Mechanical Engineering Exam > Mechanical Engineering Questions > A high pressure cylinder consists of a steel ...
Start Learning for Free
A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.
- a)+2.56[(45/r) ² – 1]
- b)1.824[(45/r) ² – 1]
- c)-1.824[(45/r) ² – 1]
- d)None of the listed
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A high pressure cylinder consists of a steel tube with inner and outer...
Explanation: σ(t)=+PD₂²[D₃²/4r² – 1]/ [D₃²-D₂²].
Most Upvoted Answer
A high pressure cylinder consists of a steel tube with inner and outer...
Understanding the Problem
The high-pressure cylinder consists of a steel tube with given inner and outer diameters and is jacketed by another steel tube. We need to determine the tangential stresses due to the shrink fit of the jacket.
Given Data
- Inner diameter of the steel tube (d1) = 30 mm
- Outer diameter of the steel tube (d2) = 60 mm
- Outer diameter of the jacketed tube (d3) = 90 mm
- Maximum principal stress (σ) = 80 N/mm²
Concept of Tangential Stress
The tangential stress due to a shrink fit can be calculated using the formula derived from the theory of thick-walled cylinders. The tangential stress (τ) is influenced by the radial position (r) within the cylinder:
- τ = σ + [(1 - (d1/r)²) * σ]
Where:
- σ is the maximum principal stress
- r is the distance from the center of the cylinder
Calculating the Tangential Stress
1. Determine the radius (r):
- For the outer jacket, r = d3/2 = 90/2 = 45 mm.
2. Substitute into the tangential stress formula:
- The expression becomes τ = 80 + 2.56[(45/r)² – 1].
3. Evaluate at specific points:
- Using the outer jacket radius (r = 45 mm), we find τ.
Selecting the Correct Option
From the calculations, the derived expression for the tangential stress due to the shrink fit leads to option b) 1.824[(45/r)² – 1] being correct. It reflects the relationship between the stress, the geometry of the cylinder, and the material properties involved.
Conclusion
The understanding of how the maximum principal stress and radii interplay in a high-pressure cylinder is crucial for accurate calculations in mechanical engineering applications.
The high-pressure cylinder consists of a steel tube with given inner and outer diameters and is jacketed by another steel tube. We need to determine the tangential stresses due to the shrink fit of the jacket.
Given Data
- Inner diameter of the steel tube (d1) = 30 mm
- Outer diameter of the steel tube (d2) = 60 mm
- Outer diameter of the jacketed tube (d3) = 90 mm
- Maximum principal stress (σ) = 80 N/mm²
Concept of Tangential Stress
The tangential stress due to a shrink fit can be calculated using the formula derived from the theory of thick-walled cylinders. The tangential stress (τ) is influenced by the radial position (r) within the cylinder:
- τ = σ + [(1 - (d1/r)²) * σ]
Where:
- σ is the maximum principal stress
- r is the distance from the center of the cylinder
Calculating the Tangential Stress
1. Determine the radius (r):
- For the outer jacket, r = d3/2 = 90/2 = 45 mm.
2. Substitute into the tangential stress formula:
- The expression becomes τ = 80 + 2.56[(45/r)² – 1].
3. Evaluate at specific points:
- Using the outer jacket radius (r = 45 mm), we find τ.
Selecting the Correct Option
From the calculations, the derived expression for the tangential stress due to the shrink fit leads to option b) 1.824[(45/r)² – 1] being correct. It reflects the relationship between the stress, the geometry of the cylinder, and the material properties involved.
Conclusion
The understanding of how the maximum principal stress and radii interplay in a high-pressure cylinder is crucial for accurate calculations in mechanical engineering applications.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer?
Question Description
A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer? 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 high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer?.
A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer? 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 high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stresses due to shrink shift in jacket.a)+2.56[(45/r) ² – 1]b)1.824[(45/r) ² – 1]c)-1.824[(45/r) ² – 1]d)None of the listedCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup