Page 245 - Soil and water contamination, 2nd edition

232 Soil and Water Contamination

-1
During this time, the water has travelled a distance of 5702 s × 0.2 m s = 8260 m. Thus,
the suspended sediment concentration has diminished by 75 percent over a distance of
8260 m.
If the water flow around the particles is laminar , the settling velocity w can be described by
s
Stokes’s law . Stokes’s law assumes that the upward force according to Archimedes’ principle
and the shear stress es during settling are in equilibrium with the gravity force. For spherical
particles, Stokes’s law is:
1 ( ) g d 2
w s w (12.16)
s
18 M
-3
-3
where ρ = the density of the solid particles [M L ], ρ = the density of water [M L ],
s w
-1
-3
-1
-1
-1
μ = the dynamic viscosity of water (= 1.14 10 kg m s ) [M L T ], g = the gravitational
-2
-2
acceleration constant (= 9.8 m s ) [L T ], and d = the diameter of the particles. As
mentioned above, Equation (12.16) is only valid for laminar flow around the particle. The
flow regime (laminar or turbulent flow ) is described by the Reynolds number . For flow
around the particles the Reynolds number is defined as:
w d
Re s w (12.17)
M
where Re = Reynolds number [-]. If the Reynolds number is sufficiently small (< 1) then the
flow around the particles is laminar . If the Reynolds number is greater than 1 (in general,
this is the case for particles larger than about 100–150 μm) then the settling velocity can be
approximated by (Fair et al., 1968):
4 ( s w ) g d (12.18)
w
s
3 C d w
where C = the Newton’s drag coefficient [-], which is estimated by:
d
24 3
C d . 0 34 (12.19)
Re Re
If the Reynolds number exceeds 2000 (in general, this is the case for solid particles larger
than about 1.4 mm), then C becomes independent of Re. In this case, the settling velocity
d
can be approximated by:
w 3 . 3 ( s w ) g d (12.20)
s
Particles that are not spherical have a somewhat slower settling velocity (up to a factor of
about 1.4 less).
As can be seen from Equations (12.16), (12.18), and (12.20), the settling velocity
depends on both the diameter and the specific density of the particles. Considering the
variety in the nature and size of the particles, it is practically impossible to formulate one

mass balance for all suspended matter . Usually, suspended matter is subdivided on the basis
of the nature and size of the particles, or a mass balance is formulated for the most abundant
class of suspended matter. Apart from that, the particle size distribution and densities of
the particles in natural waters are difficult to measure directly. An important feature of fine
particles is that they tend to coagulate to form flocs. The flocculation process occurs if the
thickness of the ‘diffuse layer ’ surrounding the particle, which is governed by the chemical
composition of the water, decreases, enabling the particles to approach each other more
closely (see Section 4.2.3). The flocculation process is also favoured by the presence of sticky

10/1/2013 6:45:07 PM
Soil and Water.indd 244 10/1/2013 6:45:07 PM
Soil and Water.indd 244