Change In Length Of Thin Cylindrical Shell Given Internal Fluid Pressure Calculator

Formula Used:

\[ \Delta L = \frac{P_i \times D \times L_{cylinder}}{2 \times t \times E} \times \left( \frac{1}{2} - \nu \right) \]

Internal Pressure (P_i):

Diameter of Shell (D):

Length of Cylindrical Shell (L_cylinder):

Thickness of Thin Shell (t):

Modulus of Elasticity (E):

Poisson's Ratio (ν):

Change in Length (ΔL):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Change in Length of Thin Cylindrical Shell?

The change in length of a thin cylindrical shell refers to the axial deformation that occurs when the shell is subjected to internal fluid pressure. This deformation is a result of the combined effects of hoop stress and longitudinal stress in the cylindrical structure.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \Delta L = \frac{P_i \times D \times L_{cylinder}}{2 \times t \times E} \times \left( \frac{1}{2} - \nu \right) \]

Where:

\( \Delta L \) — Change in length (m)
\( P_i \) — Internal pressure (Pa)
\( D \) — Diameter of shell (m)
\( L_{cylinder} \) — Length of cylindrical shell (m)
\( t \) — Thickness of thin shell (m)
\( E \) — Modulus of elasticity (Pa)
\( \nu \) — Poisson's ratio

Explanation: The formula calculates the axial deformation of a thin cylindrical shell under internal pressure, considering material properties and geometric parameters.

3. Importance of Change in Length Calculation

Details: Calculating the change in length is crucial for designing pressure vessels, piping systems, and cylindrical structures to ensure they can withstand internal pressure without excessive deformation or failure.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a thin cylindrical shell?
A: A thin cylindrical shell is one where the thickness is small compared to the diameter (typically t/D ≤ 1/20), allowing for simplified stress analysis.

Q2: Why does Poisson's ratio affect the length change?
A: Poisson's ratio accounts for the lateral contraction/expansion that occurs simultaneously with axial deformation due to the internal pressure.

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 pressure vessels with closed ends subjected to uniform internal pressure.

Q5: What are the limitations of this calculation?
A: The formula assumes linear elastic material behavior, small deformations, and uniform wall thickness. It may not be accurate for thick-walled cylinders or materials with non-linear behavior.