Aerodynamic Diameter Calculator

To calculate the aerodynamic diameter, plug in the values for the Stokes number, dynamic viscosity, particle density, and velocity into the formula. Solve for the square root of the result.

Aerodynamic diameter is an important concept in physics, especially when discussing the behavior of particles in the air. This is often used to calculate the size of aerosol particles or other small objects in motion. The aerodynamic diameter refers to the size of a particle with the same settling velocity as a sphere of unit density.

It helps scientists and engineers understand how particles behave under the influence of gravity and air resistance. This calculation is essential in fields such as meteorology, environmental science, and industrial processes where aerosols are involved.

Formula:

The formula to calculate aerodynamic diameter $d_a$ is:

$$d_a = \sqrt{\frac{18 \cdot St \cdot \mu}{\rho_p \cdot v}$$

Where:

• $St$ is the Stokes number
• $\mu$ is the dynamic viscosity of air
• $\rho_p$ is the particle density
• $v$ is the particle velocity

How to Calculate ?

1. Identify the values of the Stokes number, dynamic viscosity of air, particle density, and velocity.
2. Substitute these values into the aerodynamic diameter formula.
3. Solve the equation by calculating the square root of the resulting expression.

Solved Calculations

Example 1:

Given:

• Stokes number (St) = 0.05
• Dynamic viscosity of air ($\mu$) = 0.018 Pa·s
• Particle density ($\rho_p$) = 1200 kg/m³
• Velocity ($v$) = 2 m/s

$$d_a = \sqrt{\frac{18 \cdot 0.05 \cdot 0.018}{1200 \cdot 2}}$$$$d_a = \sqrt{\frac{0.0162}{2400}} = \sqrt{0.00000675} \approx 0.0026 \, m$$

Answer: The aerodynamic diameter is approximately 0.0026 meters.

Example 2:

Given:

• Stokes number (St) = 0.08
• Dynamic viscosity of air ($\mu$) = 0.02 Pa·s
• Particle density ($\rho_p$) = 1500 kg/m³
• Velocity ($v$) = 3 m/s

$$d_a = \sqrt{\frac{18 \cdot 0.08 \cdot 0.02}{1500 \cdot 3}}$$$$d_a = \sqrt{\frac{0.0288}{4500}} = \sqrt{0.0000064} \approx 0.0025 \, m$$

Answer: The aerodynamic diameter is approximately 0.0025 meters.

What is Aerodynamic Diameter Calculator ?

To calculate the aerodynamic diameter, it is essential to understand its significance in the study of particles, especially aerosols.

The aerodynamic diameter refers to the diameter of a sphere that has the same settling velocity as the particle in question when subjected to a specific airflow. This concept helps compare particles of different shapes and densities by standardizing their behavior in a fluid.

The formula for calculating aerodynamic diameter often involves parameters like mass median aerodynamic diameter and particle size distribution. When working with aerosols, it’s crucial to note the difference between aerodynamic diameter and geometric diameter, as they can affect how particles are inhaled and deposited in the respiratory system. For example, PM2.5 refers to particulate matter with an aerodynamic diameter of less than 2.5 micrometers.

Final Words:

Using an aerodynamic diameter calculator can simplify these calculations, providing quick results while considering various factors. Understanding the aerodynamic diameter helps researchers and professionals assess air quality and the potential health impacts of airborne particles.