14. Design of Pressure Vessels free study notes

1. Introduction

A pressure vessel is a container designed to hold gases or liquids at a pressure different from atmospheric pressure. These are widely used in industries such as power plants, chemical processing, oil & gas, and refrigeration.

2. Applications

• Boilers
• Air receivers
• Gas storage tanks
• Heat exchangers
• Nuclear reactors

3. Classification of Pressure Vessels

(a) Based on Shape

• Cylindrical vessels
• Spherical vessels
• Conical vessels

(b) Based on Wall Thickness

• Thin-walled vessels (t < d/20)
• Thick-walled vessels (t ≥ d/20)

4. Stresses in Thin Cylindrical Pressure Vessels

(a) Hoop (Circumferential) Stress

$\sigma_h = \frac{p d}{2 t}$

• Acts along circumference
• Maximum stress

(b) Longitudinal Stress

$\sigma_l = \frac{p d}{4 t}$

• Acts along length
• Half of hoop stress

(c) Radial Stress

• Acts along thickness
• Usually negligible in thin vessels

5. Design of Thin Cylindrical Shell

Thickness Calculation

From hoop stress:$$t = \frac{p d}{2 \sigma_{allowable}}$$

• Add corrosion allowance
• Consider joint efficiency

With Joint Efficiency (η)

$$t = \frac{p d}{2 \sigma_t \eta}$$

6. Design of Spherical Pressure Vessel

Stress in Sphere

$\sigma = \frac{p d}{4 t}$σ=4tpd​

• Lower stress than cylindrical → more efficient

7. Thick-Walled Pressure Vessels

When thickness is large, stress varies across thickness.

Lame’s Equations

$\sigma_r = A – \frac{B}{r^2}, \quad \sigma_\theta = A + \frac{B}{r^2}$

Where:

• $\sigma_r$σr​ = radial stress
• $\sigma_\theta$σθ​ = hoop stress

8. Design Considerations

• Internal pressure
• Material strength
• Temperature effects
• Corrosion allowance
• Weld joint efficiency
• Safety factor

9. Materials for Pressure Vessels

• Carbon steel
• Alloy steel
• Stainless steel
• Composite materials

Desired properties:

• High strength
• Ductility
• Corrosion resistance
• Weldability

10. Failure Theories Used

• Maximum principal stress theory
• Maximum shear stress theory
• Distortion energy theory

11. Design Codes and Standards

• ASME Boiler and Pressure Vessel Code
• Indian Boiler Regulations (IBR)

Ensure safety and reliability

12. Openings and Reinforcement

• Openings weaken the vessel
• Reinforcement provided around:
  • Nozzles
  • Manholes

13. Advantages of Spherical Vessels

• Uniform stress distribution
• Minimum material required
• High strength

14. Disadvantages

• Difficult fabrication
• Expensive
• Complex supports

15. Applications

• LPG storage tanks
• Boilers
• Chemical reactors
• Compressed gas cylinders

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