Change In Diameter Of Vessel Given Internal Fluid Pressure Calculator

Formula Used:

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

Internal Pressure (P_i):

Inner Diameter (D_i):

Thickness (t):

Modulus of Elasticity (E):

Poisson's Ratio (μ):

Change in Diameter (Δd):

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1. What is Change in Diameter of Vessel?

The change in diameter of a vessel refers to the deformation that occurs when internal fluid pressure is applied to a thin-walled cylindrical shell. This calculation is essential in pressure vessel design and structural engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the radial expansion of a cylindrical vessel under internal pressure, accounting for material properties and geometric dimensions.

3. Importance of Diameter Change Calculation

Details: Accurate calculation of diameter change is crucial for designing pressure vessels, pipelines, and storage tanks to ensure structural integrity and prevent failure under operating conditions.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Internal pressure in Pascals, dimensions in meters, and Poisson's ratio as a dimensionless quantity between 0 and 0.5.

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 and deformation calculations.

Q2: What are typical values for modulus of elasticity?
A: For steel: ~200 GPa, aluminum: ~70 GPa, concrete: ~30 GPa. The value depends on the specific material composition.

Q3: When is this formula applicable?
A: This formula is valid for thin-walled cylindrical pressure vessels where the wall thickness is much smaller than the radius (typically t < D_i/20).

Q4: How does internal pressure affect diameter change?
A: Higher internal pressure causes greater radial expansion. The relationship is linear - doubling the pressure doubles the diameter change.

Q5: What materials is this calculator suitable for?
A: This calculator works for isotropic materials that behave elastically under the applied pressure, such as metals, plastics, and composite materials.