5.6 Drag

Drag Force

  • Drag is a resisting force opposing the motion of an object through a fluid (air or water).

  • Commonly known as air resistance.

  • Important in biological contexts for microscopic movement in water.

Characteristics of Drag Force

  • Direction: Opposite to the velocity of the object.

  • Magnitude: Increases with the object's speed.

Complexity of Drag

  • More complex than friction.

  • Originates from two different physical principles:

    • Inertial forces (e.g., baseball through air).

    • Viscous forces (e.g., sphere in thick fluid like honey).

Drag Force Models

  • For objects in high-speed air: (Dext(drag)extisproportionaltohov2l2)(D ext{ (drag)} ext{ is proportional to } ho v^2 l^2) where:

    • $\rho$: density of fluid

    • $v$: speed of the object

    • $l$: characteristic size of the object

  • For objects in thick fluids: (Dextisproportionaltonlv)(D ext{ is proportional to } n l v) where:

    • $n$: viscosity of fluid

Reynolds Number (RE)

  • Dimensionless number to compare internal and viscous forces:
    (RE=ρv2l2nlu=ρvln)(RE = \frac{\rho v^2 l^2}{n l u} = \frac{\rho v l}{n})

  • RE high (>$1,000$): Dominance of inertial drag (e.g., baseball).

  • RE low (<$1,000$): Dominance of viscous drag.

Fluid Properties

  • Density (SI units: kg/m³) and viscosity (SI units: Pa·s).

  • Viscosity varies with temperature.

Characteristic Size (l)

  • Can refer to object height, width, or diameter.

  • For irregular shapes, small differences in dimensions have minimal effect on RE values.

Practical Example

  • A basketball ($75 mm$ diameter) in $20^ ext{°}C$ air at $20 ext{ m/s}$ has a high Reynolds number, indicating dominance of inertial drag.