Velocity of a falling object

Description

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers (or surfaces) or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, drag forces depend on velocity. Drag force is proportional to the velocity for a laminar flow and the squared velocity for a turbulent flow. Even though the ultimate cause of a drag is viscous friction, the turbulent drag is independent of viscosity.

Drag forces always decrease fluid velocity relative to the solid object in the fluid’s path.

The velocity as a function of time for an object falling through a non-dense medium, and released at zero relative-velocity v = 0 at time t = 0, is roughly given by a function involving a hyperbolic tangent.

Related formulas

Variables

utvelocity of the falling object (m/s)
mmass of falling object (kg)
gStandard gravity
ρdensity of the fluid through which the object is falling (kg/m3)
Aprojected area of the falling object (m2)
Cddrag coefficient (dimensionless)
ttime (s)