Home Back

Shell Thickness for Critical External Pressure Calculator

Critical External Pressure Formula:

\[ p_c = \frac{2.42 \times E}{(1 - u^2)^{3/4}} \times \frac{(t/D_o)^{5/2}}{(L/D_o) - 0.45 \times (t/D_o)^{1/2}} \]

N/mm²
mm
mm
mm

1. What is Critical External Pressure?

Definition: Critical External Pressure is the maximum pressure that a vessel or pipe can withstand without collapsing under an external load.

Purpose: This calculation helps engineers design pressure vessels that can safely operate under external pressure conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ p_c = \frac{2.42 \times E}{(1 - u^2)^{3/4}} \times \frac{(t/D_o)^{5/2}}{(L/D_o) - 0.45 \times (t/D_o)^{1/2}} \]

Where:

  • \( p_c \) — Critical external pressure (N/mm²)
  • \( E \) — Modulus of elasticity (N/mm²)
  • \( u \) — Poisson's ratio (±5%)
  • \( t \) — Vessel thickness (mm)
  • \( D_o \) — Shell outer diameter (mm)
  • \( L \) — Length of shell (mm)

Explanation: The formula calculates the buckling pressure of cylindrical shells under external pressure.

3. Importance of Critical Pressure Calculation

Details: Proper calculation ensures vessel integrity under vacuum or external pressure conditions, preventing catastrophic failures.

4. Using the Calculator

Tips: Enter all required parameters. Poisson's ratio typically ranges from 0.2 to 0.5 (default 0.3 ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical Poisson's ratio for metals?
A: For most metals, Poisson's ratio is about 0.3 ±5%. For steel, it's typically 0.28-0.32.

Q2: How does shell length affect critical pressure?
A: Longer shells generally have lower critical pressures due to increased buckling risk.

Q3: What safety factor should be applied?
A: Typically a safety factor of 3-5 is used for external pressure design.

Q4: Does this formula account for imperfections?
A: No, this is the theoretical value. Real-world vessels require additional safety margins.

Q5: What units should be used?
A: Consistent units must be used (mm for dimensions, N/mm² for pressure and modulus).

Shell Thickness for Critical External Pressure Calculator© - All Rights Reserved 2025