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.

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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