Internal Diameter Of Vessel Given Hoop Stress And Efficiency Of Longitudinal Joint Calculator

Formula Used:

\[ Di = \frac{\sigma_\theta \times 2 \times t \times \eta_l}{Pi} \]

Hoop Stress In Thin Shell (σθ):

Pascal

Thickness Of Thin Shell (t):

Meter

Efficiency Of Longitudinal Joint (ηl):

Unitless

Internal Pressure In Thin Shell (Pi):

Pascal

Inner Diameter Of Cylindrical Vessel (Di):

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1. What Is The Inner Diameter Formula?

The formula calculates the inner diameter of a cylindrical vessel based on hoop stress, thickness, joint efficiency, and internal pressure. This is essential for designing pressure vessels and ensuring structural integrity under internal pressure.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ Di = \frac{\sigma_\theta \times 2 \times t \times \eta_l}{Pi} \]

Where:

\( Di \) — Inner Diameter of Cylindrical Vessel (Meter)
\( \sigma_\theta \) — Hoop Stress in Thin Shell (Pascal)
\( t \) — Thickness Of Thin Shell (Meter)
\( \eta_l \) — Efficiency of Longitudinal Joint (Unitless)
\( Pi \) — Internal Pressure in Thin Shell (Pascal)

Explanation: The formula relates the internal diameter to the hoop stress, material thickness, joint efficiency, and internal pressure, ensuring the vessel can withstand the applied loads.

3. Importance Of Inner Diameter Calculation

Details: Accurate calculation of inner diameter is crucial for pressure vessel design, ensuring safety, compliance with standards, and optimal performance under operating conditions.

4. Using The Calculator

Tips: Enter hoop stress in Pascal, thickness in meters, joint efficiency (between 0 and 1), and internal pressure in Pascal. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is hoop stress?
A: Hoop stress is the circumferential stress in a cylindrical pressure vessel caused by internal pressure.

Q2: Why is joint efficiency important?
A: Joint efficiency accounts for the strength reduction due to welding or other joining methods, affecting the overall vessel integrity.

Q3: What units should be used?
A: Use consistent SI units: stress and pressure in Pascal, thickness and diameter in meters.

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.

Q5: How is this used in engineering?
A: This calculation is fundamental in mechanical and civil engineering for designing pressure vessels, pipes, and storage tanks.