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Questions and Answers
What is the formula for the longitudinal stress (σL) in a cylindrical vessel?
What is the relationship between the longitudinal stress (σL) and circumferential stress (σt) in a thin-walled pressure vessel?
What is the total force experienced by the wall in the longitudinal direction in a cylindrical vessel?
What is the strength requirement for longitudinal joints compared to girth joints?
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What is the formula for the circumferential stress (σt) in a cylindrical vessel?
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What is the mode of failure in a thin-walled pressure vessel subjected to excessive gas pressure?
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What is the primary reason for using semispherical end caps in cylindrical pressure vessels?
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A cylindrical pressure vessel is subjected to an internal pressure of 3.5 MPa. If the stress is limited to 140 MPa, what is the maximum internal pressure allowed?
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What is the unit weight of water at standard temperature in the SI system?
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A water tank 5 m in diameter and 8 m high is completely filled. What is the minimum thickness of the tank if the plate stress is limited to 40 MPa?
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A vertical cylindrical steel tank 3 m in diameter and 6 m high has a wall thickness of 12 mm. What is the circumferential stress if the tank is filled with water?
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What is the primary factor affecting the longitudinal stress in a cylindrical pressure vessel?
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What is the maximum internal pressure that a tank can withstand if the permissible stress is limited to 5 MPa?
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What is the minimum required thickness of a boiler plate if the internal pressure is 2 MPa and the permissible tensile stress is 120 MPa?
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What is the maximum diameter of a boiler if the efficiency of the longitudinal joint is 90% and that of the circumferential joint is 40%?
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What is the minimum number of bolts required to hold a cap on a pipe if the allowable stress in the bolts is 92 MPa and the initial stress is 60 MPa?
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What is the primary factor that determines the maximum height of water in a tank if the stress is limited to 5 MPa?
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What is the purpose of a gasket in a pipe flange?
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Study Notes
Thin-Walled Pressure Vessels
- Cylindrical pressure vessels have semispherical end caps to reduce stress in the tank.
Calculating Stress in Thin-Walled Pressure Vessels
- Tangential stress (Hoop stress) formula: σt = pD / (2t)
- Longitudinal stress (Meridional stress) formula: σL = pD / (4t)
Sample Problems
Problem 2.3.1
- Cylindrical steel pressure vessel with diameter 500 mm, wall thickness 20 mm, and internal pressure 3.5 MPa
- Calculate tangential and longitudinal stress in the cylinder
- Calculate maximum internal pressure to limit stress to 140 MPa
Problem 2.3.2
- Water tank with diameter 5 m, height 8 m, and plate stress limited to 40 MPa
- Calculate minimum thickness of the tank
Problem 2.3.3
- Vertical cylindrical steel tank with diameter 3 m, height 6 m, and wall thickness 12 mm
- Calculate circumferential stress when filled with water
- Calculate longitudinal stress when filled with water
Unit Weight of Water
- Approximately 9810 N/m³ or 9.81 kN/m³ at standard temperature (4°C)
Rupture of Thin-Walled Pipes
- Pipe rupture occurs in the circumferential or hoop direction due to excessive gas pressure
- Formula: σt = 2σL
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Description
Calculate the tangential and longitudinal stress in a cylindrical steel pressure vessel subjected to internal pressure. Understand the design of semispherical end caps in pressure vessels to reduce stress.
