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A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall thickness (in mm) for safe design must be _____. (Answer to the nearest integer)
Correct answer is '10'. Can you explain this answer?
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Most Upvoted Answer
A thin gas cylinder with an internal radius of 100 mm is subject to a...
In thin cylinder circumferential stress is greater than longitudinal stress_ So minimum cylinder wall thickness for safe design must be calculated from circumferential stress i.e. σ = Pr/t
So t = Pr/σ
Given that,
Internal radius (r) = 100 mm
Internal pressure (P) = l0 MPa
Max permissible working stress
t = 10 mm
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Community Answer
A thin gas cylinder with an internal radius of 100 mm is subject to a...
Given data:
Internal radius of the gas cylinder (r) = 100 mm = 0.1 m
Internal pressure (P) = 10 MPa = 10 × 10^6 Pa
Maximum permissible working stress (σ_max) = 100 MPa = 100 × 10^6 Pa
Formula:
The hoop stress (σ_h) in a thin-walled cylinder can be calculated using the formula:
σ_h = P × r / t
Where:
σ_h = Hoop stress
P = Internal pressure
r = Internal radius
t = Wall thickness
Calculation:
To ensure safe design, the hoop stress should be less than or equal to the maximum permissible working stress.
Therefore, we can write the inequality as:
σ_h ≤ σ_max
Substituting the values in the formula:
P × r / t ≤ σ_max
Solving for t:
t ≥ P × r / σ_max
Substituting the given values:
t ≥ (10 × 10^6) × (0.1) / (100 × 10^6)
t ≥ 1 × 10^6 / 10 × 10^6
t ≥ 0.1 mm
Conclusion:
The minimum cylinder wall thickness for safe design must be 0.1 mm. Since the answer needs to be rounded to the nearest integer, the correct answer is 1 mm.
Internal radius of the gas cylinder (r) = 100 mm = 0.1 m
Internal pressure (P) = 10 MPa = 10 × 10^6 Pa
Maximum permissible working stress (σ_max) = 100 MPa = 100 × 10^6 Pa
Formula:
The hoop stress (σ_h) in a thin-walled cylinder can be calculated using the formula:
σ_h = P × r / t
Where:
σ_h = Hoop stress
P = Internal pressure
r = Internal radius
t = Wall thickness
Calculation:
To ensure safe design, the hoop stress should be less than or equal to the maximum permissible working stress.
Therefore, we can write the inequality as:
σ_h ≤ σ_max
Substituting the values in the formula:
P × r / t ≤ σ_max
Solving for t:
t ≥ P × r / σ_max
Substituting the given values:
t ≥ (10 × 10^6) × (0.1) / (100 × 10^6)
t ≥ 1 × 10^6 / 10 × 10^6
t ≥ 0.1 mm
Conclusion:
The minimum cylinder wall thickness for safe design must be 0.1 mm. Since the answer needs to be rounded to the nearest integer, the correct answer is 1 mm.
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A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall thickness (in mm) for safe design must be _____. (Answer to the nearest integer)Correct answer is '10'. Can you explain this answer?
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A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall thickness (in mm) for safe design must be _____. (Answer to the nearest integer)Correct answer is '10'. 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 thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall thickness (in mm) for safe design must be _____. (Answer to the nearest integer)Correct answer is '10'. 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 thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall thickness (in mm) for safe design must be _____. (Answer to the nearest integer)Correct answer is '10'. Can you explain this answer?.
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