Consider a spherical body falling from rest through a large column of viscous fluid. The forces acting on body are

(a) Weight (vertically downward)
(b) Buoyant Force (B) (vertically upward)
(c) Viscous Force (`F_v`) (vertically upward)

Initially, `v= 0`

So, `F_v = 0`

`F_text(net) = mg- B`

and body accelerates downwards. As the velocity of body increases, `F_v` increases and at some stage,

`F_text(net) = mg - B - F_v = 0`

`mg-B = F_v`

Acceleration of body becomes zero and it moves downwards with constant velocity. This constant velocity is called `text(Terminal velocity)` (`v_t`).

At terminal velocity `v_t`

`(4pi)/3R^3rhog-(4pi)/3R^3sigmag=6pietaRv_t`

Where, `rho=` density of material of sphere ; `sigma=` density of fluid ; `eta=` coefficient of viscosity of fluid

`v_t=2/9\((rho-sigma))/eta\R^2g`