Thickness Of Pressurized Cylinder From Bernie's Equation Calculator

Bernie's Equation:

\[ t_w = \frac{d_i}{2} \times \left( \sqrt{\frac{\sigma_t + (1 - \nu) \cdot P_i}{\sigma_t - (1 + \nu) \cdot P_i}} - 1 \right) \]

Inner Diameter Of Pressurized Cylinder:

Permissible Tensile Stress In Pressurized Cylinder:

Poisson's Ratio Of Pressurized Cylinder:

Internal Pressure On Cylinder:

Thickness Of Pressurized Cylinder Wall:

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1. What Is Bernie's Equation?

Bernie's Equation calculates the thickness of a pressurized cylinder wall based on inner diameter, permissible tensile stress, Poisson's ratio, and internal pressure. It provides an accurate assessment of the required wall thickness to withstand internal pressure while maintaining structural integrity.

2. How Does The Calculator Work?

The calculator uses Bernie's equation:

\[ t_w = \frac{d_i}{2} \times \left( \sqrt{\frac{\sigma_t + (1 - \nu) \cdot P_i}{\sigma_t - (1 + \nu) \cdot P_i}} - 1 \right) \]

Where:

\( t_w \) — Thickness of pressurized cylinder wall (m)
\( d_i \) — Inner diameter of pressurized cylinder (m)
\( \sigma_t \) — Permissible tensile stress in pressurized cylinder (Pa)
\( \nu \) — Poisson's ratio of pressurized cylinder
\( P_i \) — Internal pressure on cylinder (Pa)

Explanation: The equation accounts for the stress distribution in cylindrical pressure vessels and ensures the wall thickness is sufficient to prevent failure under internal pressure.

3. Importance Of Cylinder Wall Thickness Calculation

Details: Accurate wall thickness calculation is crucial for designing pressure vessels, ensuring safety, preventing catastrophic failures, and optimizing material usage in engineering applications.

4. Using The Calculator

Tips: Enter inner diameter in meters, permissible tensile stress in Pascals, Poisson's ratio (typically between 0.1-0.5), and internal pressure in Pascals. All values must be valid and positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Poisson's ratio?
A: For most metals and alloys, Poisson's ratio ranges between 0.1 and 0.5, with common values around 0.3 for steel and aluminum.

Q2: Why is wall thickness calculation important?
A: Proper wall thickness ensures pressure vessels can withstand internal pressures without failure, preventing accidents and ensuring operational safety.

Q3: What units should be used for input values?
A: Use meters for diameter, Pascals for stress and pressure, and dimensionless value for Poisson's ratio.

Q4: Are there limitations to this equation?
A: The equation assumes homogeneous material properties and may need adjustment for very high pressures, extreme temperatures, or composite materials.

Q5: How does internal pressure affect wall thickness?
A: Higher internal pressures require thicker walls to maintain structural integrity and prevent failure due to hoop stress.