Density Of Material Given Maximum Radial Stress In Solid Disc Calculator

Density of Material Formula:

\[ \rho = \frac{8 \times \sigma_r}{\omega^2 \times (3 + \nu) \times r_{outer}^2} \]

Radial Stress (σr):

Pascal

Angular Velocity (ω):

rad/s

Poisson's Ratio (ν):

Outer Radius Disc (router):

meter

Density Of Disc (ρ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Density of Material Formula?

The density of material formula calculates the density of a solid disc based on radial stress, angular velocity, Poisson's ratio, and outer radius. This formula is particularly useful in mechanical engineering and material science for analyzing rotating disc systems.

2. How Does the Calculator Work?

The calculator uses the density formula:

\[ \rho = \frac{8 \times \sigma_r}{\omega^2 \times (3 + \nu) \times r_{outer}^2} \]

Where:

\( \rho \) — Density of disc (kg/m³)
\( \sigma_r \) — Radial stress (Pascal)
\( \omega \) — Angular velocity (rad/s)
\( \nu \) — Poisson's ratio
\( r_{outer} \) — Outer radius of disc (meter)

Explanation: The formula relates material density to the stress and rotational characteristics of a solid disc, accounting for material properties through Poisson's ratio.

3. Importance of Density Calculation

Details: Accurate density calculation is crucial for designing rotating machinery components, predicting material behavior under stress, and ensuring structural integrity in mechanical systems.

4. Using the Calculator

Tips: Enter radial stress in Pascals, angular velocity in rad/s, Poisson's ratio (typically between 0.1-0.5), and outer radius in meters. All values must be positive and within valid ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is radial stress in a rotating disc?
A: Radial stress is the stress component acting perpendicular to the radius of the disc, caused by centrifugal forces during rotation.

Q2: Why is Poisson's ratio important in this calculation?
A: Poisson's ratio accounts for the material's tendency to expand or contract in directions perpendicular to the applied stress, affecting the stress distribution in the disc.

Q3: What are typical density values for engineering materials?
A: Common engineering materials range from about 2700 kg/m³ for aluminum to 7800 kg/m³ for steel and 8000 kg/m³ for bronze.

Q4: When is this formula most applicable?
A: This formula is particularly useful for analyzing solid discs with uniform thickness rotating at constant angular velocity.

Q5: Are there limitations to this equation?
A: The formula assumes homogeneous material properties, constant angular velocity, and may have limitations for very high rotational speeds or complex disc geometries.