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A closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.?
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A closed cylindrical vessel made of steel plates 4 mm thick with plane...
Given data:
- Thickness of steel plates (t) = 4 mm
- Pressure of fluid (p) = 3 N/m^2
- Diameter of cylinder (d) = 25 cm = 0.25 m
- Length of cylinder (l) = 75 cm = 0.75 m
- Modulus of elasticity (E) = 2.1 x 10^5 N/m^2
- Poisson's Ratio (μ) = 0.286
Formulae:
- Longitudinal stress (σl) = pd/4t
- Hoop stress (σh) = pd/2t
- Change in diameter (Δd) = -(μ/2)[(σl/σh) + (σh/σl)]
- Change in length (Δl) = -μ[Δd/d]
- Change in volume (ΔV) = πd^2l(Δd/4 + Δl)
Calculation:
- Longitudinal stress (σl) = (3 N/m^2)(0.25 m)/(4 x 10^-3 m) = 1875 N/m^2
- Hoop stress (σh) = (3 N/m^2)(0.25 m)/(2 x 10^-3 m) = 3750 N/m^2
- Change in diameter (Δd) = -(0.286/2)[(1875 N/m^2)/(3750 N/m^2) + (3750 N/m^2)/(1875 N/m^2)] = -0.00097 m = -0.97 mm
- Change in length (Δl) = -(0.286)(-0.00097 m)/(0.25 m) = 0.0011 m = 1.1 mm
- Change in volume (ΔV) = π(0.25 m)^2(0.75 m)(-0.00097 m/4 + 0.0011 m) = -3.2 x 10^-5 m^3
Answer:
- Longitudinal stress (σl) = 1875 N/m^2
- Hoop stress (σh) = 3750 N/m^2
- Change in diameter (Δd) = -0.97 mm
- Change in length (Δl) = 1.1 mm
- Change in volume (ΔV) = -3.2 x 10^-5 m^3
Explanation:
- A closed cylindrical vessel made of steel plates is subjected to a fluid pressure. The stress in the cylinder wall is calculated using the formula for longitudinal stress and hoop stress.
- The change in diameter, length and volume of the cylinder is determined using Poisson's ratio and the formulae for change in diameter, change in length and change in volume.
- The given values are substituted in the formulae to obtain the numerical values of the stresses and the changes in dimensions and volume.
- The negative sign in the change in diameter and volume indicates that they decrease due to the applied pressure.
- Thickness of steel plates (t) = 4 mm
- Pressure of fluid (p) = 3 N/m^2
- Diameter of cylinder (d) = 25 cm = 0.25 m
- Length of cylinder (l) = 75 cm = 0.75 m
- Modulus of elasticity (E) = 2.1 x 10^5 N/m^2
- Poisson's Ratio (μ) = 0.286
Formulae:
- Longitudinal stress (σl) = pd/4t
- Hoop stress (σh) = pd/2t
- Change in diameter (Δd) = -(μ/2)[(σl/σh) + (σh/σl)]
- Change in length (Δl) = -μ[Δd/d]
- Change in volume (ΔV) = πd^2l(Δd/4 + Δl)
Calculation:
- Longitudinal stress (σl) = (3 N/m^2)(0.25 m)/(4 x 10^-3 m) = 1875 N/m^2
- Hoop stress (σh) = (3 N/m^2)(0.25 m)/(2 x 10^-3 m) = 3750 N/m^2
- Change in diameter (Δd) = -(0.286/2)[(1875 N/m^2)/(3750 N/m^2) + (3750 N/m^2)/(1875 N/m^2)] = -0.00097 m = -0.97 mm
- Change in length (Δl) = -(0.286)(-0.00097 m)/(0.25 m) = 0.0011 m = 1.1 mm
- Change in volume (ΔV) = π(0.25 m)^2(0.75 m)(-0.00097 m/4 + 0.0011 m) = -3.2 x 10^-5 m^3
Answer:
- Longitudinal stress (σl) = 1875 N/m^2
- Hoop stress (σh) = 3750 N/m^2
- Change in diameter (Δd) = -0.97 mm
- Change in length (Δl) = 1.1 mm
- Change in volume (ΔV) = -3.2 x 10^-5 m^3
Explanation:
- A closed cylindrical vessel made of steel plates is subjected to a fluid pressure. The stress in the cylinder wall is calculated using the formula for longitudinal stress and hoop stress.
- The change in diameter, length and volume of the cylinder is determined using Poisson's ratio and the formulae for change in diameter, change in length and change in volume.
- The given values are substituted in the formulae to obtain the numerical values of the stresses and the changes in dimensions and volume.
- The negative sign in the change in diameter and volume indicates that they decrease due to the applied pressure.
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A closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.?
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A closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.? 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 closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.?.
A closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.? 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 closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.?.
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A closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.?, a detailed solution for A closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.? has been provided alongside types of A closed cylindrical vessel made of steel plates 4 mm thick with plane ends carries a fluid under a pressure of 3N / m * m ^ 3 . The diamter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and op stresses in the cylinder wall and determine the change in diameter, length and volume of cylinder. E = 2.1 * 10 ^ 5N / m * m ^ 2 and Poisson's Ratio = 0.286.? theory, EduRev gives you an
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