Internal Diameter Of Vessel Given Longitudinal Stress In Cylindrical Vessel Material Calculator

Formula Used:

\[ D_i = \frac{\sigma_l \times 4 \times t}{P_i} \]

Inner Diameter of Cylinder (Di):

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1. What is the Inner Diameter Calculation?

The inner diameter calculation determines the internal diameter of a cylindrical vessel based on longitudinal stress, shell thickness, and internal pressure. This is crucial for designing pressure vessels that can withstand internal forces without failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D_i = \frac{\sigma_l \times 4 \times t}{P_i} \]

Where:

\( D_i \) — Inner diameter of cylinder (m)
\( \sigma_l \) — Longitudinal stress (Pa)
\( t \) — Thickness of thin shell (m)
\( P_i \) — Internal pressure (Pa)

Explanation: The formula calculates the maximum internal diameter that can be safely achieved given the material properties and operating conditions.

3. Importance of Inner Diameter Calculation

Details: Accurate diameter calculation is essential for pressure vessel design, ensuring structural integrity, safety compliance, and optimal performance under internal pressure conditions.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is longitudinal stress in a cylindrical vessel?
A: Longitudinal stress is the stress acting along the length of the cylinder, caused by internal pressure trying to separate the vessel ends.

Q2: Why is thickness important in this calculation?
A: Thickness directly affects the vessel's ability to withstand internal pressure. Thicker walls allow for larger diameters under the same stress conditions.

Q3: What units should be used for input values?
A: All inputs should be in SI units - Pascals for stress and pressure, meters for thickness and diameter.

Q4: Are there limitations to this formula?
A: This formula applies to thin-walled cylindrical vessels where the thickness is small compared to the diameter (typically t < D/20).

Q5: How does internal pressure affect the inner diameter?
A: Higher internal pressure requires either thicker walls or smaller diameters to maintain the same longitudinal stress level.