Internal Fluid Pressure In Thin Cylindrical Vessel Given Change In Diameter Calculator

Formula Used:

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

Change in Diameter (Δd):

Thickness Of Thin Shell (t):

Modulus of Elasticity (E):

Inner Diameter of Cylinder (D_i):

Poisson's Ratio (μ):

Internal Pressure (P_i):

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1. What is Internal Fluid Pressure in Thin Cylindrical Vessel?

Internal fluid pressure in a thin cylindrical vessel refers to the pressure exerted by the fluid contained within the vessel. This pressure causes stress in the vessel walls and leads to deformation, including changes in diameter.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the internal pressure based on the observed change in diameter, material properties, and geometric parameters of the cylindrical vessel.

3. Importance of Internal Pressure Calculation

Details: Accurate calculation of internal pressure is crucial for designing pressure vessels, ensuring structural integrity, and preventing failures in engineering applications involving cylindrical containers.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is considered a "thin" cylindrical vessel?
A: A vessel is considered thin when the wall thickness is less than 1/10 of the inner diameter (t < D_i/10).

Q2: Why is Poisson's ratio important in this calculation?
A: Poisson's ratio accounts for the material's tendency to contract in directions perpendicular to the applied stress, affecting the deformation behavior.

Q3: What are typical values for modulus of elasticity?
A: For steel: ~200 GPa, aluminum: ~70 GPa, copper: ~110 GPa. Values vary depending on the specific material and its treatment.

Q4: Can this formula be used for thick-walled cylinders?
A: No, this formula is specifically derived for thin-walled cylinders. Thick-walled vessels require more complex formulas that account for stress variations through the wall thickness.

Q5: What safety factors should be considered in practical applications?
A: Engineering designs typically include safety factors of 2-4 times the calculated pressure, depending on the application, material properties, and regulatory requirements.