Environmental Engineering Reference
In-Depth Information
60
50
Sphere (1.25 g cm
-3
)
Sphere (1.09 g cm
-3
)
Melosira italica
40
30
20
10
0
0
1
2
3
4
5
6
7
Volume (1000
μ
m
3
)
FIGURE 2.10
Sinking velocities of spherical particles with two different densities and of a
filamentous diatom,
Melosira,
as a function of volume. The diatom can be found suspended
in water and has a density of approximately 1.2 g cm
3
(data from Reynolds, 1984).
Calculation of the sinking rates of particles in water provides a good
example of the ramifications of properties of water and scale in aquatic
habitats. In general, larger and denser particles sink more rapidly. This re-
lationship can be calculated for small spherical objects using Stokes law:
2
gr
2
)
9
(
U
where
U
is velocity,
g
is gravitation acceleration,
r
is the radius of the
sphere,
is the viscosity. The relationship between sinking rate and density of spheres
as a function of size can be seen in Fig. 2.10. This relationship can be used
to predict how long particles will remain suspended in water (Example
2.2).
Objects that deviate from spherical form can sink more slowly.
Melosira
is an alga that lives suspended in water. It has cylindrical cells and increases
in size by adding the cylindrical cells end to end. Thus, the volume of the
colony can increase with a much greater increase in surface area than if the
colony was spherical. The relationship for viscous force (
F
v
) predicts that
this will lead to an increase in viscous force and thus a slower sinking rate
relative to a sphere (Fig. 2.10). The slower sinking allows
Melosira
to stay
in the lighted water column and grow.
is the density of the sphere,
is the density of the liquid, and
FORCES THAT MOVE WATER
Solar heating and
evaporation
of water are central to water movement.
This energy input drives the hydrologic cycle by evaporating water from
the ocean that is deposited subsequently as precipitation on land. When
water flows downhill in rivers or groundwater, it releases the potential
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