Environmental Engineering Reference
In-Depth Information
where:
k
s,y
=
modified
k
s
for a canal depth
y
;
reference
k
s
for a canal depth of 1.0 m, based on a well
maintained, large canal section.
The
k
s
, the smoothness factor, should be carefully estimated and is
based on:
•
k
s,1 m
=
Canal geometry, expressed by the side slope
m
and a
b
/
y
ratio;
•
Roughness (irregularities) of the bottom and side walls; including flow
obstruction due to weeds (height and density of vegetation, including
flattening of it at high flows);
•
Sediment transport, namely the suspended and bed load.
For any canal the roughness changes during the year and will be a min-
imum shortly after maintenance and a maximum when no maintenance is
done. Recommended
k
s
values for a 1 m deep earthen canal are 12, 24, 36
and 42.5 for none, poor, fair and good maintenance conditions, respec-
tively. The Table C.1 gives these
k
s
values as function of the maintenance
conditions.
Table C.1.
Smoothness factors as function of maintenance conditions (for earthen canals).
Maintenance
None
Poor
Fair
Good
k
s,1
.
0m
12
24
36
42.5
The recommended
k
s
values fora1mdeep canal and the modified
k
s
value as function of the water depth (see equation C.4 and C.5) result in
the graph as presented in Figure C.1.
For one value of
k
s
, one bottom slope S and one side slope m still an
infinite range of bed width/depth ratios (
b
/
y
) can be selected. Minimizing
the wetted perimeter
P
gives the 'best' hydraulic cross sections and the
b
/
y
ratio is:
(
(1
b
y
=
2
∗
+
m
2
)
−
m
)
(C.6)
where:
y
=
water depth (m)
b
=
bottom width (m)
m
=
cotangent of side slope (1)
The 'best' hydraulic section with the smallest perimeter
P
results in
a maximum flow at minimum cost. However, the best hydraulic section
is rarely applied, because it will not be stable due to the relatively deep
excavations and a change in discharge heavily affects the water depth and
the velocity. A deep section is nevertheless applied wherever possible,
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