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A pressure vessel in the form of a thin cylinder of 1 m diameter and 1mm plate thickness is subjected to an internal fluid pressure of 0.2MPa. The maximum shear stress in the material is
- a)37.5 MPa
- b)0 MPa
- c)25 MPa
- d)50 MPa
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A pressure vessel in the form of a thin cylinder of 1 m diameter and ...
D = 1 m = 103 mm t = 1 mm P = 0.2 MPa
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τmax =
= 50 MPa
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A pressure vessel in the form of a thin cylinder of 1 m diameter and ...
Calculation of Maximum Shear Stress in the Pressure Vessel
Given data:
Diameter of the cylinder (D) = 1 m
Thickness of the cylinder (t) = 1 mm = 0.001 m
Internal pressure (P) = 0.2 MPa
From the theory of thin cylinders, the hoop stress (σ_h) can be calculated as:
σ_h = P*D/(2*t)
Substituting the given values, we get:
σ_h = 0.2*1/(2*0.001) = 100 MPa
The maximum shear stress (τ_max) in the material can be calculated as:
τ_max = σ_h/2
Substituting the value of σ_h, we get:
τ_max = 100/2 = 50 MPa
Therefore, option D (50 MPa) is the correct answer.
Explanation
A pressure vessel is a container that holds a fluid under pressure. When a fluid is contained inside a vessel, it exerts a force on the walls of the vessel. This force is called the internal pressure. A thin-walled cylinder is a common shape for a pressure vessel. The stress in a thin-walled cylinder is mainly due to the hoop stress, which is the stress that acts circumferentially around the cylinder.
The maximum shear stress in a material is half of the hoop stress. This is because the hoop stress is the stress that acts in the circumferential direction, and the shear stress acts in the radial direction. The radial direction is perpendicular to the circumferential direction, so the maximum shear stress occurs at a 45-degree angle to the circumferential direction. At this angle, the shear stress is equal to half of the hoop stress.
In this question, we are given the diameter and thickness of the cylinder, as well as the internal pressure. Using the formula for hoop stress, we can calculate the hoop stress in the material. Then, using the formula for maximum shear stress, we can calculate the maximum shear stress in the material. The correct answer is option D, which gives the value of the maximum shear stress as 50 MPa.
Given data:
Diameter of the cylinder (D) = 1 m
Thickness of the cylinder (t) = 1 mm = 0.001 m
Internal pressure (P) = 0.2 MPa
From the theory of thin cylinders, the hoop stress (σ_h) can be calculated as:
σ_h = P*D/(2*t)
Substituting the given values, we get:
σ_h = 0.2*1/(2*0.001) = 100 MPa
The maximum shear stress (τ_max) in the material can be calculated as:
τ_max = σ_h/2
Substituting the value of σ_h, we get:
τ_max = 100/2 = 50 MPa
Therefore, option D (50 MPa) is the correct answer.
Explanation
A pressure vessel is a container that holds a fluid under pressure. When a fluid is contained inside a vessel, it exerts a force on the walls of the vessel. This force is called the internal pressure. A thin-walled cylinder is a common shape for a pressure vessel. The stress in a thin-walled cylinder is mainly due to the hoop stress, which is the stress that acts circumferentially around the cylinder.
The maximum shear stress in a material is half of the hoop stress. This is because the hoop stress is the stress that acts in the circumferential direction, and the shear stress acts in the radial direction. The radial direction is perpendicular to the circumferential direction, so the maximum shear stress occurs at a 45-degree angle to the circumferential direction. At this angle, the shear stress is equal to half of the hoop stress.
In this question, we are given the diameter and thickness of the cylinder, as well as the internal pressure. Using the formula for hoop stress, we can calculate the hoop stress in the material. Then, using the formula for maximum shear stress, we can calculate the maximum shear stress in the material. The correct answer is option D, which gives the value of the maximum shear stress as 50 MPa.
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A pressure vessel in the form of a thin cylinder of 1 m diameter and 1mm plate thickness is subjected to an internal fluid pressure of 0.2MPa. The maximum shear stress in the material isa) 37.5 MPab) 0 MPac) 25 MPad) 50 MPaCorrect answer is option 'D'. Can you explain this answer?
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