Internal Fluid Pressure In Thin Cylindrical Vessel Given Longitudinal Strain Calculator

Formula Used:

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

Longitudinal Strain (ε):

unitless

Thickness Of Thin Shell (t):

Modulus of Elasticity (E):

Inner Diameter of Cylinder (D_i):

Poisson's Ratio (ν):

unitless

Internal Pressure in thin shell (P_i):

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1. What is Internal Fluid Pressure Calculation?

The internal fluid pressure calculation determines the pressure inside a thin cylindrical vessel based on longitudinal strain, material properties, and geometric parameters. This is essential for designing and analyzing pressure vessels in various engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( P_i \) — Internal Pressure in thin shell (Pa)
\( \varepsilon_{longitudinal} \) — Longitudinal Strain (unitless)
\( t \) — Thickness Of Thin Shell (m)
\( E \) — Modulus of Elasticity Of Thin Shell (Pa)
\( D_i \) — Inner Diameter of Cylinder (m)
\( \nu \) — Poisson's Ratio (unitless)

Explanation: The formula relates internal pressure to the longitudinal strain experienced by the cylindrical vessel, accounting for material properties and geometry.

3. Importance of Internal Pressure Calculation

Details: Accurate internal pressure calculation is crucial for ensuring structural integrity, preventing failures, and optimizing design of pressure vessels in chemical, petroleum, and power generation industries.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure Poisson's Ratio is between 0 and 0.5, and all dimensional values are positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a thin cylindrical vessel?
A: A thin cylindrical vessel is one where the wall thickness is small compared to its diameter (typically thickness/diameter ≤ 1/20).

Q2: Why is Poisson's Ratio important in this calculation?
A: Poisson's Ratio accounts for the lateral contraction that occurs when a material is stretched longitudinally, which affects the stress 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. For rubber-like materials, it can approach 0.5.

Q4: When is this formula applicable?
A: This formula applies to thin-walled cylindrical vessels under internal pressure where the stress distribution can be assumed uniform through the thickness.

Q5: What are the limitations of this approach?
A: This approach may not be accurate for thick-walled vessels, vessels with end effects, or vessels made of materials with non-linear elastic behavior.