Thickness Of Cylindrical Vessel Given Resisting Force On Thin Cylindrical Vessel Calculator

Formula Used:

\[ t = \frac{F}{\sigma_l \cdot \pi \cdot D_i} \]

Force on Cylindrical Shell (F):

Longitudinal Stress (σl):

Inner Diameter of Cylinder (Di):

Thickness Of Thin Shell (t):

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1. What is the Thickness Calculation Formula?

The formula calculates the thickness of a thin cylindrical shell based on the applied force, longitudinal stress, and inner diameter. It's derived from the relationship between these mechanical properties in pressure vessel design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t = \frac{F}{\sigma_l \cdot \pi \cdot D_i} \]

Where:

\( t \) — Thickness of thin shell (m)
\( F \) — Force on cylindrical shell (N)
\( \sigma_l \) — Longitudinal stress (Pa)
\( D_i \) — Inner diameter of cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the required thickness to withstand a given force while maintaining acceptable stress levels in the cylindrical vessel.

3. Importance of Thickness Calculation

Details: Accurate thickness calculation is crucial for pressure vessel design, ensuring structural integrity, safety, and optimal material usage while preventing failure under operating conditions.

4. Using the Calculator

Tips: Enter force in Newtons, longitudinal stress in Pascals, and inner diameter in meters. All values must be positive and greater than zero for valid results.

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 its diameter (typically t/D < 1/20), allowing for simplified stress analysis.

Q2: When is this formula applicable?
A: This formula applies to thin-walled cylindrical pressure vessels subjected to internal pressure, where hoop stress and longitudinal stress are the primary considerations.

Q3: What are typical longitudinal stress values?
A: Longitudinal stress values depend on the material properties and design requirements, typically ranging from tens to hundreds of MPa for common engineering materials.

Q4: Are there limitations to this equation?
A: This equation assumes uniform stress distribution and is primarily valid for thin-walled cylinders under internal pressure. Thick-walled vessels require more complex analysis.

Q5: How does temperature affect the calculation?
A: Temperature affects material properties (stress values) and may cause thermal expansion, which should be considered in high-temperature applications.