Finally, the gradation coefficient G is calculated using Equation 3.9.
D50 D84 1 0.33mm 0.44mm
1
G=
+
=
+
2 0.24mm 0.33mm
2
D16 D50
G = 1.35
Gravel Bed Channel
A gravel bed stream channel was sampled and the grain size analysis yielded the following
results (Table 3.8):
Table 3.8. Gravel Bed Material Size Distribution.
Size Range
Percent of Total Weight
(mm)
in Size Range
.125 - .250
0.1
.250 - .500
1.6
.500 - 1.00
1.7
1.00 - 2.00
6.3
2.00 - 4.00
31.8
4.00 - 8.00
58.5
From this size distribution calculate the following statistics: the geometric mean of each size
range; the effective diameter Dm; the fall velocity of each size range; the Dm, D16, D50, D84, D90
sizes; and the gradation coefficient.
The geometric mean size is calculated as the square root of the product of the end points of a
given size range. For the largest size range:
Di = [(4) (8)]1/2 = 5.66 mm.
Likewise the rest of the size ranges are calculated, with the results shown in Table 3.9.
The effective diameter of the sample distribution is calculated with Equation 3.12:
(0.1) (0.177mm) + ....(58.5) (5.66mm)
n
i=1 pi Dsi
Dm =
=
100
100
431.9
Dm = 100 = 4.32 mm
The fall velocity is calculated with the use of Figure 3.1 at 60o F, for each geometric mean size.
For the largest geometric mean size: Di = 5.66 mm, ω = 0.518 m/s. Likewise the rest of the
size ranges, the results are shown in Table 3.9.
The gravel bed material size distribution was plotted on log-probability paper (Figure 3.24) from
which the following values were obtained:
3.54
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