Environmental Engineering Reference
In-Depth Information
material size (Chitale, 1994). These equations, with minor changes to
coefficients and some redefinition of the silt factor, are still widely used.
Some of the equations given by Lacey are (Ackers, 1992):
√
2520
d
f
=
(4.1)
4
.
836
Q
0
.
5
=
P
(4.2)
0
.
6459(
fR
)
0
.
5
v
=
(4.3)
0
.
000315
f
5
/
3
Q
1
/
6
S
o
=
(4.4)
where:
f
=
Lacey's silt factor for a sediment size
d
d
=
sediment size (m)
P
=
wetted perimeter (m)
discharge (m
3
/s)
Q
=
R
=
hydraulic radius (m)
v
=
mean velocity (m/s)
bottom slope
According to Lacey (1958), these equations are applicable within the
following range of flow and sediment characteristics:
•
S
o
=
Discharge in the range of 0.15-150 m
3
/s
•
Bed material is non-cohesive
•
Bed form characterised by ripples
•
Bed material size in the range of 0.15-0.40 mm
•
Bed load is relatively small
The following steps are recommended when using the Lacey equations
for the design of earthen canals for a given diameter
d
and discharge
Q
:
•
Determine the factor
f
for the given diameter
d
;
•
Find the bottom slope
S
o
and the perimeter
P
;
•
By trial and error determine the velocity
v
and area
A
=
Q/v
and the
hydraulic radius
R
;
•
Determine the cross section both by using the perimeter
P
and the
hydraulic radius R and by assuming that the cross section is trapezoidal
with a side slope
m
2(1V:2H).
Table 4.1 gives an example of the main dimensions of an earthen
canal designed according to the Lacey method for a canal that conveys a
discharge in the range from 1-8 m
3
/s and that transports sediment with
a diameter
d
=
0.001 and 0.0005 m, respectively. The
f
values for these
diameters are 1.58745 and 1.1225, respectively. The side slope
m
is 2.
As an extra illustration, the table also gives the bottom width
B
and
the water depth
y
as well as the Manning's roughness coefficient that has
been calculated from the equation
=
1
n
R
2
/
3
S
1
/
2
=
v
o
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