# Forces Acting on Airborne Particles

 The forces acting on an aerosol particle in still air are: Gravitational Force, W Bouyancy Force, Drag Force,

### Gravitational Force

The weight of a spherical particle of diameter d is expressed as:

where is the density of the particle and g is the acceleration due to gravity.

### Bouyancy Force

 According to Archimedes' Bouyancy Principle, the bouyant force exerted on a floating body is equal to the weight of the fluid displaced by the body. The Bouyancy Force exerted on a spherical particle is: where is the gas density.

### Drag Force

 Sir Isaac Newton derived the general equation for the resistance force on a sphere moving through a gas while investigating the ballistics of cannon balls. Newton theorized that a sphere must push aside a volume of gas equal to the projected area of the sphere times its velocity. The general form of Newton's resistance equation is: where is the drag force on the sphere, is the drag coefficient, and V is the relative velocity between the gas and the sphere. This equation is valid for all subsonic particle motion, from cannon balls to aerosol particles (or for instance, apples...assuming they're spherical).

### Drag Coefficient

The coefficient of drag, , is dependent upon Reynold's number (Re). For flow around a sphere, there are three regions for the drag coefficient: the Stoke's Law region, the Transition region, and Newton's Law region.

These relationship between drag coefficient and Reynold's number is depicted in the following figure:

******* Cd - Re figure here.

• Transition region: 1<Re<1000

• Newton's Law region: 1000<Re<
• In the Newton's Law region, is nearly constant.