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.

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

Integrated Publishing, Inc. |