Morris & Fan. Reservoir Sedimentation Handbook
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SEDIMENT PROPERTIES 5.15
where µ = dynamic viscosity. The unit of dynamic viscosity, also termed absolute vis-
cosity or simply viscosity, is the Pascal-second (Pa•s = N•s/m
2
= kg/m•s), defined as a
shear stress of 1 Pa (1 N/m
2
) developed in a homogeneous medium, in laminar flow,
between two plane layers 1 m apart and moving at a relative velocity of 1 m/s. In the cgs
system the poise (P) is the unit of dynamic viscosity and may be converted to SI units as
follows: 1P = 10
-1
Pa•s. Kinematic viscosity is equal to the dynamic viscosity divided
by the fluid density:
(5.17)
Ki
nematic viscosity has units of m
2
/s. Liquid viscosity decreases as temperature
increases, as shown in Table 5.2. The dynamic viscosity µ of water in units of Pa•s at
temperature T in kelvin can be estimated within about 1 percent from the following
equation (White, 1979):
(5.18)
whe
re T
o
= 273.16°K (0°C) and µ
o
= 0.001792 kg/(m•s).
TABLE 5.2 Physical Characteristics of Water as a Function of Temperature
Temp, °C
0 5 10 15 20 25 30 40
Viscosity or dynamic viscosity
(μ, 10
-3
Pa•s = 10-3 N•s/m
2
)
1.781 1.518 1.307 1.139 1.002 0.890 0.798 0.653
Kinematic viscosity
(ν, 10
-6
m
2
/s)
1.785 1.519 1.306 1.139 1.003 0.893 0.800 0.658
Density of pure water
(ρ, kg/m
3
)
999.8 1000.0 999.7 999.1 998.2 997.0 995.7 992.2
Specific weight of pure water
(γ, N/m
3
)
9805 9807 9804 9798 9789 9777 9764 9730
5.5.2 Reynolds Number
The Reynolds number Re indicates the ratio of inertial forces to viscous forces and
determines whether hydraulic forces at the particle boundary which resist sediment
motion are laminar or turbulent. Different equations are applicable in each case. Laminar
flow occurs when the fluid viscosity significantly affects flow, such as the low velocity
flow through porous media and the settling of small (silt and clay) particles. The
Reynolds number is used as the criterion for differentiating between the laminar and
turbulent flow range, and its value is expressed as a function of fluid velocity V, a
characteristic length D, and kinematic viscosity :
(5.19)
SEDIMENT PROPERTIES 5.16
Different characteristic lengths are used with different hydraulic sections, and thus the
absolute values of Re associated with the transition from laminar to turbulent flow also
vary depending on the characteristic length used. For discrete particles settling in a fluid,
the particle Reynolds number is computed as
(5.20)
wh
ere the characteristic length is the particle diameter d, the terminal velocity of the
particle relative to the fluid is , and fluid density is .
5.5.3 Settling Velocity of Silts and Clays
The settling velocity of silts and clays falls in the laminar range. Terminal fall velocity
(ω
t
) of fine sediment varies directly with the difference in specific weights of the
sediment and the fluid, and the square of the particle diameter, as given by Stokes'
equation:
(5.21)
Thi
s corresponds approximately to a particle Reynolds number less than 1. Stokes'
equation predicts the terminal velocity for discrete particles large enough to overcome
Brownian motion, with smooth rigid boundaries, approximately spherical in shape, and
settling at a uniform velocity in a quiescent fluid where fluid viscosity is the only force
resisting the falling particle. The settling diameters of small particles as determined from
column settling tests are computed from the observed fall velocity and Stokes' equation.
This procedure determines the sedimentation diameter of small particles, normally the
parameter of interest in transport studies, rather than their true size or shape. From
Stokes' equation, the settling velocity for the largest-size silt particle (60X 10
-6
m) can be
computed as 3.2 X 10
-3
m/s in water at 20°C where µ = 1.007 X 10
-3
kg/(m•s) and (
S
- )
= 1.65 X 103 kg/m
3
. The particle Reynolds number for this condition may be computed
as 0.5.
5.5.4 Settling Velocity of Coarse Grains
The fall velocity of a sphere over the full range of Reynolds numbers may be expressed
as a function of the drag coefficient C
D
, gravitational constant g, particle diameter d, and
specific weight by:
(5.22)
For
laminar flow, the drag coefficient is given by C
D
= 24/Re, and in this range settling
velocity is not greatly affected by particle shape. However, in the turbulent range the drag
coefficient cannot be expressed analytically and the settling velocity must be determined
experimentally. Figure 5.10 may be used to determine the fall velocity of coarse
sediment.
5.5.5 Simplified Equations for Fall Velocity
Rubey (1931) developed an equation to estimate terminal fall velocity over the full range
of particle diameters, which may be expressed in the following form:
SEDIMENT PROPERTIES 5.17
SEDIMENT PROPERTIES 5.18
(5.23)
whe
re = terminal fall velocity, m/s;
S
and = density of sediment and water respec-
tively, kg/m
3
; µ = viscosity or dynamic viscosity, (N•s)/m
2
, and d = particle diameter, m.
This equation is best used in a programmable calculator. The following is an example
computation for d = 1 mm at 20°C.
Val
ues of viscosity are given in the appendixes.
For grain diameter d greater than 2 mm, the fall velocity can be approximated by the
following equations:
= 3.32d
0.5
in m/s, d in mm (5.24)
= 6.01d
0.5
in ft/s, d in ft (5.25)
where = terminal fall velocity of the particle (Yang, 1996). For water, changes in vis-
cosity (temperature) have a negligible effect on the fall velocity of particles in this size
range.
5.5.6 Effect of Concentration on Settling Velocity
If suspended sediment is dispersed throughout the water column, sediment particles will
settle more slowly than in clear water, and the settling rate is said to be hindered. The
decrease in fall velocity caused by an increase in sediment concentration may be esti-
mated from Fig. 5.11 (McNown and Lin, 1952), which shows the ratio of particle settling
velocity ω
0
in clear water to the settling velocity ω
c
for sediment concentrations up to 9
percent by weight, and for Reynolds numbers less than 1.3 (i.e., laminar flow). These
curves are based on laboratory experiments of quiescent settling of sediments not affected
by flocculation and may not be directly applicable to field conditions.
5.5.7 Sweep Flocculation and Hindered Settling
Particles settling through the water column can agglomerate into flocs as the larger and
faster-settling particles sweep downward, overtaking and entraining the smaller ones.
Through this process the settling velocity can increase over time as a result of floc
growth. Similarly, if sediment concentration increases with depth because of the settling
of sediment from above, the settling velocity can become increasingly hindered with
depth by the higher concentration. In either case, the settling velocity will be variable
over time. McLaughlin (1959) devised a method to measure the average settling velocity,
and to also determine whether settling is hindered or accelerated by floc growth. This
method only measures the growth of sweep floc due to sedimentation. It does not provide
information on the extent of flocculation that exists before the test begins. Although the
procedure is outlined as a laboratory test, it might also be adapted to field measurements
in a reservoir, without interferences such as density currents.
SEDIMENT PROPERTIES 5.19
FIGURE 5.11 Effects of suspended solids concentration on the fall velocity of sediment
in water (McNown and Lin,1952).
Error! Bookmark not defined.Consider sediment in a settling column (Fig. 5.12a).
Sedi
ment flux in the vertical (z) direction is w¯ C, where w¯ is the local instantaneous mean
sed
iment settling velocity and C is the local instantaneous sediment concentration.
Consider a thin slice of water within the cylinder and a small time step. Continuity of
mass across this slice requires that the change in the rate of sediment flux, the difference
between the amount of sediment falling into the slice from above less that falling out the
bottom of the slice, must equal the change of sediment concentration within the slice.
This may be expressed as
SEDIMENT PROPERTIES 5.20
FIGURE 5.12 (a) An idealized settling column with three measurement locations is shown on the
left The right shows a concentration profile diagram in which instantaneous concentration profiles
are shown as solid lines, and lines of constant settling velocity are dashed. (b) Concentration profile
diagram for bentonite clay and alum in water (after McLaughlin, 1959).
(5.26)
Thi
s relationship may be rearranged as:
(5.27)
an
d in this form it can be used to calculate w¯ , the mean settling velocity of the
sus
pension.
The experimental apparatus consists of a settling column from which a sequence of
samples are removed by pipet or withdrawal ports at different levels. The sample is
agitated at time t = 0 so that it has a uniform initial concentration equal to 100 percent of
the mean sample concentration. At subsequent points in time, the concentration at the
surface is taken as zero and the concentration at different depths is measured by with
drawing samples. These samples may be extracted from all levels simultaneously a times
t
1
, t
2
, and t
3
, thereby creating concentration profiles T
1
, T
2
,and T
3
(Fig. 5.12a), or they
may be extracted at different points in time and the concentration profiles at different
points in time determined by interpolation (Fig. 5.12b). In the concentration profile
diagram, solid lines show the concentration profile at different moments in time, and
dashes indicate lines of equal settling velocity. Because the liquid volume is being
reduced, for each sample the adjusted depth is recorded and the average settling velocity
z/t computed. Dashed isovelocity lines are then interpolated. An experiment performed
by McLaughlin using alum and bentonite clay in a 1.2-m-tall cylinder with three
withdrawal ports produced the concentration profile diagram shown in Fig. 5.12b. If this
settling rate of the sediment is neither hindered nor accelerated by flocculation, the
dashed isovelocity lines will be vertical. If flocculation causes the settling rate to
increase, the dashed isovelocity lines will slope toward the left, but if settling is hindered
SEDIMENT PROPERTIES 5.21
they will slope to the right. In Fig. 5.12b flocculation is the predominant effect.
To compute settling velocity at any depth, such as z
t
in Fig. 5.12a, the areas defined
by the polygons 025, 024, and 023 are calculated and the values plotted against times t
1
,
t
2
and t
3
, respectively. If this is performed for a sufficient number of concentration pro-
files at a given depth, a smooth curve will result, the slope of which at any point in time
is the right side of Eq. (5.27). Since the concentration is known from the diagram, the fall
velocity can be computed as a function of time. Such a plot is presented in Fig. 5.13,
corresponding to the concentration profile diagram in Fig. 5.12b. In this sample, settling
velocity increased with time, peaked simultaneously at all depths, then decreased.
FIGURE 5.1
3 Local mean settling velocity as a function of time for bentonite clay
and alum in water (McLaughlin, 1959).
5.6 LABORATORY AND FIELD ANALYSIS OF SEDIMENT
CONCENTRATION
Streambeds in hilly or mountainous areas often contain beds consisting of gravel,
cobbles, and boulders. These are termed gravel-bed streams, even though the grains may
be larger than gravel size. It is usually neither practical nor necessary to transport large-
diameter sediments from gravel-bed streams to the laboratory, and sediment larger than
about 0.5 cm is normally sized in the field by direct measurement, as described in Sec.
8.8 and 8.9.
The total suspended sediment concentration in a sample, including both coarse and
fine sediment, may be determined by filtration, evaporation, or specific gravity. All
methods will measure both the organic and inorganic fractions unless they are previously
separated. In eutrophic systems, organisms and organic matter suspended in the water
column may contribute significantly to the suspended sediment if solids concentrations
are very low.
5.6.1 Filtration Method
In the filtration method, the water sample is passed through a preweighed filter, such as a
SEDIMENT PROPERTIES 5.22
glass fiber filter in a Gooch crucible. The filter containing the sediments is then oven-
dried, cooled in a desiccator, and weighed. Sediment weight is computed as the final less
the original (tare) weight. Filtration has the advantage of eliminating the need to
compensate for dissolved solids in the water, and it can also be more rapid that the evap-
oration method. However, filter media will quickly become clogged if more than several
hundred milligrams per liter of fines is present.
5.6.2 Evaporation Method
In the evaporation method, the sample is first allowed to settle to the bottom of the
sample bottle. Settling time depends on the nature of the sediment; for clays, settling may
require weeks and small amounts of flocculant may have to be added. Samples should
settle in the dark to prevent biological growth. After settling, the supernatant is discarded
and the residual aliquot of native water (usually about 20 to 50 mL) is poured into an
evaporating dish, and distilled water is used to rinse the remaining sediment. After the
water is evaporated without boiling, the dry sample is heated to 110°C for at least 1 h,
then cooled in a desiccator and weighed. A correction for dissolved solids should be
made in waters high in dissolved solids or low in suspended solids. The weight of
dissolved solids is determined by evaporating a sample aliquot of settled or filtered water.
If dissolved solids constitute a significant percentage of the total solids in the sample, a
correction should be made. In environments having relatively stable dissolved solids
levels, using a constant-volume aliquot of native water in all samples that are evaporated
produces a constant correction factor.
5.6.3 Specific Gravity Bottle
With the specific gravity of water known as a function of temperature, the sediment con-
tent in a sample can be measured as the difference between the weight of clear native
water (not distilled water), and of the sample when weighed in a specific gravity bottle.
This method has the advantage of providing almost instantaneous values of sediment
concentration because it does not require sample desiccation. It is therefore well-suited
for field monitoring during operations such as reservoir flushing. It can be used with any
size of sediment. The tare weight of each bottle should be recorded when it is filled with
clear native water, all bubbles must be carefully eliminated from within the stoppered
bottle, and the bottle exterior must be carefully dried before weighing. For field use, the
balance must be placed in an area completely unaffected by vibration, such as may occur
in machinery buildings. Because this method measures the small differences in weighs
between 100 mL of clear water and the same volume of turbid water, contained in a
bottle weighing about 40 g, it is best used for sediment concentrations exceeding 250
mg/L
5.6.4 Sediment Volume
In streams where most or all sediments are sands, the sediment can be settled in an
Imhoff cone, and the sediment content expressed as milliliters per liter. This method is
useful in monitoring sediment release events because results can be obtained after short
settling time, on the order of 1 min. However, this method requires that a calibration
curve be constructed for each site where this method is used, to develop a relationship
between settled sediment volume and sediment mass. During every event when this
method is used, several samples should be collected and analyzed in a laboratory to
confirm the original calibration. Because the grain size distribution can change
significantly over the course of an event, it is also important that samples be taken at
different periods as the calibration curve may shift during an event. In addition to speed,
this method has the advantage of simplicity in equipment and procedure.
SEDIMENT PROPERTIES 5.23
5.7 LABORATORY ANALYSIS OF SEDIMENT SIZE
Particle size analysis is required to determine the settling and transport characteristics of
both suspended and deposited sediments. The laboratory sequence for size analysis of
sediment samples is summarized in Fig. 5.14, and the applicability of various techniques
for size classification are summarized in Table 5.3. The type of analysis to be performed
depends on the amount of sediment available and the grain size limits.
F
IGURE 5.14 Generalized flow diagram for concentration and grain size analysis of
suspended sediment samples. These procedures may be modified as appropriate for
sample characteristics and study requirements (Guy, 1969
).
SEDIMENT PROPERTIES 5.24
TABLE 5.3 Application Range for Sediment Test Methods for Grain Size Analysis
Method
Size range,
mm
Sample size,
mm
Concentration
range, g/L
Direct measurement >5 Single grains --
Immersion >5 Single grains --
Sieves 0.062 - 32 >0.05 --
Pipet 0.002 – 0.062 2-5 2.0 – 5.0
VA Tube*: 0.062 – 2.0 --
L = 120, D = 2.1 0.062 – 0.25 0.05 – 0.8 --
L = 120, D = 3.4 0.062 – 0.40 0.4 – 2.0 --
L = 120, D = 5.0 0.062 – 0.60 0.8 – 4.0 --
L = 120, D = 7.0 0.062 – 1.0 1.6 – 6.0 --
L = 180, D = 10.0 0.062 – 2.0 5 – 15 --
BW tube
† 0.002 – 0.062 0.5 – 1.8 1.0 – 3.5
Hydrometer 0.002 – 0.062 >30
* L = tube length, D = tube diameter, cm. Size ranges are given as sieve diameters.
† May be extended to the range of 0.03-0.35 mm by increasing the concentration in the
tube up to 10 g/L, with higher concentrations tending to give more accurate results. For sizes over
0.25 mm, results of the first withdrawal for the fastest-settling particles become erratic, and are
undependable for diameters over 0.35 mm.
‡ Depends on hydrometer.
Source: Adapted from Guy (1969).
Suspended sediment samples may contain less than a gram of sediment whereas deposit
samples may contain hundreds of grams of material for sizing. Samples having both
coarse and fine sediments must be split and analyzed using two methods, such as sieve-
pipet, VA tube-pipet, or BW tube-VA tube. (VA stands for visual accumulation; BW
stands for bottom withdrawal.) Guy (1969) provides a detailed description of sediment
laboratory techniques.
5.7.1 Use of Deflocculants
Fine silts and clays may occur in nature either in dispersed or flocculated forms, and the
tendency for riverine sediments to flocculate may vary as a function of season or stage.
Sedimentation studies typically require information on the settling velocity in natural
waters, and the use of a deflocculant and distilled water can give very misleading results
by producing a grain size classification much finer, and sedimentation velocities much
slower, than occur in native water. In sedimentation and transport studies it is generally
inappropriate to use a deflocculant to characterize suspended sediments, since the
analysis seeks to determine the settling characteristics of the sediment in the reservoir
with natural water and not the exact size of individual grains. When clays naturally occur
in a flocculated state and have settling velocities more typical of fine silts, it is necessary
to use this higher settling velocity in sedimentation modeling. On the other hand,
substances such as pesticides and nutrients such as phosphorus are adsorbed largely on to
clay particles because of their high surface area. Knowledge of the clay fraction in
suspended or deposited material, independent of its settling velocity, can be important for
tracking environmentally reactive substances. Thus, in some types of studies,
information on both the sedimentation size of the flocculated particles and the size of
their component grains can be important. In every case, it is essential to state whether or
not a deflocculant was used in the sizing of fines, and split samples should be run with