4.13.5 Problem 4 Calculation of Total Bed-Material Discharge
Using Colby's Method
In applying the Colby (1964) method, the required data are: the mean velocity, the depth,
the median size or size distribution of the bed material, the water temperature and the fine
sediment (wash load) concentration. The mean velocity and the depth of flow may be
obtained by hydraulic calculations, as in Problem 3. However, to obtain best results from
calculations, directly measured values of velocity and depth are required.
For purposes of comparison, the sample problem used to illustrate Einstein's method is
solved using the Colby method. The required data are taken from Table 4.8 established by
hydraulic calculations. In addition, the water temperature and the fine sediment concentration
are assumed to equal 70F and 10,000 ppm, respectively. For convenience, the calculations
are summarized in tables. Two procedures are presented. Table 4.10 gives the calculations
using the mean diameter of bed material, whereas Table 4.11 gives the calculations for
individual fractions using the bed material size distribution. Note that depths, y, of 5.07 ft and
6.03 ft from Table 4.8 are not shown in Tables 4.10 and 4.11 since the corresponding
velocities are greater than 10 ft/sec. The Colby curves (Figure 4.13) are limited to 10 ft/sec.
Table 4.10. Bed Material Load Calculations for Sample Problem by Applying the Colby
Method (Median Diameter).
y
W
V
qn
k1
k2
k3
qT
QT
1
2
3
4
5
6
7
8
9
1.36
103
2.93
14.5
0.92
1.20
0.99
16
1,648
1.76
136
4.44
50.0
0.91
1.21
0.99
56
7,616
2.50
170
6.63
135.0
0.91
1.22
0.99
150
25,500
3.30
194
8.38
220.0
0.90
1.23
0.99
243
47,142
4.14
234
9.92
325.0
0.90
1.25
0.99
365
85,410
Notes:
(1)
y, ft (mean depth), taken from Table 4.8
(2)
W, ft (surface width), taken from Table 4.8
(3)
V, fps (average velocity), taken from Table 4.8
qn tons/day-ft (uncorrected sediment discharge per unit width of channel), taken from Figure 4.13
(4)
for the given V, y, and D50
(5)
k1 = f (y, T) (correction factor for temperature), given in Figure 4.14
k2 = f (y, Cf) (correction factor for fine sediment concentration), given in Figure 4.14
(6)
(7)
k3 = f (D50) (correction factor for sediment size), given in Figure 4.14
qT = [1+(k1k2 -1) k3]qn tons/day-ft (true bed material discharge per unit width of stream), given by
(8)
Equation 4.46
QT = WqT tons/day (bed material discharge for all size fractions for entire cross section)
(9)
4.50
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