Density Of Cylinder Material Given Hoop Stress (For Thin Cylinder) Calculator

Formula Used:

\[ \rho = \frac{\sigma_{\theta}}{\omega \times r_{disc}} \]

Hoop Stress in Disc (\(\sigma_{\theta}\)):

Pascal

Angular Velocity (\(\omega\)):

rad/s

Disc Radius (\(r_{disc}\)):

Density Of Disc (\(\rho\)):

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1. What is the Density Calculation Formula?

The formula \(\rho = \frac{\sigma_{\theta}}{\omega \times r_{disc}}\) calculates the density of cylinder material based on hoop stress, angular velocity, and disc radius. This is particularly useful for thin cylinder applications in engineering and material science.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \rho = \frac{\sigma_{\theta}}{\omega \times r_{disc}} \]

Where:

\(\rho\) — Density of disc material (kg/m³)
\(\sigma_{\theta}\) — Hoop stress in disc (Pascal)
\(\omega\) — Angular velocity (rad/s)
\(r_{disc}\) — Disc radius (m)

Explanation: The formula relates material density to the hoop stress generated by rotational motion, providing insight into material properties under centrifugal forces.

3. Importance of Density Calculation

Details: Accurate density calculation is crucial for material selection, structural design, and stress analysis in rotating machinery and pressure vessel applications.

4. Using the Calculator

Tips: Enter hoop stress in Pascals, angular velocity in rad/s, and disc radius in meters. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is hoop stress in a cylinder?
A: Hoop stress is the circumferential stress in a cylinder wall caused by internal or external pressure, or rotational forces.

Q2: Why is angular velocity important in this calculation?
A: Angular velocity determines the centrifugal forces acting on the material, which directly affects the hoop stress and thus the calculated density.

Q3: What are typical density values for engineering materials?
A: Common engineering materials range from 1,000-2,700 kg/m³ for polymers and composites to 7,000-8,000 kg/m³ for steels and heavier metals.

Q4: Are there limitations to this formula?
A: This formula is specifically designed for thin cylinders and may not be accurate for thick-walled cylinders or complex geometries.

Q5: Can this calculator be used for educational purposes?
A: Yes, this calculator is suitable for educational demonstrations and engineering students learning about material properties and stress analysis.