where:
=
Sediment concentration in parts per million by weight
Ct
=
Fall velocity of the sediment, m/s (ft/s)
ω
Kinematic viscosity, m2/s (ft2/s)
=
ν
=
V*
Shear velocity ( gRS ) , m/s (ft/s)
V
=
Velocity, m/s (ft/s)
=
Critical Velocity, m/s (ft/s)
Vcr
S
=
Energy slope
In the above equations, the dimensionless critical velocity is given by:
Vcr
2.5
VD
(4.53)
=
+ 0.66 for 1.2 < * 50 < 70
VD
ω
ν
log * 50 - 0.06
ν
and
Vcr
V* D50
(4.54)
= 2.05 for
≥ 70
ω
ν
An example of calculating total bed-material discharge using Equation 4.51 is given in
Section 4.12 (SI) and Section 4.13 (English).
4.8 CONVERSION FACTORS
There are numerous ways of expressing sediment transport. These include rate of transport
and concentration. The rate of sediment transport can be expressed as a volumetric rate
(m3/s, ft3/s), or mass or weight rates (metric-tons/day, tons/day). The concentration relates
volume or weight of sediment to the total volume or weight of the sediment-water mixture and
is converted to a rate of sediment transport by including the water discharge.
The following equations can be used to convert from a volumetric rate to a mass transport.
Qs (metric-tons/day) = Qs (m3/s) x γs / g x 86400 / 1000
(4.55)
Qs (tons/day) = Qs (ft3/s) x γs x 86400 / 2000 = Qs (ft3/s) x γs x 43.2
(4.56)
A common unit for sediment concentration is milligrams per liter (Cmg/l), which is the ratio of
the mass of sediment to the total volume of water and sediment. Concentrations are often
expressed as parts per million by multiplying the concentration by 106. Four ways of
expressing concentration are:
Concentration by volume: Cv = sediment volume/total volume
(4.57)
Concentration by weight: Cw = sediment weight/total weight = CvSg / [1+(Sg-1)Cv]
(4.58)
Concentration as parts per millions by weight: Cppm = 106Cw
(4.59)
Concentration as mg/l: Cmg/l = 106CvSg
(4.60)
4.31
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