Time for terminal velocity to be attained

As t approaches infinity, u approaches the Stokes velocity = pg/X as given in equation (6.8). 

Theoretically a particle never reaches its terminal velocity but for practical purposes it can be assumed that the velocity is sufficiently near the terminal velocity for the error to be neglected. From equation (6.19) the velocity is 0.99 times the terminal velocity when  

From Table 6.3 it can be seen that the assumption that a particle from rest reaches its terminal velocity instantaneously does not introduce any appreciable errors. 

The distance covered, h, during the acceleration time is given by integration of equation (6.19)  

Since t is very small, the distance fallen in achieving a velocity equal to 0.99 times the settling velocity at low Reynolds numbers is also very small. 

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