Stoke’s Law and Terminal Velocity
If a spherical body of radius r is dropped in a viscous fluid, it is first accelerated and then it’s acceleration becomes zero and it attains a constant velocity called terminal velocity.
(i) Weight of the body (W) = mg
= (volume density) × g = 4/3 πr3 ρδ
(ii) Upward thrust (T) = weight of the fluid displaced
= (volume × density) of the fluid × g = 4/3 Πr3 σδ
(iii) Viscous force (F) = 6 Πŋrv
When the body attains terminal velocity the net force acting on the body is zero. ∴ W – T – F = 0 or F = W – T