Environmental Engineering Reference
In-Depth Information
This equation gives the total equivalent roughness due to the grain size of
the bed material and the bed form created due to movement of the particles.
There are two possible stages for which the equivalent roughness needs to
be investigated; one is without any movement of the particles (plane bed)
and the other with movement of the particles (bed forms).
Van Rijn (1982) proposes the roughness due to the grains as:
k s =
3 d 90 and assuming a regular sediment size distribution k s =
4 . 5 d 50
for d 90 =
1 . 5 d 50 .
When the velocity increases the bed material starts moving and the
bed feature changes. According to van Rijn (1982) the term k s is related
to the bed form height, bed form steepness and bed form shape. The
following relationship is given for k s :
k s
=
f ( , , γ )
(5.17)
for ripples:
20 γ r r r
λ r
k s
=
(5.18)
for dunes:
k s
e 25 d d )
=
1 . 1 γ d d (1
(5.19)
where:
r =
ripple height
=
50 to 200 * d 50 (m)
γ r =
ripple presence ( γ r =
1 for ripples only)
λ r =
ripple length
=
500 to 1000 d 50 (m)
γ d =
form factor
=
0.7 for field conditions and 1.0 for laboratory
conditions
d =
dune height (m)
λ d =
dune length (m)
=
7.3 * h
5.2.4 Roughness of the side slopes
The roughness height due to the surface material is related to the median
particle diameter ( d 50 )as k s =
4 . 5 d 50 . This value is recommended for a
rigid boundary, but for a movable bed of loose material the roughness
will be higher, because a perfectly plane side slope will not exist in nat-
ural conditions and small irregularities will always be present. Van Rijn
(1993) suggests a minimum value of k s =
0.01 m. Moreover the Manning's
roughness coefficient for an ideally finished earthen canal is 0.016 to 0.020
(Chow, 1983). This coefficient ( n ) is an average value that is assumed to
 
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