# Terminal velocity (creeping flow conditions)

## Description

The terminal velocity of a falling object is the velocity of the object when the sum of the drag force and buoyancy equals the downward force of gravity acting on the object. Since the net force on the object is zero, the object has zero acceleration.

In fluid dynamics, an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving.

For very slow motion of the fluid, the inertia forces of the fluid are negligible (assumption of massless fluid) in comparison to other forces. Such flows are called creeping flows and the condition to be satisfied for the flows to be creeping flows is the Reynolds number, Re <<1.

## Variables

V_{t} | Terminal velocity (m/s) |

g | Standard gravity |

d | Diameter of the spherical object (m) |

μ | Fluid viscosity (N*s/m^{2}) |

ρ_{s} | Density of the falling object (kg/m^{3}) |

ρ | Density of the fluid through which the object is falling (kg/m^{3}) |