By substituting Equations 3.4 and 3.5 into Equation 3.6, the expression:
2 K 2 ρs
- 1 gD s
CD K 1 ρ
Four dimensionless variables describing fall velocity result from dimensional analysis of
, CD , s , 2 = 0
The drag coefficient CD is dependent on the particle Reynolds number (Re = ρ ωDs/), the
shape, and the surface texture of the particle, where is dynamic viscosity of the fluid. The
ratio K2/K1 is usually replaced by the Corey shape factor Sp (Equation 3.1).
The relations between the fall velocity of particles and the other variables are given in
Figures 3.1 and 3.2.
Drag coefficient CD vs particle Reynolds number Rep for spheres and natural
sediments with shape factors Sp equal to 0.3, 0.5, 0.7, and 0.9. Also, sediment
diameter Ds vs. fall velocity ω and temperature To (Brown 1950, p. 781).