The minimum required thickness of a pressure vessel is calculated using specific formulas derived from codes and standards like ASME Boiler and Pressure Vessel Code, Section VIII, Division 1. The exact formula varies depending on the geometry of the vessel component (e.g., cylindrical shell, spherical shell, head) and the specific code being used. However, the general principles and variables involved are consistent. This response will cover the typical approach for calculating the minimum thickness of a cylindrical shell.
Cylindrical Shell Minimum Thickness Calculation (Example based on ASME Section VIII, Division 1)
The most common formula for calculating the minimum thickness of a cylindrical shell is:
t = (P * R) / (S * E - 0.6 * P)Where:
- t = Minimum required thickness of the shell (inches or mm)
- P = Design pressure (psi or MPa)
- R = Inside radius of the shell (inches or mm)
- S = Allowable stress for the material at the design temperature (psi or MPa)
- E = Longitudinal joint efficiency (dimensionless, typically between 0.6 and 1.0, depending on the type of weld and inspection)
Understanding the Variables
- Design Pressure (P): This is the maximum pressure the vessel is designed to withstand during normal operation. It's a critical factor in determining the required thickness.
- Inside Radius (R): Using the inside radius is crucial. Sometimes the outside radius is given, so be sure to calculate the inside radius correctly.
- Allowable Stress (S): This is the maximum stress the material can safely handle at the design temperature, as determined by the relevant code. It's based on the material's yield strength and tensile strength, with a safety factor applied. This value is found in the code tables.
- Longitudinal Joint Efficiency (E): This factor accounts for the strength of the longitudinal welds in the vessel. A higher joint efficiency allows for a thinner vessel. Full radiography generally allows for an E=1.0. Spot radiography usually results in a lower value, such as E=0.85 or 0.7. No radiography will require a even lower joint efficiency.
Example Calculation (Using provided video information)
Let's use the values from the video:
- P = 600 psi
- R = 24 inches
- S = 20,000 psi
- E = 1.0
Plugging these values into the formula:
t = (600 psi * 24 inches) / (20,000 psi * 1.0 - 0.6 * 600 psi)
t = 14,400 / (20,000 - 360)
t = 14,400 / 19,640
t = 0.733 inches (approximately)Therefore, based on these parameters and the specified formula, the minimum required thickness of the cylindrical shell would be approximately 0.733 inches.
Considerations and Cautions
- Corrosion Allowance: This calculation only gives the minimum required thickness. In practice, a corrosion allowance is added to account for material loss due to corrosion over the vessel's lifespan. The code will specify the minimum corrosion allowance to be used.
- Code Compliance: Always refer to the applicable code (e.g., ASME Section VIII, Division 1) for the specific formulas, allowable stress values, and joint efficiency requirements. The values and formulas can change based on code editions and specific circumstances. This is a simplified example and not a substitute for consulting the code itself.
- Other Components: This calculation only applies to cylindrical shells. Different formulas are used for spherical shells, heads (e.g., elliptical, hemispherical, torispherical), and other vessel components.
- External Pressure: This formula is for internal pressure. Vessels subject to external pressure require different calculation methods to prevent collapse.
- Reinforcement: Openings (nozzles, manways) require reinforcement to compensate for the material removed. These calculations are more complex and must comply with code requirements.
In summary, calculating the minimum thickness of a pressure vessel involves using code-specified formulas, understanding the relevant variables (design pressure, radius, allowable stress, joint efficiency), and considering factors like corrosion allowance and reinforcement requirements.
