good as that for stations whose records were used." An example showing bed sediment
discharge calculations by the Colby method is presented in Section 4.13.
4.5.5 Relative Influence of Variables
The study of the relative influence of viscosity, slope, bed sediment size and depth on bed
sediment and water discharge is examined in this section using Einstein's bed-load function
(1950) and Colby's (1964) relationships. Einstein's bed-load function is chosen because it is
the most detailed and comprehensive treatment from the point of fluid mechanics. Colby's
relations are chosen because of the large amount and range of data used in their
development.
The data required to compute the bed material discharge using Einstein's relations are: S =
channel slope; D65 = size of bed material for which 65 percent is finer; D35 = size of bed
material for which 35 percent is finer; Di = size of bed sediment in fraction i; ν = kinematic
perimeter of the bed; Pw = wetted perimeter of the banks; iB = percentage of bed sediment in
fraction i; γs = specific weight; and V = average velocity.
To study the relative influence of variables on bed material and water discharges, the data
taken by the U.S. Geological Survey from October 1, 1940 to October 1, 1970 on the Rio
Grande near Bernalillo, New Mexico are used. The width of the channel reach was 82.3 m
(270 ft). In the analysis, the energy slope was varied from 0.7S to 1.5 S , in which S is the
average bed slope assumed to be equal to the average energy slope. Further, the kinematic
viscosity was varied to correspond with variations in temperature from 39.2 to l00F
inclusive. The variation of D65, D50, Di, and iB was accomplished by using the average bed
material distribution given by Nordin (1964) and shifting the curve representing the average
bed sediment distribution along a line parallel to the abscissa drawn through D50. The
average water temperature was assumed to be equal to 70F and the average energy
gradient of the channel was assumed to be equal to 0.00095. The water and sediment
discharges were computed independently for each variation of the variables and for three
subreaches of the Rio Grande of differing width near Bernalillo. The applicability of the
results depends on the reliability of the modified Einstein bed-load function and Colby's
relationships used in the analysis rather than on the choice of data.
The computed water and sediment discharges are plotted in Figures 4.15, 4.16, and 4.17
and show the variation of sediment discharge due to changes in bed material size, slope and
temperature for any given water discharge. Figure 4.15 shows that when the bed sediment
becomes finer, the sediment discharge increases considerably. The second most important
variable affecting sediment discharge is the slope variation (Figure 4.16). Temperature is
third in importance (Figure 4.17). The effects of variables on sediment discharge were
studied over approximately the same range of variation for each variable.
Figure 4.18 shows the variation of the sediment discharge due to changes in the depth of
flow for any given discharge, computed using Colby's (1964) relations. The values of depth
of flow varied from 1.0 to 10.0 ft, the median diameter of the bed sediment is maintained
constant equal to 0.030 mm, the water temperature is assumed constant and the
concentration of fine sediment is assumed less than 10,000 ppm. The channel width is also
maintained constant at 82.3 m (270 ft). In Figure 4.18, the curves for constant depth of flow
show a steep slope. This indicates that the capacity of the stream to transport sands
increases very fast for a small increase of discharge at constant depth. Similar figures can
be developed for other sizes of bed material, and the relations can be modified to include the
effect of washload and viscosity effects.
4.24
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