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the overall roughness value. Different methods are available to determine
the equivalent (or composite) roughness (
k
se
) of a section. Yen (2002)
discussed in detail the different aspects of computing equivalent roughness
of an open canal.
Method 1.
Vanoni (1975), Chow (1983), and Raudkivi (1990) have
stated that the equivalent roughness of a cross section can be found by
considering the total cross section as an area composed by a number of
subsections. The mean velocity and energy gradient of each subsection is
the same as the velocity and energy gradient of the entire cross section. The
equivalent roughness for the whole cross section is then determined by:
N
A
=
A
i
(5.24)
i
=
1
vP
2
/
3
i
3
/
2
vP
2
/
3
n
e
S
1
/
2
3
/
2
N
n
i
=
(5.25)
S
1
/
2
i
=
1
This was proposed independently by Horton and by Einstein (Chow,
1983).
N
2
/
3
P
i
n
3
/
2
i
P
n
e
=
i
=
1
Method 2.
This method was proposed by Pavlovskiı, by Muhlhofer, and by
Einstein and Banks (Chow, 1983). Chow (1983), Krishnamurthy and
Christensen (1972), and Motayed and Krishnamurthy (1980) assumed
that the total hydraulic resistance in a cross section is equal to the summa-
tion of the flow-resisting forces in each subsection and that the hydraulic
radius of each subsection is equal to the radius of the whole cross section.
The total force resisting the flow is equal to the sum of the forces resisting
the flow in each subsection.
N
v
2
n
2
R
4
/
3
τP
=
τ
i
P
i
with
τ
=
ρgRS
and
S
=
(5.26)
i
=
1
N
1
/
2
P
i
n
i
P
n
e
=
i
=
1
Method 3.
Ida (1960) derived a relation by equating the discharge through
all the subsections with the whole section. Asano et al. (1985) modified
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