Environmental Engineering Reference
In-Depth Information
F
as function of the discharge
Q
, the bottom slope
S
and the roughness
coefficient
n
. From these data follows the cross-sectional area
A
, the
hydraulic radius
R
and the velocity
v
; the latter should be within a certain
range in view of erosion and sedimentation. From the known discharge
Q
, the appropriate side slope
m
and a criterion for the optimal
b
/
y
ratio,
the other canal dimensions can be derived.
The discharge
Q
that a cross-section with a certain area
A
can convey
increases for a larger hydraulic radius or for a smaller wetted perimeter. A
section with a certain area
A
and the smallest wetted perimeter will convey
the largest discharge and is called the best hydraulic section. However, this
does not mean that these cross-sections are always optimal. In case the
water level is below the ground surface a narrow canal will give minimum
excavation, for canals with the water surface above the ground level a
wide canal will result in less excavation.
The flow in a canal is time and space related. The flow is steady if the
water depth, discharge and cross section do not change with respect to
time. When these parameters do not change with respect to space, then
the flow is uniform. The most often used equations for uniform flow are
the de Chézy, Strickler and Manning formulae.
These formulae are:
R
0
.
5
S
0
.
5
Q
=
A
∗
C
∗
∗
de Chézy
(C.1)
R
2
/
3
S
0
.
5
Q
=
A
∗
k
s
∗
∗
Strickler
(C.2)
1
n
∗
R
2
/
3
S
0
.
5
Q
=
A
∗
∗
Manning
(C.3)
where:
Q
flow rate (m
3
/s)
=
wetted area (m
2
)
A
=
S
=
bottom slope (1)
R
=
hydraulic radius (m)
C
=
de Chézy flow resistance coefficient
k
s
=
Strickler smoothness factor
Manning roughness factor
The exponent '2/3' in the Strickler and in the Manning formula is not
a constant, but it varies with the channel shape and roughness. Therefore
some approximations use a modified
k
s
as function of the water depth
y
.
Based on field investigations and studies the modified
k
s
value can be
expressed as:
n
=
y
1/3
k
s,y
=
k
s,1 m
∗
for
y <
1
.
0 m
(C.4)
y
1/6
k
s,y
=
k
s,1 m
∗
for
y >
1
.
0 m
(C.5)
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