Equation 4.48 was developed for channels with steep slopes for sand and fine gravel beds

experiencing critical and super-critical flows [Simons, et al. (1981), Julien (1995)]. The range

of parameters utilized to develop this equation is shown in Table 4.2.

Table 4.2. Range of Parameters Equation 4.48 Developed by Simons et al.

Parameter

Value Range

SI Units

Froude Number

14

--

Velocity

1.98 7.92

m/s

Bed Slope

0.005 0.040

m/m

m2/s

Unit Discharge, q

3.05 60.96

Particle Size, D50

> 0.062

mm

As the depth increases for a given velocity, the intensity of the turbulent transfer properties

decreases for these sizes. The increase in area available for suspended sediment with the

increased depth does not totally counterbalance the reduced turbulent transfer

characteristics. The result is an inverse dependence of transport rate on depth for these

larger sizes. The sizes with no dependence (Cs2 = 0) on depth in their transport rate fall

between these two extremes.

When applying the equations resulting from Table 4.1, care should be taken to assure that

the range of parameters being used is not out of range with those used to develop the

equations (Table 4.2). If conditions are within the ranges outlined in Table 4.2 the regression

equations should provide results within ten percent of the values computed using the Meyer-

Peter and Mller bedload and Einstein suspended load equations for the steep conditions in

Table 4.2.

There are several other checks that should be made in order to ensure the equations are

applicable to a given problem. The equations are based on the assumption that all the

sediment sizes present can be moved by the flow. If this is not true, armoring will take place.

developed for sand-bed channels, they do not apply to conditions when the bed material is

cohesive. Equation 4.48 would overpredict transport rates in a cohesive channel.

An example of the application of the basic power function relationship is given in Section

4.12 (SI) and Section 4.13 (English).

Kodoatie et al. (1999) modified a Posada (1995) equation using nonlinear optimization and

the field data for different sizes of riverbed sediment. A description of the development and

validation of this equation is presented in Appendix B. The resulting equation is:

qt = aV b y c S d

(4.50)

where:

qt

=

Sediment transport rate, metric tons/m/day (tons/ft/day)

V

=

Mean flow velocity, m/s (ft/s)

y

=

Mean flow depth, m (ft)

S

=

Energy slope

a, b, c, and d

=

Regression coefficients

4.29

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