Thickness of Pressurized Cylinder from Clavarino's Equation Calculator

Clavarino's Equation:

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

Inner Diameter of Pressurized Cylinder (d_i):

Permissible Tensile Stress (σ_t):

Poisson's Ratio (μ):

Internal Pressure (P_i):

Thickness of Pressurized Cylinder Wall (t_w):

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1. What is Clavarino's Equation?

Clavarino's equation is used to calculate the wall thickness of a pressurized cylinder considering both radial and tangential stresses. It provides a more accurate thickness calculation by incorporating Poisson's ratio effect on the stress distribution in thick-walled cylinders.

2. How Does the Calculator Work?

The calculator uses Clavarino's equation:

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

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

Explanation: The equation accounts for the biaxial stress state in thick-walled cylinders and the effect of Poisson's ratio on stress distribution.

3. Importance of Cylinder Wall Thickness Calculation

Details: Accurate wall thickness calculation is crucial for pressure vessel design to ensure structural integrity, prevent failure under internal pressure, and maintain safety standards while optimizing material usage.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: When should Clavarino's equation be used instead of Lame's equation?
A: Clavarino's equation is preferred when considering the effect of Poisson's ratio on stress distribution, particularly for thick-walled cylinders where this effect becomes significant.

Q2: What is the typical range for Poisson's ratio in engineering materials?
A: For most metals and alloys, Poisson's ratio ranges between 0.25-0.35. For rubber-like materials, it can approach 0.5.

Q3: What safety factors should be considered in practical applications?
A: Engineering design typically includes safety factors of 2-4 depending on the application, material properties, and regulatory requirements.

Q4: Can this equation be used for external pressure applications?
A: No, this equation is specifically derived for internal pressure conditions. Different equations are used for external pressure scenarios.

Q5: What are the limitations of Clavarino's equation?
A: The equation assumes homogeneous, isotropic material, constant internal pressure, and neglects end effects and temperature variations.