Tangential Stress in Thick Cylinder Subjected to Internal Pressure Calculator

Formula Used:

\[ \sigma_{tang} = \frac{P_i \times d_i^2}{(d_o^2 - d_i^2)} \times \left( \frac{d_o^2}{4 \times r^2} + 1 \right) \]

Internal Pressure on Cylinder (P_i):

Inner Diameter of Pressurized Cylinder (d_i):

Outer Diameter of Pressurized Cylinder (d_o):

Radius of Pressurized Cylinder (r):

Tangential Stress in Pressurized Cylinder (σ_tang):

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1. What is Tangential Stress in Pressurized Cylinder?

Tangential stress in pressurized cylinder is the stress experienced by the cylinder walls when the direction of the deforming force is perpendicular to central axis. It represents the circumferential stress that develops in the wall of a thick-walled cylinder when subjected to internal pressure.

2. How Does the Calculator Work?

The calculator uses the formula for tangential stress in thick-walled cylinders:

\[ \sigma_{tang} = \frac{P_i \times d_i^2}{(d_o^2 - d_i^2)} \times \left( \frac{d_o^2}{4 \times r^2} + 1 \right) \]

Where:

\( \sigma_{tang} \) — Tangential stress in pressurized cylinder (Pa)
\( P_i \) — Internal pressure on cylinder (Pa)
\( d_i \) — Inner diameter of pressurized cylinder (m)
\( d_o \) — Outer diameter of pressurized cylinder (m)
\( r \) — Radius of pressurized cylinder (m)

Explanation: This formula calculates the circumferential stress at a specific radial position in a thick-walled cylinder subjected to internal pressure.

3. Importance of Tangential Stress Calculation

Details: Accurate calculation of tangential stress is crucial for designing pressure vessels, piping systems, and cylindrical containers to ensure they can withstand internal pressures without failure. It helps determine the required wall thickness and material specifications for safe operation.

4. Using the Calculator

Tips: Enter internal pressure in Pascals (Pa), diameters and radius in meters (m). All values must be positive, and the outer diameter must be greater than the inner diameter. Ensure consistent units for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between tangential and radial stress?
A: Tangential stress acts circumferentially around the cylinder, while radial stress acts perpendicular to the cylinder wall. Both are important in pressure vessel design.

Q2: When is this formula applicable?
A: This formula is specifically for thick-walled cylinders where the wall thickness is significant compared to the diameter, typically when the ratio of outer to inner diameter is greater than 1.1.

Q3: What are typical units for these calculations?
A: While SI units (Pa for pressure, m for dimensions) are used here, other unit systems can be used as long as consistency is maintained throughout the calculation.

Q4: How does tangential stress vary across the cylinder wall?
A: Tangential stress is maximum at the inner surface and decreases toward the outer surface of thick-walled cylinders under internal pressure.

Q5: What safety factors should be considered?
A: Engineering designs typically include safety factors that account for material properties, operating conditions, and potential stress concentrations not captured by this basic formula.