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 (A)</p> Signup and view all the answers

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

<p>σt = pD / 2t (D)</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 (A)</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 (C)</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 (A)</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 (B)</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 (A)</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 (D)</p> Signup and view all the answers

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

<p>Internal pressure (C)</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 (D)</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 (D)</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 (B)</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 (C)</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 (D)</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 (A)</p> Signup and view all the answers

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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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