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

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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