Diameter Of Thin Cylindrical Shell Given Volumetric Strain Calculator

Formula Used:

\[ D = \frac{\varepsilon_v \times 2 \times E \times t}{P_i \times \left(\frac{5}{2} - \mu\right)} \]

Volumetric Strain (εv):

Modulus of Elasticity (E):

Thickness of Shell (t):

Internal Pressure (Pi):

Poisson's Ratio (μ):

Diameter of Shell (D):

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1. What is the Diameter Calculation Formula?

The formula calculates the diameter of a thin cylindrical shell based on volumetric strain, modulus of elasticity, thickness, internal pressure, and Poisson's ratio. It's derived from the relationship between stress, strain, and material properties in thin-walled pressure vessels.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D = \frac{\varepsilon_v \times 2 \times E \times t}{P_i \times \left(\frac{5}{2} - \mu\right)} \]

Where:

\( D \) — Diameter of Shell (m)
\( \varepsilon_v \) — Volumetric Strain
\( E \) — Modulus of Elasticity (Pa)
\( t \) — Thickness of Shell (m)
\( P_i \) — Internal Pressure (Pa)
\( \mu \) — Poisson's Ratio

Explanation: The formula relates the dimensional changes (volumetric strain) to the applied pressure and material properties of the cylindrical shell.

3. Importance of Shell Diameter Calculation

Details: Accurate diameter calculation is crucial for pressure vessel design, structural integrity assessment, and predicting deformation under internal pressure in thin-walled cylindrical structures.

4. Using the Calculator

Tips: Enter all values in appropriate units. Volumetric strain is dimensionless, modulus and pressure in Pascals, thickness in meters, and Poisson's ratio between 0-0.5.

5. Frequently Asked Questions (FAQ)

Q1: What is volumetric strain?
A: Volumetric strain is the ratio of change in volume to the original volume of a material under stress.

Q2: What is Poisson's ratio?
A: Poisson's ratio is the ratio of transverse strain to axial strain when a material is stretched or compressed.

Q3: What is the typical range for Poisson's ratio?
A: For most engineering materials, Poisson's ratio ranges between 0.0 and 0.5, with 0.3 being common for many metals.

Q4: When is this formula applicable?
A: This formula applies to thin-walled cylindrical pressure vessels where the thickness is small compared to the diameter (typically t/D < 0.1).

Q5: What are the limitations of this calculation?
A: The formula assumes linear elastic material behavior, small deformations, and uniform stress distribution throughout the shell thickness.