Inner Diameter of Thin Cylinder given Longitudinal Stress Calculator

Formula Used:

\[ d_i = \frac{4 \times t_w \times \sigma_l}{P_i} \]

Thickness of Pressurized Cylinder Wall:

Longitudinal Stress in Pressurized Cylinder:

Internal Pressure on Cylinder:

Inner Diameter of Pressurized Cylinder:

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1. What is the Inner Diameter of Thin Cylinder Formula?

The formula calculates the inner diameter of a pressurized thin-walled cylinder based on wall thickness, longitudinal stress, and internal pressure. It's derived from the fundamental stress analysis of cylindrical pressure vessels.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_i = \frac{4 \times t_w \times \sigma_l}{P_i} \]

Where:

\( d_i \) — Inner diameter of pressurized cylinder (m)
\( t_w \) — Thickness of pressurized cylinder wall (m)
\( \sigma_l \) — Longitudinal stress in pressurized cylinder (Pa)
\( P_i \) — Internal pressure on cylinder (Pa)

Explanation: This formula relates the geometric parameters and stress state of a thin-walled cylindrical pressure vessel under internal pressure.

3. Importance of Cylinder Diameter Calculation

Details: Accurate calculation of inner diameter is crucial for pressure vessel design, structural integrity assessment, and ensuring safe operation under internal pressure conditions.

4. Using the Calculator

Tips: Enter wall thickness in meters, longitudinal stress in Pascals, and internal pressure in Pascals. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a "thin-walled" cylinder?
A: Typically, a cylinder is considered thin-walled when the wall thickness is less than 1/20 of the inner diameter.

Q2: How does longitudinal stress differ from hoop stress?
A: Longitudinal stress acts parallel to the cylinder's axis, while hoop stress acts circumferentially around the cylinder.

Q3: What are typical units for these parameters?
A: Wall thickness in mm or m, stresses in MPa or Pa, pressure in MPa, Pa, or bar, and diameter in mm or m.

Q4: Are there limitations to this formula?
A: This formula is valid for thin-walled cylinders with uniform wall thickness and homogeneous material properties under internal pressure.

Q5: How does temperature affect the calculation?
A: Temperature changes can affect material properties and thermal stresses, which should be considered separately in detailed analysis.