Terminal Velocity Derivation

What is Terminal Velocity?

Terminal velocity is defined as the highest velocity attained by an object falling through a fluid. It is observed when the sum of drag force and buoyancy is equal to the downward gravity force acting on the object. The acceleration of the object is zero as the net force acting on the object is zero.

How to find Terminal Velocity?

In fluid mechanics, for an object to attain its terminal velocity, it should have a constant speed against the force exerted by the fluid through which it is moving.

v_t is the terminal velocity, m is the mass of the falling object, g is the acceleration due to gravity, C_d is the drag coefficient, 𝜌 density of the fluid through which the object is falling, and A is the area projected by the object.