68
2 Water at Rest and in Motion
t
drag
l
weight
Fig. 2.30: Balance of weight and drag forces for sphere
which is valid for very small spherical particles and very small Reynolds numbers, Re = w D /v < 0.2. For example, for organic suspended particles with
density close to water, say Ps = 1.1 X 10 3 kg/m 3 (or 1.1 g/cm 3 ), a typical
terminal velocity w is 1.23 m/year for particle diameter D = Ip,m and 1105
m/year for diameter D = 30p,m (Dera, 1992).
The terminal velocity for mineral particles which are not spherical combine
the effects of grain size, shape, and composition of the fluid and viscosity.
This velocity can only be determined experimentally. Numerous laboratory
experiments suggest the following formulae for terminal velocities of commonly
occurring fine, medium and coarse sands (Hallermeier, 1981):
A
18
for
A < 39
wD
AO.7
(2.95)
for
39 < A < 10 4
V
6
1.05 AO. 5
for
A> 10 4 ,
in which A = [(Ps/Pw) - 1] (gD 3 /v 2 ) is the 'buoyancy index'. Normalized empirical terminal velocity (w D / v) for sand particles and spheres, as a function of
buoyancy index, is shown in Fig. 2.31. For very fine particles (or for buoyancy
index A < 39), terminal velocity is equal to that given by the Stokes' formula