Inner Diameter of Thin Cylinder given Tangential Stress Calculator

Formula Used:

\[ d_i = \frac{2 \times t_w \times \sigma_{tang}}{P_i} \]

Thickness of Pressurized Cylinder Wall:

Tangential 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, tangential 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:

\[ d_i = \frac{2 \times t_w \times \sigma_{tang}}{P_i} \]

Where:

\( d_i \) — Inner diameter of pressurized cylinder (m)
\( t_w \) — Thickness of pressurized cylinder wall (m)
\( \sigma_{tang} \) — Tangential stress in pressurized cylinder (Pa)
\( P_i \) — Internal pressure on cylinder (Pa)

Explanation: This formula relates the internal diameter to the wall thickness, tangential stress, and internal pressure in a thin-walled cylindrical pressure vessel.

3. Importance of Inner Diameter Calculation

Details: Calculating the inner diameter is crucial for pressure vessel design, structural integrity assessment, and ensuring safe operating conditions in various engineering applications.

4. Using the Calculator

Tips: Enter wall thickness in meters, tangential 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 cylinder?
A: A thin-walled cylinder is one where the wall thickness is small compared to its diameter (typically t/d < 1/20).

Q2: What is tangential stress?
A: Tangential stress (hoop stress) is the stress acting circumferentially around the cylinder, perpendicular to the longitudinal axis.

Q3: When is this formula applicable?
A: This formula applies to thin-walled cylinders under internal pressure where the stress distribution is assumed uniform through the wall thickness.

Q4: What are the limitations of this formula?
A: The formula assumes uniform stress distribution and may not be accurate for thick-walled cylinders or cylinders with significant end effects.

Q5: How does internal pressure affect the inner diameter?
A: Higher internal pressure requires either thicker walls or results in higher tangential stress for a given inner diameter.