Thickness Of Vessel Given Change In Diameter Calculator

Formula Used:

\[ t = \frac{P_i \cdot D_i^2}{2 \cdot \Delta d \cdot E} \cdot \left(1 - \frac{\mu}{2}\right) \]

Internal Pressure (P_i):

Inner Diameter (D_i):

Change in Diameter (Δd):

Modulus of Elasticity (E):

Poisson's Ratio (μ):

Thickness Of Thin Shell (t):

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1. What is the Thickness Calculation Formula?

The thickness calculation formula determines the required thickness of a thin-walled vessel based on internal pressure, diameter changes, material properties, and Poisson's ratio. This is essential for ensuring structural integrity and safety in pressure vessel design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t = \frac{P_i \cdot D_i^2}{2 \cdot \Delta d \cdot E} \cdot \left(1 - \frac{\mu}{2}\right) \]

Where:

\( t \) — Thickness of thin shell (m)
\( P_i \) — Internal pressure (Pa)
\( D_i \) — Inner diameter (m)
\( \Delta d \) — Change in diameter (m)
\( E \) — Modulus of elasticity (Pa)
\( \mu \) — Poisson's ratio

Explanation: The formula calculates the required thickness to withstand internal pressure while accounting for material deformation characteristics.

3. Importance of Thickness Calculation

Details: Accurate thickness calculation is crucial for pressure vessel safety, preventing failures, ensuring regulatory compliance, and optimizing material usage in engineering design.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Internal pressure, inner diameter, change in diameter, and modulus of elasticity must be positive values. Poisson's ratio should be between 0 and 0.5.

5. Frequently Asked Questions (FAQ)

Q1: What is a thin-walled vessel?
A: A thin-walled vessel is one where the wall thickness is less than 1/10 of the vessel's diameter, allowing for simplified stress calculations.

Q2: Why is Poisson's ratio important in this calculation?
A: Poisson's ratio accounts for the material's tendency to expand or contract in directions perpendicular to the applied stress, affecting the deformation behavior.

Q3: What are typical values for modulus of elasticity?
A: For steel: ~200 GPa, aluminum: ~70 GPa, copper: ~110 GPa. Values vary by material type and treatment.

Q4: When should this formula not be used?
A: This formula is for thin-walled vessels under internal pressure. It may not be accurate for thick-walled vessels, external pressure, or complex loading conditions.

Q5: How does temperature affect the calculation?
A: Temperature affects material properties (E and μ) and may cause thermal expansion. For high-temperature applications, use temperature-adjusted material properties.