Inner Diameter of Thin Spherical Shell given Permissible Tensile Stress Calculator

Formula Used:

\[ \text{Inner diameter of pressurized cylinder} = \frac{4 \times \text{Thickness of pressurized cylinder wall} \times \text{Permissible Tensile stress in pressurized cylinder}}{\text{Internal pressure on cylinder}} \] \[ d_i = \frac{4 \times t_w \times \sigma_t}{P_i} \]

Thickness of pressurized cylinder wall:

Permissible Tensile stress in pressurized cylinder:

Internal pressure on cylinder:

Inner diameter of pressurized cylinder:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Inner Diameter of Thin Spherical Shell Formula?

The formula calculates the inner diameter of a pressurized cylindrical shell based on wall thickness, permissible tensile stress, and internal pressure. It's derived from thin-walled pressure vessel theory and ensures structural integrity under internal pressure.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula relates the inner diameter to wall thickness, material strength, and internal pressure for thin-walled cylindrical pressure vessels.

3. Importance of Inner Diameter Calculation

Details: Accurate calculation of inner diameter is crucial for designing pressure vessels, ensuring they can withstand internal pressures without failure while maintaining structural integrity.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a thin-walled pressure vessel?
A: A pressure vessel where the wall thickness is less than about 1/10 of the radius, allowing for simplified stress analysis.

Q2: When is this formula applicable?
A: This formula is valid for thin-walled cylindrical pressure vessels where the thickness is small compared to the diameter.

Q3: What factors affect the inner diameter calculation?
A: The calculation depends on material strength (tensile stress), wall thickness, and the internal pressure the vessel must withstand.

Q4: Are there limitations to this formula?
A: This formula assumes uniform stress distribution and is primarily valid for thin-walled vessels. Thick-walled vessels require more complex calculations.

Q5: How does safety factor relate to this calculation?
A: The permissible tensile stress typically includes a safety factor to account for material variations and unexpected load conditions.