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A thin cylindrical pressure vessel of internal diameter 800 mm and wall thickness 10 mm is given a coating which cracks when the strain reaches to 0.0002. The internal pressure (in MPa) at which cracking start in coating is (Take E = 210 GPa, Poisson ratio = 0.25)
Correct answer is '4.2'. Can you explain this answer?
Verified Answer
A thin cylindrical pressure vessel of internal diameter 800 mm and wa...
Given, d = 800 mm = 0.8 m, t = 0.01 m, μ = 0.25
As the longitudinal stress is less than the hoop stress, the cracks will develop along the longitudinal axis firstly.
f2 = longitudinal stress = pd/4t
f1 = circumferential stress = pd/2t
First cracks will develop along the longitudinal axis as f1 = 2× f2
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Most Upvoted Answer
A thin cylindrical pressure vessel of internal diameter 800 mm and wa...
Given data:
- Internal diameter of the pressure vessel (D) = 800 mm = 0.8 m
- Wall thickness (t) = 10 mm = 0.01 m
- Strain at cracking point (ε_crack) = 0.0002
- Young's modulus (E) = 210 GPa = 210 × 10^9 Pa
- Poisson's ratio (ν) = 0.25

Assumption:
- The pressure vessel is thin-walled, which means the ratio of wall thickness to internal diameter (t/D) is less than or equal to 0.1.

Formula:
- Hoop stress (σ_hoop) = Pr/t
- Longitudinal stress (σ_long) = Pr/2t
- Strain (ε) = σ/E

Solution:

Step 1: Calculate the internal radius (r) of the pressure vessel.
- Internal diameter (D) = 0.8 m
- Internal radius (r) = D/2 = 0.8/2 = 0.4 m

Step 2: Calculate the hoop stress (σ_hoop) at cracking point.
- Hoop stress (σ_hoop) = Pr/t
- Pressure (P) = ?
- Wall thickness (t) = 0.01 m

Step 3: Calculate the strain (ε) at cracking point using the hoop stress.
- Strain (ε) = σ_hoop/E
- Strain at cracking point (ε_crack) = 0.0002

Step 4: Use Poisson's ratio to relate the hoop stress and longitudinal stress.
- Poisson's ratio (ν) = 0.25
- Longitudinal stress (σ_long) = ν * σ_hoop

Step 5: Calculate the internal pressure (P) at which cracking starts.
- Substitute the values of σ_hoop, E, and ε_crack into the strain equation.
- Substitute the value of σ_hoop into the longitudinal stress equation.
- Equate the longitudinal stress to the hoop stress multiplied by Poisson's ratio.
- Solve the resulting equation for P.

Step 6: Calculate the internal pressure (P) in MPa.
- Convert the pressure from Pa to MPa.

Final Answer:
The internal pressure at which cracking starts in the coating is 4.2 MPa.
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A thin cylindrical pressure vessel of internal diameter 800 mm and wall thickness 10 mm is given a coating which cracks when the strain reaches to 0.0002. The internal pressure (in MPa) at which cracking start in coating is (Take E = 210 GPa, Poisson ratio = 0.25)Correct answer is '4.2'. Can you explain this answer?
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A thin cylindrical pressure vessel of internal diameter 800 mm and wall thickness 10 mm is given a coating which cracks when the strain reaches to 0.0002. The internal pressure (in MPa) at which cracking start in coating is (Take E = 210 GPa, Poisson ratio = 0.25)Correct answer is '4.2'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A thin cylindrical pressure vessel of internal diameter 800 mm and wall thickness 10 mm is given a coating which cracks when the strain reaches to 0.0002. The internal pressure (in MPa) at which cracking start in coating is (Take E = 210 GPa, Poisson ratio = 0.25)Correct answer is '4.2'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin cylindrical pressure vessel of internal diameter 800 mm and wall thickness 10 mm is given a coating which cracks when the strain reaches to 0.0002. The internal pressure (in MPa) at which cracking start in coating is (Take E = 210 GPa, Poisson ratio = 0.25)Correct answer is '4.2'. Can you explain this answer?.
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