Thin-Walled Pressure Vessels
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Questions and Answers

What is the formula for the longitudinal stress (σL) in a cylindrical vessel?

  • σL = pD / 2t
  • σL = pD / t
  • σL = pD / 8t
  • σL = pD / 4t (correct)
  • What is the relationship between the longitudinal stress (σL) and circumferential stress (σt) in a thin-walled pressure vessel?

  • σt = σL
  • σt = σL / 4
  • σt = 2σL (correct)
  • σt = σL / 2
  • What is the total force experienced by the wall in the longitudinal direction in a cylindrical vessel?

  • PT = pDL / 2
  • PT = pA (correct)
  • PT = pDL
  • PT = pDL / 4
  • What is the strength requirement for longitudinal joints compared to girth joints?

    <p>Longitudinal joints should be twice the strength of girth joints</p> Signup and view all the answers

    What is the formula for the circumferential stress (σt) in a cylindrical vessel?

    <p>σt = pD / 2t</p> Signup and view all the answers

    What is the mode of failure in a thin-walled pressure vessel subjected to excessive gas pressure?

    <p>Circumferential failure</p> Signup and view all the answers

    What is the primary reason for using semispherical end caps in cylindrical pressure vessels?

    <p>To reduce the stress in the tank</p> Signup and view all the answers

    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?

    <p>6.5 MPa</p> Signup and view all the answers

    What is the unit weight of water at standard temperature in the SI system?

    <p>9810 N/m³</p> Signup and view all the answers

    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?

    <p>12 mm</p> Signup and view all the answers

    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?

    <p>40 MPa</p> Signup and view all the answers

    What is the primary factor affecting the longitudinal stress in a cylindrical pressure vessel?

    <p>Internal pressure</p> Signup and view all the answers

    What is the maximum internal pressure that a tank can withstand if the permissible stress is limited to 5 MPa?

    <p>5 MPa</p> Signup and view all the answers

    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?

    <p>2.5 cm</p> Signup and view all the answers

    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%?

    <p>750 mm</p> Signup and view all the answers

    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?

    <p>8</p> Signup and view all the answers

    What is the primary factor that determines the maximum height of water in a tank if the stress is limited to 5 MPa?

    <p>Tank geometry</p> Signup and view all the answers

    What is the purpose of a gasket in a pipe flange?

    <p>To provide a seal between the flange and the pipe</p> Signup and view all the answers

    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.

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