Module 8: Flow at low and high Reynolds numbers
  Lecture 26: Creeping flow, Stokes-law and terminal velocity
 
 
  • One of the applications of Stoke's law is to calculate terminal velocity of a sphere in a quiescent fluid. Let us consider a sphere falling under gravity in stagnant fluid :
 
(Fig. 26a)
There are 3 forcess acting on the sphere
  1. Gravity
  2. Buoyancy
  3. drag (viscous) forces
Therefore,

 

When the particle acquires a steady-velocity or it reaches a constant (terminal) velocity 

  

Therefore,