RESEARCH· ·1970·

B166
TABLE 3.-Settling time for a 1 O-micron-diameter quartz sphere
in sea water and in pure water
Mean
Depth (meters) Salinity 1 tempel1\- Settling velocity
(in parts per ture (em/sec)
thousand) (0°0) 1
0-200 ____ _ 34. 6 10. 8 0. 00648131
200-400 ____ _ 34. 6 9. 3 . 00620758
400-600 ____ _ 34. 5 6. 5 . 00572845
600~800 ____ _ 34.4 4. 3 . 00539250
34. 3 3. 3 . 00524531
34. 5 2. 9 . 00518623
34. 7 2. 7 . 00514343
34. 8 2. 6 . 00513419
34. 9 2. 4 . 00509835
34. 9 2. 1 . 00505166
34. 8 1.6 . 00497223
Total ___________________________________ _
800-1, ooo ___ _
1,000-1,500 __ 1, 500-2, ooo __ _
2,000-2,500 __ _
2, 500-3,000 __ _
3, 000-3, 500 ___ 3, 500-4, ooo ___ _
0-200 ____________ _
200-400 ____________ _
400-600 ____________ _
600-800 ____________ _
800-1,000 __________ _
1, 000-1, 500 ___________ _
1,500-2,000 __________ _
2, 000-2, 500 ___________ _
2, 500-3, ooo ___________ _
~000-~500 ___________ _
~500-4,000 ___________ _
Sea water
Pure water
10. 8 0. 00696160
9. 3 . 00673683
6. 5 . 00620190
4. 3 . 00579040
3. 3 . 00559932
2. 9 . 00553728
2. 7 . 00550004
2. 6 . 00547994
2. 4 . 00544676
2. 1 . 00539128
1.6 . 00530232
Total ___________________________________ _
1 From Mathews (1939).
Total time to
settle (hours)
SEDIMENTATION
857. 27
894. 85
969. 93
1, 030. 40
1, 059. 32
2,678. 09
2,699. 78
2, 705. 63
2, 724. 80
2, 748. 76
2, 793. 30
21, 162. 13
(881. 76 days)
798. 08
824. 74
895. 66
959. 23
992. 06
2,508. 78
2, 525. 25
2, 534. 21
2, 549. 72
2,575. 99
2,619.17
19, 782. 89
(824.29 days)
They are considered resistances to settling velocity and
are called inertial forces. Stokes' law does not take
these forces into consideration, as it applies only to a
perfect sphere. Failure to consider these factors in
velocity calculations results in significant errors for
nonspherical particles whose Reynolds number exceeds
1.0. Blanchard (1967) experimentally determined that
for a 25-micron-diameter quartz sphere the upper limit
where Stokes' equation holds is at a Reynolds number
of 0.02.
The most important factor, other than fluid properties,
affecting settling velocity is size. Shape has been
considered secondary in importance, yet many of the
discrepancies in settling velocity for a particular particle
size are due to differences in shape (Schultz and
others, 1954). Composition is important because it
determines the specific gravity of the particle: Also,
many biological particles dissolve rapidly, and their
size, shape, and surface texture may change as they
settle. Some may be totally dissolved before reaching
the bottom of the sea.
CONCLUSIONS
Regardless of the factors not considered by Stokes'
law, it is apparent that determination of settling velocities
in sea water must take into account the basic differences
between fresh water and sea water. Where
errors of as much as 6 percent are significant in calculating
settling velocity, the viscosity and specific
gravity of sea water must be taken into account. A
new table giving absolute values of the viscosity of
sea water should be carefully compiled to aid· those
actually involved in calculating the settling velocities
of minerals in sea water. International sea water
standards should be used for control. Such standards
have been prepared by the Hydrographic Laboratory
of the International Council for the Exploration of
the Sea in Copenhagen, Denmark.
REFERENCES
Blanchard, M. B., 1967, Method for determining the density of
microsize spherical particles : Geol. Soc. America Bull.,
v. 78, p. 385-404.
Hidaka, Koji, 1954, A contribution to the theory of upwelling
and coastal currents: Am. Geophys. Union Trans., v. 35,
no. 3, p. 431-444.
Hodgman, C. D., ed., 1960, Handbook of chemistry and physics,
42d ed. : Cleveland, Ohio, Chemical Rubber Publishing Co.,
3,481 p. [repr. 1961].
Krilmmel, 0., and Ruppin, E., 1906, 'tiber die innere Reibung des
Seewassers: Wiss. Meeresunters. ( N,F.), 9 ( Abt. Kiel),
p. 27-36.
Mathews, D. J., 1939, Tables of the velocity of sound in pure
water and sea water for use· in echo-sounding and soundranging,
2d ed: Hydrographic Dept., The Admiralty, London,
52 p.
Schultz, E. F., Wilde, R. H., and Albertson, M. L., 1954, Influence
of shape on the fall velocity of sedimentary particles :
Omaha, Nebr., U.S. Army Corps Engineers, Missouri River·
Div., MRD Sediment Ser., no. 5, 161 p.
U.S. Navy Hydrographic Office, 1952, Tables for sea water
density: Pub. 615, Washington, D.C., 265 p.