Inner Diameter Of Pressurized Cylinder From Clavarino's Equation Calculator

Clavarino's Equation:

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

Thickness of Pressurized Cylinder Wall (t_w):

Permissible Tensile Stress (σ_t):

Poisson's Ratio (μ):

Internal Pressure (P_i):

Inner Diameter of Pressurized Cylinder (d_i):

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1. What is Clavarino's Equation?

Clavarino's Equation is used to calculate the inner diameter of a pressurized cylindrical vessel based on wall thickness, material properties, and internal pressure. It provides a theoretical foundation for designing pressure vessels that can withstand internal pressures safely.

2. How Does the Calculator Work?

The calculator uses Clavarino's Equation:

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

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)
\( \mu \) — Poisson's ratio of pressurized cylinder
\( P_i \) — Internal pressure on cylinder (Pa)

Explanation: The equation calculates the maximum allowable inner diameter for a given wall thickness and material properties under specific internal pressure conditions.

3. Importance of Inner Diameter Calculation

Details: Accurate calculation of inner diameter is crucial for designing pressure vessels, piping systems, and cylindrical containers that must withstand internal pressures safely without failure.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for length, Pascals for pressure/stress). Ensure Poisson's ratio is between 0.1 and 0.5 for most engineering materials.

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 0.25 and 0.35. Rubber-like materials can have values close to 0.5.

Q2: When is Clavarino's equation applicable?
A: This equation is used for thick-walled cylinders where the ratio of outer to inner diameter is greater than 1.1.

Q3: What are the limitations of this equation?
A: The equation assumes homogeneous, isotropic material and elastic behavior. It may not be accurate for very high pressures or materials with non-linear behavior.

Q4: How does internal pressure affect the required wall thickness?
A: Higher internal pressures require thicker walls or smaller inner diameters to maintain structural integrity and safety margins.

Q5: What safety factors should be considered?
A: Engineering designs typically include safety factors of 2-4 depending on the application, material properties, and regulatory requirements.