Hoop Stress In Thin Cylinder Given Tangential Velocity Of Cylinder Calculator

Formula Used:

\[ \sigma_{\theta} = v_t \times \rho \]

Hoop Stress In Disc:

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1. What is Hoop Stress in Thin Cylinder?

Hoop stress is the circumferential stress in a cylinder or disc that occurs when pressure is applied from the inside. It's a fundamental concept in mechanical engineering and material science, particularly in pressure vessel design and rotating machinery analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{\theta} = v_t \times \rho \]

Where:

\( \sigma_{\theta} \) — Hoop Stress in Disc (Pa)
\( v_t \) — Tangential Velocity (m/s)
\( \rho \) — Density Of Disc (kg/m³)

Explanation: This formula calculates the circumferential stress in a rotating disc or cylinder based on its tangential velocity and material density.

3. Importance of Hoop Stress Calculation

Details: Accurate hoop stress calculation is crucial for designing safe and efficient rotating machinery, pressure vessels, and structural components. It helps prevent material failure and ensures structural integrity under rotational forces.

4. Using the Calculator

Tips: Enter tangential velocity in m/s and density in kg/m³. Both values must be positive numbers. The calculator will compute the hoop stress in Pascals (Pa).

5. Frequently Asked Questions (FAQ)

Q1: What is tangential velocity in this context?
A: Tangential velocity refers to the linear speed of a point on the rotating disc's circumference, measured in meters per second.

Q2: Why is material density important for hoop stress?
A: Density affects the centrifugal forces generated during rotation, which directly influence the circumferential stress in the material.

Q3: What are typical units for hoop stress?
A: Hoop stress is typically measured in Pascals (Pa) in the SI system, or pounds per square inch (psi) in imperial units.

Q4: When is this formula applicable?
A: This formula is particularly useful for thin-walled cylinders and rotating discs where the thickness is small compared to the diameter.

Q5: What safety factors should be considered?
A: Engineering designs typically include safety factors to account for material variations, manufacturing tolerances, and unexpected load conditions.