Original Diameter Of Vessel Given Change In Diameter Calculator

Formula Used:

\[ d = \frac{\Delta d \times (2 \times t \times E)}{\sqrt{P_i \times (1 - \frac{\mu}{2})}} \]

Change in Diameter (Δd):

Thickness Of Thin Shell (t):

Modulus of Elasticity Of Thin Shell (E):

Internal Pressure in thin shell (P_i):

Poisson's Ratio (μ):

Original Diameter (d):

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1. What is Original Diameter Of Vessel Given Change In Diameter?

This calculation determines the original diameter of a thin-walled vessel when the change in diameter due to internal pressure is known. It's based on the relationship between material properties, pressure, and dimensional changes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d = \frac{\Delta d \times (2 \times t \times E)}{\sqrt{P_i \times (1 - \frac{\mu}{2})}} \]

Where:

\( d \) — Original Diameter (m)
\( \Delta d \) — Change in Diameter (m)
\( t \) — Thickness Of Thin Shell (m)
\( E \) — Modulus of Elasticity Of Thin Shell (Pa)
\( P_i \) — Internal Pressure in thin shell (Pa)
\( \mu \) — Poisson's Ratio

Explanation: The formula calculates the original diameter by considering the material's elastic properties and the deformation caused by internal pressure.

3. Importance of Original Diameter Calculation

Details: Calculating the original diameter is crucial for pressure vessel design, structural analysis, and understanding material behavior under pressure conditions.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, Pascals for pressure). Ensure Poisson's Ratio is between 0 and 0.5. All input values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is Poisson's Ratio and why is it important?
A: Poisson's Ratio describes how a material deforms in directions perpendicular to the applied load. It's crucial for accurate stress-strain calculations.

Q2: What materials is this formula applicable to?
A: This formula applies to elastic, isotropic materials that follow Hooke's law within their elastic limits.

Q3: How accurate is this calculation for real-world applications?
A: The calculation provides theoretical values based on ideal conditions. Real-world factors like material imperfections and boundary conditions may affect accuracy.

Q4: Can this formula be used for thick-walled vessels?
A: No, this formula is specifically derived for thin-walled vessels where the thickness is small compared to the diameter.

Q5: What are typical values for Poisson's Ratio?
A: For most metals, Poisson's Ratio ranges between 0.25-0.35. Rubber has a higher value (~0.5), while cork has a lower value (~0.0).