Aerodynamic Diameter Calculator

Formula

The formula to calculate the Aerodynamic Diameter ( $d_a$ ) is:

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

Where:

$d_a$ is the aerodynamic diameter (μm)
$St$ is the Stokes number (dimensionless)
$\mu$ is the air viscosity (μPa·s)
$\rho_p$ is the particle density (kg/m³)
$v$ is the flow velocity (m/s)

Definitions

Aerodynamic Diameter: A measure used to describe the size of aerosol particles based on their behavior in the air. It is defined as the diameter of a spherical particle with a density of 1 g/cm³ that has the same settling velocity as the particle in question. This measure is important in various fields such as environmental health, aerosol science, and air quality monitoring, as it affects how particles behave in the atmosphere, including their transport, deposition, and respiratory deposition in human lungs.
Stokes Number (St): A dimensionless number that characterizes the behavior of particles suspended in a fluid flow.
Air Viscosity (μ): The measure of the air's resistance to deformation, typically measured in micropascal-seconds (μPa·s).
Particle Density (ρ_p): The density of the particle, typically measured in kilograms per cubic meter (kg/m³).
Flow Velocity (v): The speed at which the air or fluid is moving, typically measured in meters per second (m/s).

Example

Let's say the Stokes number is 0.5, the air viscosity is 18.27 μPa·s, the particle density is 1000 kg/m³, and the flow velocity is 0.1 m/s. Using the formula:

$d_a = \sqrt{\frac{18 \cdot 0.5 \cdot 18.27}{1000 \cdot 0.1}}$

We get:

$d_a \approx 1.28 \text{ μm}$

So, the aerodynamic diameter is approximately 1.28 μm.

Activity Median Aerodynamic Diameter

Definition: The activity median aerodynamic diameter (AMAD) is the median aerodynamic diameter of particles in a sample, weighted by their activity.

Formula: $\text{AMAD} = \left( \frac{\sum (d_i^3 \cdot A_i)}{\sum A_i} \right)^{\frac{1}{3}}$

$\text{AMAD}$ : Activity median aerodynamic diameter
$d_i$ : Diameter of particle $i$
$A_i$ : Activity of particle $i$

Example: $\text{AMAD} = \left( \frac{(2^3 \cdot 10) + (3^3 \cdot 20)}{10 + 20} \right)^{\frac{1}{3}}$

AMAD: $\text{AMAD}$
Diameters: 2 µm, 3 µm
Activities: 10, 20

Mass Median Aerodynamic Diameter

Definition: The mass median aerodynamic diameter (MMAD) is the median aerodynamic diameter of particles in a sample, weighted by their mass.

Formula: $\text{MMAD} = \left( \frac{\sum (d_i^3 \cdot m_i)}{\sum m_i} \right)^{\frac{1}{3}}$

$\text{MMAD}$ : Mass median aerodynamic diameter
$d_i$ : Diameter of particle $i$
$m_i$ : Mass of particle $i$

Example: $\text{MMAD} = \left( \frac{(1^3 \cdot 5) + (4^3 \cdot 15)}{5 + 15} \right)^{\frac{1}{3}}$

MMAD: $\text{MMAD}$
Diameters: 1 µm, 4 µm
Masses: 5, 15

How to Calculate the Diameter

Definition: The diameter of a circle is the distance across the circle through its center.

Formula: $D = 2r$

$D$ : Diameter
$r$ : Radius

Example: $D = 2 \times 5$

Diameter: $D$
Radius: $r = 5$

Diameter Length Calculator Formula

Definition: The diameter length calculator formula helps determine the diameter of a circle based on its circumference.

Formula: $D = \frac{C}{\pi}$

$D$ : Diameter
$C$ : Circumference
$\pi$ : Pi (approximately 3.14159)

Example: $D = \frac{31.4}{3.14159}$

Diameter: $D$
Circumference: $C = 31.4$
Pi: $\pi = 3.14159$

How to Calculate Average Diameter

Definition: The average diameter is the mean diameter of a set of circular objects.

Formula: $\text{Average Diameter} = \frac{\sum d_i}{n}$

$\text{Average Diameter}$ : Average diameter
$d_i$ : Diameter of object $i$
$n$ : Number of objects

Example: $\text{Average Diameter} = \frac{5 + 6 + 7}{3}$

Average Diameter: $\text{Average Diameter}$
Diameters: 5, 6, 7
Number of objects: $n = 3$

Formula for Calculating Diameter

Definition: The formula for calculating the diameter of a circle involves its radius or circumference.

Formula: $D = 2r$ or $D = \frac{C}{\pi}$

$D$ : Diameter
$r$ : Radius
$C$ : Circumference
$\pi$ : Pi (approximately 3.14159)

Example: $D = 2 \times 4$ or $D = \frac{25.12}{3.14159}$

Diameter: $D$
Radius: $r = 4$
Circumference: $C = 25.12$
Pi: $\pi = 3.14159$