Table 4.9. Bed-Material Load Calculations for Sample Problem by Applying the Einstein
(1950) Procedure.
D
iB
iBqB
iBQB
ξ
Ψ*
R′b
Ψ′
ϕ*
D/X
1
2
3
4
5
6
7
8
9
10
119.0
0.0267
1.90
2.90
1.08
1.23
5.08
0.00162
0.178
0.5
330.0
0.0561
4.00
1.73
1.00
1.74
2.54
1.0
845.0
0.1150
8.20
0.90
1.00
2.35
1.27
2.0
1,510.0
0.1800
12.80
0.60
1.00
2.16
0.85
3.0
2,560.0
0.2530
18.00
0.43
1.00
2.05
0.63
4.0
3,950.0
0.3160
22.50
0.35
1.00
2.03
0.51
5.0
6,350.0
0.3800
27.00
0.29
1.00
1.98
0.42
6.0
0.00115
0.402
0.5
3.38
0.82
1.36
2.44
2.45
0.0471
210.0
1.0
1.69
1.16
1.10
1.27
5.50
0.1060
623.0
2.0
0.85
1.57
1.01
0.61
12.60
0.2420
1,780.0
3.0
0.56
1.44
1.04
0.41
19.00
0.3640
3,050.0
4.0
0.42
1.37
1.05
0.30
26.00
0.5000
5,050.0
5.0
0.34
1.35
1.05
0.25
31.50
0.6040
7,540.0
6.0
0.28
1.32
1.05
0.20
39.00
0.7490
12,900.0
0.00081
0.320
0.5
2.54
0.61
2.25
3.03
1.75
0.0155
69.0
1.0
1.27
0.87
1.26
1.09
6.80
0.0600
353.0
2.0
0.63
1.17
1.10
0.49
15.80
0.1390
1,020.0
3.0
0.42
1.08
1.12
0.33
23.50
0.2070
1,730.0
4.0
0.32
1.04
1.15
0.25
31.50
0.2790
2,820.0
5.0
0.25
1.01
1.17
0.20
39.50
0.3490
4,360.0
6.0
0.21
0.99
1.19
0.17
46.00
0.4060
6,980.0
0.00057
0.058
0.5
1.80
0.43
5.40
5.15
0.58
0.00056
2.5
1.0
0.90
0.61
2.28
1.39
5.10
0.00500
29.4
2.0
0.45
0.83
1.37
0.44
17.50
0.01710
126.0
3.0
0.30
0.76
1.52
0.32
25.00
0.02460
206.0
4.0
0.22
0.72
1.60
0.25
31.50
0.31000
313.0
5.0
0.18
0.71
1.65
0.20
39.50
0.03870
483.0
6.0
0.15
0.70
1.70
0.18
43.50
0.04260
732.0
103E
Z
I1
-I2
PEI1+I2+1
iTqT
iTQT
iTQT
iBQB
11
12
13
14
15
16
17
18
19
400
2.38
3.78
0.078
0.44
1.42
0.03800
168
670
1335
1.84
2.65
0.131
0.74
1.71
0.09580
561
3,928
3,771
1.30
1.88
0.240
1.27
2.44
0.28100
2,050
30,500
6,496
0.98
1.53
0.385
2.01
3.44
0..61700
5,170
113,000
10,745
0.78
1.33
0.560
2.80
4.75
1.20000
12,100
324,000
16,333
0.63
1.18
0.810
3.85
6.78
2.13000
26,500
800,000
27,142
0.54
1.08
1.090
4.90
9.20
3.48000
59,800
1,940,000
335
0.07540
1.60
0.68
0.117
2.88
1.69
1,330
0.22700
2.14
1.19
0.210
2.02
1.31
6,660
0.91000
3.76
2.33
0.450
1.44
0.92
2.44000
20,400
6.73
3.85
0.830
1.17
0.70
5.65000
57,100
11.30
5.70
1.370
1.01
0.56
10.40000
129,000
17.20
8.10
2.120
0.90
0.45
19.60000
335,000
26.00
10.50
2.950
0.83
0.38
1.19
1.94
0.230
1.29
2.23
0.03450
153
0.92
1.36
0.520
2.60
4.16
0.25000
1,460
0.65
0.97
1.530
6.10
12.20
1.70000
12,500
0.49
0.79
3.350
11.00
28.70
5.95000
49,700
0.39
0.68
6.200
17.50
56.00
15.00000
157,000
0.32
0.61
9.800
25.50
92.00
32.00000
397,000
0.27
0.55
15.000
36.00
146.00
59.50000
1,020,000
0.85
1.12
0.720
3.35
5.55
0.00312
14
0.65
0.86
2.440
8.10
20.00
0.10000
587
0.46
0.61
8.400
21.50
74.40
1.26000
9,350
0.35
0.49
19.300
41.00
183.00
4.50000
37,600
0.28
0.43
32.000
63.00
312.00
9.68000
97,800
0.23
0.38
51.000
91.00
516.00
20.00000
248,000
0.19
0.35
70.000
122.00
722.00
30.80000
526,000
4.48