(Note that Cmg/l equals the ratio of the mass of sediment in milligrams to the volume of the
water-sediment mixture in liters.)
In these equations, Sg is the specific gravity of the sediment (γs/γ). For sediment
concentrations (Cppm) less than 100,000 there is less than a 7 percent difference between
Cppm and Cmg/l. The difference is less than 1 percent for concentrations less than 10,000
ppm or mg/l. For low concentrations, they are often considered equivalent. This is because
the weight of the sediment is small compared to the weight of the water. At these low
concentrations, an approximate rate of sediment transport can be estimated by
Qs = Cppm x 10-6 x Qwater / Sg
where Qs and Qwater are in m3/s or ft3/s.
The exact conversion is:
Q s = Cppm x 10 -6 x Q water /(S g (1 - Cppm x 10 -6 ))
(4.62)
When sediment is eroded or deposited, the volumetric transport rate must include the void
space between the sediment particles. The void space, or porosity, is the ratio of voids to
the total volume and often ranges from 35 to 45 percent. The volume of eroded or deposited
material for a time interval, ∆t, is
V = Qs x ∆t / (1 - η)
(4.63)
where Qs is the rate excess (or deficit) sediment transport and η is the porosity of the bed
material.
4.9 APPLICATION OF SELECTED SEDIMENT TRANSPORT EQUATIONS
No single sediment transport equation can encompass all alluvial channel conditions.
Therefore, an equation should be selected based on the particular river bed material and flow
characteristics. When possible, the results of the sediment transport calculations should be
compared with measured sediment transport. The equations presented in this section have
broad application; however, other equations can, and should also be considered.
There are several sources for obtaining recommendations on the applicability of sediment
transport equations. Appendix B includes a review of ten sediment transport equations. The
review tested the equations with a large compilation of field data that encompasses a wide
range of bed material, from silts to gravel, and a wide range of river sizes, from 1 m width to
over 1000 meters in width. The BRI-STARS manual (Molinas 2000) presents a comparison
of several sediment transport equations with a variety of measured data. The HEC-6 manual
(U.S. Army Corps of Engineers) refers to Vanoni (1975) as a guide to the applicability of
sediment transport equations. Another source for recommendations on suitability of various
transport functions is the SAM Hydraulic Design Package for Channels (Thomas et al. 2000).
If more than one equation appears suitable, one should apply the equations and determine
which one provides the most reasonable results. This is most easily done using sediment
transport programs such as BRI-STARS, HEC-6 and SAM. Table 4.4 includes a list of
sediment transport relationships and the application of each equation.
4.32
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