composed of a tube 250 mm internal diameter and 25 mm thick shrunk on a tube of 250 mm external diameter and 25 mm thick. The radial pressure at the junction is 9 N/mm2 . The compound tube is subjected to an internal fluid pressure of 90 N/mm2 . Find the variation of the hoop stress over the wall of the compound tube and sketch the stress distribution diagram. ? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A compound tube is composed of a tube 250 mm internal diameter and 25 mm thick shrunk on a tube of 250 mm external diameter and 25 mm thick. The radial pressure at the junction is 9 N/mm2 . The compound tube is subjected to an internal fluid pressure of 90 N/mm2 . Find the variation of the hoop stress over the wall of the compound tube and sketch the stress distribution diagram. ? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A compound tube is composed of a tube 250 mm internal diameter and 25 mm thick shrunk on a tube of 250 mm external diameter and 25 mm thick. The radial pressure at the junction is 9 N/mm2 . The compound tube is subjected to an internal fluid pressure of 90 N/mm2 . Find the variation of the hoop stress over the wall of the compound tube and sketch the stress distribution diagram. ?.
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