Understanding the Critical Calculation of Design Pressure in Pressure Vessels

Design pressure calculation ensures safety and integrity in pressure vessel engineering. It defines the maximum allowable pressure a vessel can withstand.

This article explores detailed formulas, common values, and real-world applications for accurate design pressure determination.

• Calculate design pressure for a cylindrical pressure vessel operating at 150°C with internal pressure of 2.5 MPa.
• Determine the design pressure for a spherical pressure vessel subjected to external pressure of 1.2 MPa and temperature of 100°C.
• Find the design pressure for a pressure vessel made of carbon steel with a corrosion allowance of 2 mm and operating pressure of 3 MPa.
• Calculate the design pressure considering hydrostatic test pressure of 4 MPa and operating pressure of 2.8 MPa for a vertical pressure vessel.

Comprehensive Tables of Common Values for Design Pressure Calculation

Fundamental Formulas for Calculating Design Pressure in Pressure Vessels

Design pressure calculation is governed by standards such as ASME Section VIII Division 1 and EN 13445. The formulas vary depending on vessel geometry and loading conditions.

1. Design Pressure from Operating Pressure

The design pressure is typically set higher than the maximum operating pressure to include safety margins:

• P_design: Design pressure (MPa)
• P_op: Maximum operating pressure (MPa)
• F_safety: Safety factor, typically 1.1 to 1.5

This factor accounts for pressure surges, inaccuracies, and future operating conditions.

2. Minimum Required Thickness for Cylindrical Shells

According to ASME Section VIII, the minimum thickness t for a cylindrical shell under internal pressure is:

• t: Minimum required thickness (mm)
• P: Design pressure (MPa)
• R: Inside radius of the shell (mm)
• S: Allowable stress of the material at design temperature (MPa)
• E: Joint efficiency (dimensionless)
• c: Corrosion allowance (mm)

This formula ensures the shell thickness withstands the internal pressure without yielding.

3. Minimum Required Thickness for Spherical Shells

For spherical vessels, the thickness is calculated as:

• Variables as defined above.

The spherical geometry allows for thinner walls compared to cylindrical vessels under the same pressure.

4. Design Pressure from Test Pressure

Hydrostatic test pressure is usually higher than design pressure to verify vessel integrity:

• P_test: Test pressure (MPa)
• F_test: Test factor, typically 1.3 to 1.5
• P_design: Design pressure (MPa)

Test pressure ensures the vessel can safely handle pressures above normal operating conditions.

5. Allowable Stress Determination

Allowable stress S depends on material properties and temperature, often derived from codes or material datasheets:

• σ_y: Yield strength of material (MPa)
• σ_u: Ultimate tensile strength (MPa)

This ensures the vessel operates within elastic limits.

Detailed Real-World Examples of Design Pressure Calculation

Example 1: Cylindrical Pressure Vessel for Chemical Reactor

A cylindrical pressure vessel with an internal diameter of 1200 mm operates at 2.5 MPa and 200°C. The material is carbon steel with allowable stress of 140 MPa at this temperature. The joint efficiency is 0.85, and corrosion allowance is 3 mm. Calculate the minimum required shell thickness and design pressure.

• Step 1: Calculate design pressure assuming safety factor 1.2:

• Step 2: Calculate inside radius:

• Step 3: Calculate minimum thickness:

Calculate denominator:

Calculate thickness:

Result: Minimum shell thickness required is approximately 18.35 mm.

Example 2: Spherical Pressure Vessel for Gas Storage

A spherical vessel with an internal diameter of 2000 mm stores gas at 1.8 MPa and 50°C. The material allowable stress is 160 MPa, joint efficiency is 1.0, and corrosion allowance is 2 mm. Determine the minimum shell thickness and design pressure with a safety factor of 1.3.

• Step 1: Calculate design pressure:

• Step 2: Calculate inside radius:

• Step 3: Calculate minimum thickness:

Calculate denominator:

Calculate thickness:

Result: Minimum shell thickness required is approximately 9.32 mm.

Additional Considerations in Design Pressure Calculation

Beyond the basic formulas, several factors influence the design pressure and thickness calculations:

• Temperature Effects: Material allowable stress decreases with increasing temperature, requiring adjustments.
• External Pressure: For vessels under vacuum or external pressure, buckling calculations are necessary.
• Fatigue and Cyclic Loading: Repeated pressure cycles may require design modifications to prevent fatigue failure.
• Corrosion and Erosion: Corrosion allowance must be carefully estimated based on operating environment.
• Joint Efficiency: Weld quality and inspection methods affect the joint efficiency factor.
• Code Compliance: Adherence to ASME, EN, or API standards is mandatory for legal and safety reasons.

References and Authoritative Resources

• ASME Boiler and Pressure Vessel Code (BPVC) Section VIII
• EN 13445 – Unfired Pressure Vessels
• American Petroleum Institute (API) Standards
• Materials Data and Allowable Stress Tables

Accurate calculation of design pressure is fundamental to pressure vessel safety and performance. This article provides a detailed technical foundation for engineers and designers to apply industry standards effectively.