# Terminal velocity (under buoyancy force)

## 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.

When the buoyancy effects are taken into account, an object falling through a fluid under its own weight can reach a terminal velocity (settling velocity) if the net force acting on the object becomes zero. When the terminal velocity is reached the weight of the object is exactly balanced by the upward buoyancy force and drag force.

## Variables

Vt | Terminal velocity (m/s) |

g | Standard gravity |

d | Diameter of the object (m) |

C_{d} | Drag coefficient (dimensionless) |

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

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