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Chapter 3 - Theoretical considerations
d) Characteristic diameters
The following characteristic diameters are commonly used to describe a grain size distribution:
d 10
, d 16
, d 30
, d 50
, d 65
, d 84
or d 90
.
• d 65 and d 90 are used to characterize the determinant roughness element of the bed and as
approximation of the mean diameter of the armoring layer;
• d 50
is used as approximation of the determinant grain size of the sediment transport;
• d 16
and d 84
are used to characterize the scatter of the grain size distribution. The width of
the distribution is given with:
σ = d 84 ⁄ d 16
(3.4)
The mean diameter
p i
d m
d m
is frequently used to describe the sediment transport rate:
1
Σ∆p (
∫d i
dp
i
⋅ d i
) Σ∆p (
-------------------------
i
⋅ d i
)
= = = ------------------------- = Σ∆p (
Σ∆p i
1
i
⋅ d i
)
0
is the part (weight) of the sediment sample corresponding to the grain size .
d i
(3.5)
e) Density of the sediment
The sediment density usually ranges between ρ s
= 2630 and 2680 kg/ m 3 . Measurements for the
present study gave the following sediment density:
ρ s
= 2635 kg/ m 3 . (3.6)
f) Porosity
The porosity p
is defined as:
p
V p
= ------ =
V
V
------------------ p
V p
+ V s
(3.7)
where V p is the volume of the porosity and V s the volume of the sediments (LANG, HUDER &
AMANN, 1986, DYSLI, 1993). Three tests with the used bed material were performed. The resulting
average porosity will be used in the present study:
n = 33.6 % (3.8)
with a standard deviation of 2.9 %. The error due to the measurement technique (size of the basket,
precision of the balance) was estimated to be about 1 %.
g) Friction angles
Different friction angles can be distinguished:
• the static friction angle of repose of a soil,
• the dynamic friction angle, which is some degrees smaller than the static friction angle
• the bedload friction angle, used in some scour formulae is of the same order as the static
friction angle (BAGNOLD, 1966) (see also Paragraph 3.5.2/4)).
page 24 / November 9, 2002
Wall roughness effects on flow and scouring