The results of the bed-material discharge calculations for the sample problem using
Einstein's (1950) and Colby's (1964) methods are shown in Figure 4.21. The curves indicate
that the sediment discharge increases rapidly with an increase in water discharge. In
general, the two methods compare relatively well.
Figure 4.21. Comparison of the Einstein and Colby methods.
4.13.6 Problem 5 Calculation of Total Bed-Material Discharge Using the
Basic Power Function Relationship
Determine the bed-material discharge for the 100-year discharge for a stream with the
following data. Note that these data are not in the Fr range of Table 4.2. Compare the result
with the expanded power function application in Problem 6.
Width W = 200 ft, Depth y = 6.0 ft, Velocity V = 8.0 ft/s, Q = 9600 cfs. Sediment properties of
D50 = 0.31 mm and size distribution factor G =1.32.
Simons et al. (1981) Equation 4.48 is qs = c s1 y Cs2 V Cs3
Use Table 4.1 and cross-interpolate to obtain the values of Cs2 and Cs3. Cross-interpolate in
Table 4.1:
Cs1 = 1.63 x 10-5
Cs2 = 0.45
Cs3 = 3.64
qs = 1.63 x 10-5 (6.0)0.45 (8.00)3.64 = 0.0707 ft2/sec
Qs = 200 x 0.0707 = 14.14 ft3/sec
Using a specific gravity of 2.65
Qs = (2.65 x 62.4 x 3600 x 24 x 14.14) /2000 = 101,000 tons/day
Qs = 101,000 tons/day x 2000/2204.62 = 91,600 metric-tons/day
4.52
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