Internal Diameter Of Thin Cylindrical Vessel Given Longitudinal Strain Calculator

Formula Used:

\[ D_i = \frac{\varepsilon_{longitudinal} \times 2 \times t \times E}{P_i \times \left(\frac{1}{2} - \mu\right)} \]

Longitudinal Strain (ε):

Thickness Of Thin Shell (t):

Modulus of Elasticity (E):

Internal Pressure (P_i):

Poisson's Ratio (μ):

Inner Diameter of Cylinder (D_i):

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1. What is the Internal Diameter Calculation?

This calculator determines the inner diameter of a thin cylindrical vessel based on longitudinal strain, material properties, and internal pressure using the formula derived from thin-walled pressure vessel theory.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D_i = \frac{\varepsilon_{longitudinal} \times 2 \times t \times E}{P_i \times \left(\frac{1}{2} - \mu\right)} \]

Where:

\( D_i \) — Inner Diameter of Cylinder (m)
\( \varepsilon_{longitudinal} \) — Longitudinal Strain
\( t \) — 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: This formula relates the geometric and material properties of a thin-walled cylindrical vessel to its deformation under internal pressure.

3. Importance of Inner Diameter Calculation

Details: Accurate calculation of inner diameter is crucial for pressure vessel design, structural integrity assessment, and ensuring safe operating conditions in various engineering applications.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure Poisson's Ratio is between 0 and 0.5, and all other values are positive. Avoid values that would cause division by zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a thin-walled pressure vessel?
A: A thin-walled pressure vessel is one where the wall thickness is less than about 1/10 of the radius, allowing for simplified stress analysis.

Q2: Why is Poisson's Ratio important in this calculation?
A: Poisson's Ratio accounts for the lateral contraction/expansion that occurs when a material is stretched/compressed, affecting the strain distribution.

Q3: What are typical values for Poisson's Ratio?
A: For most metals and alloys, Poisson's Ratio ranges between 0.25 and 0.35. Rubber-like materials can approach 0.5.

Q4: When is this formula applicable?
A: This formula is valid for thin-walled cylindrical vessels under internal pressure where the thickness-to-radius ratio is small.

Q5: What are the limitations of this calculation?
A: The formula assumes homogeneous, isotropic material behavior and may not be accurate for thick-walled vessels or vessels with significant end effects.