- The force exerted on a body moving in a medium like air or water depends in a complex way upon the velocity of the body relative to the medium, the viscosity and density of the medium, the shape of the body, and the roughness of its surface.

- The most common method of mathematically modeling the drag force is the equation,

_{}

F_{D} |
= Drag Force. SI: N |

C_{D} |
= Drag Coefficient. SI: Dimensionless (Typical Values) |

A |
= Coss-sectional Area perpendicular to the flow. SI: m^{2} |

r |
= Density of the medium. SI: kg/m^{3} |

v |
= Velocity of the body relative to the medium. SI: m/s |

- The direction of the drag force is always opposite the direction of the body's velocity.

__The drag coefficient__**C**_{D }__is not constant__.**C**depends upon the velocity of the body, viscosity of the medium, the shape of the body, and the roughness of the body's surface._{D }

- The
**Reynolds number**has been found to be a useful dimensionless number that can characterize the drag coefficient's dependence upon the velocity. The Reynolds number is basically the ratio of the inertial force of the medium over its viscous force.

_{}

Re |
= Reynolds number. SI: Dimensionless |

L |
= Characteristic length of the body along the direction of flow. SI: m |

h |
= Dynamic Viscosity of the medium. SI: N s/m^{2} |

r |
= Density of the medium. SI: kg/m^{3} |

v |
= Velocity of the body relative to the medium. SI: m/s |

- For small values of the Reynolds number - called laminar flow since the flow is nonturbulant - the drag coefficient is inversely proportional to the velocity. This means that the drag force is only proportional to the body's velocity.

_{}

- When the flow is turbulent the Reynolds number is large, and the drag coefficient
**C**is approximately constant. This is the quadratic model of fluid resistance, in that the drag force is dependent on the square of the velocity._{D }

_{}

- Note that the frictional force between two surfaces is an example of a situation in which the drag force is constant and does not depend upon the body's velocity or contact surface area.

**Air Resistance on a Projectile**

The effects of both air resistance and gravity on a ball projected in to the air can be investegated. A drag constant can be varied to change the amount of air resistance. When the air resistance is large enough the ball will approach a terminal velocity quickly.