3.7 SOLVED PROBLEMS FOR ALLUVIAL CHANNEL FLOW (SI)
3.7.1 PROBLEM 1 Sediment Properties and Fall Velocities
Sand Bed Channel
The bed material size distribution of a sand bed channel is shown in Table 3.6.
Table 3.6. Sand Bed Material Size Distribution.
Size Range
Percent of Total Weight
(mm)
in Size Range
.002 - .0625
0.8
.0625 - .125
4.4
.125 - .250
14.2
.250 - .500
74.9
.500 - 1.00
5.0
1.00 - 2.00
0.5
2.00 - 4.00
0.2
From the grain size analysis calculate the following statistics: the geometric mean of each
fall velocity of each size range.
The geometric mean is calculated as the square root of the product of the end points of a given
size range.
For the first size range:
Di = [(0.002) (.0625)]1/2 = 0.011 mm.
Likewise for the remainder of the size ranges, the results are summarized in Table 3.7.
The effective diameter (Dm) of the sample distribution is calculated with the use of Equation
3.12 in Section 3.2.4.
n
i=1 pi Dsi
Dm =
100
(0.8) (0.011mm) + (4.44) (0.088mm) + ....(0.3) (2.83mm)
n
i=1 pi Dsi
Dm =
=
100
100
34.2
Dm = 100 = 0.34 mm ; which lies in the sand size.
3.52
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