Inner Diameter of Pressurized Cylinder from Bernie's Equation Calculator

Bernie's Equation:

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

Thickness of Pressurized Cylinder Wall:

Permissible Tensile Stress in Pressurized Cylinder:

Poisson's Ratio of Pressurized Cylinder:

Internal Pressure on Cylinder:

Inner Diameter of Pressurized Cylinder:

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1. What is Bernie's Equation?

Bernie's Equation calculates the inner diameter of a pressurized cylinder based on wall thickness, permissible tensile stress, Poisson's ratio, and internal pressure. It provides a theoretical foundation for designing cylindrical pressure vessels.

2. How Does the Calculator Work?

The calculator uses Bernie's Equation:

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

Where:

\( d_i \) — Inner diameter of pressurized cylinder (m)
\( t_w \) — Thickness of pressurized cylinder wall (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 under internal pressure, considering both radial and tangential stresses.

3. Importance of Inner Diameter Calculation

Details: Accurate calculation of inner diameter is crucial for designing pressure vessels, ensuring structural integrity, and maintaining safety standards in various engineering applications.

4. Using the Calculator

Tips: Enter wall thickness 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 used in pressure vessels, Poisson's ratio ranges between 0.25 and 0.35.

Q2: How does internal pressure affect the inner diameter calculation?
A: Higher internal pressure requires thicker walls or smaller diameters to maintain structural integrity and prevent failure.

Q3: What materials are commonly used for pressurized cylinders?
A: Common materials include carbon steel, stainless steel, aluminum alloys, and composite materials, each with different mechanical properties.

Q4: Are there safety factors to consider?
A: Yes, engineering design typically includes safety factors to account for material variations, manufacturing tolerances, and unexpected load conditions.

Q5: When is this equation most applicable?
A: This equation is particularly useful for thin-walled pressure vessels where the wall thickness is small compared to the diameter.