Terminal Velocity - Terminal Velocity in The Presence of Buoyancy Force

Terminal Velocity in The Presence of Buoyancy Force

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. That is

where

= weight of the object,

= buoyancy force acting on the object, and

= drag force acting on the object.

If the falling object is spherical in shape, the expression for the three forces are given below:

where

diameter of the spherical object

gravitational acceleration,

density of the fluid,

density of the object,

projected area of the sphere,

drag coefficient, and

characteristic velocity (taken as terminal velocity, ).

Substitution of equations (2–4) in equation (1) and solving for terminal velocity, to yield the following expression

.