Mathematically: 



3 

 Gravitational force (F ) = 4/3TTr p g (9) 



g s 



C n R 

 D e 

 Fluid resistance force (F ) = 6TT r ^ V — jrj- (10) 



3 

 Buoyancy force (F ) = 4/3TTr p f g (11) 



where 



3 

 p = density of grain in gm/cm 



3 



p. = density of fluid in gm/cm 



r = radius of sphere in cm 



2 

 jU = dynamic viscosity of fluid in gm/sec/cm 



V = settling velocity of solid in cm/sec 



P 2 



V 

 F p 



Cq = drag coefficient = — — / p f 



d * 2 



n 



d = nominal diameter (mm) , or the diameter of a sphere 

 having the same volume as the particle 



2r V p f 

 R = Reynolds number = 



At terminal fall velocity, the forces balance so that there is no 

 net force , 



F g " F R + F B (12) 



and from the definition (2) of Reynolds number, 



V = —|- (13) 



P 2rp f 



When solving for V standard tables are available for the determination 

 of /J and p£ (at various temperatures) and R e may be determined from the 

 tables of Schulz, et al. (1954) that take into account the drag coefficients 

 associated with various particle shapes and densities. 



