Environmental Engineering Reference
In-Depth Information
Table 4.1.
Example of the design of an earthen canal according to the Lacey method.
Lacey regime theory in SI-units
Qd
in m
mf
o
P
v
A
R
B
-bottom
y
n
-Manning
1
0.001
2
1.58745
0.000680
4.836
0.515
1.940
0.401
2.316
0.563
0.028
2
0.001
2
1.58745
0.000606
6.839
0.579
3.457
0.505
3.863
0.666
0.027
3
0.001
2
1.58745
0.000567
8.376
0.619
4.846
0.579
5.065
0.740
0.027
4
0.001
2
1.58745
0.000540
9.672
0.649
6.159
0.637
6.091
0.801
0.026
5
0.001
2
1.58745
0.000520
10.814
0.674
7.418
0.686
7.004
0.852
0.026
6
0.001
2
1.58745
0.000505
11.846
0.695
8.635
0.729
7.835
0.897
0.026
7
0.001
2
1.58745
0.000492
12.795
0.713
9.819
0.767
8.604
0.937
0.026
8
0.001
2
1.58745
0.000481
13.678
0.729
10.975
0.802
9.324
0.974
0.026
1
0.0005
2
1.12250
0.000382
4.836
0.459
2.178
0.450
1.693
0.703
0.025
2
0.0005
2
1.12250
0.000340
6.839
0.515
3.880
0.567
3.275
0.797
0.025
3
0.0005
2
1.12250
0.000318
8.376
0.551
5.440
0.649
4.459
0.876
0.024
4
0.0005
2
1.12250
0.000303
9.672
0.579
6.914
0.715
5.463
0.941
0.024
5
0.0005
2
1.12250
0.000292
10.814
0.600
8.327
0.770
6.353
0.997
0.024
6
0.0005
2
1.12250
0.000283
11.846
0.619
9.693
0.818
7.163
1.047
0.024
7
0.0005
2
1.12250
0.000276
12.795
0.635
11.021
0.861
7.913
1.092
0.024
8
0.0005
2
1.12250
0.000270
13.678
0.649
12.319
0.901
8.614
1.132
0.024
For increasing discharge
Q
, the bed width
B
, the water depth
y
and
the
B
/
y
-ratio will increase. The bottom slope
S
o
will decrease with an
increase of the discharge
Q
. The regime theory results in relatively wide
and shallow cross sections.
Simons and Albertson (1963) developed a set of regime equations
based on a large data set collected from canal systems in India and North
America. Five types of canals were identified from the collected data set
and for each category the coefficients are given for the design of a canal, as
shown in Table 4.2. Simons and Albertson's equations have a wide range
of applicability and the data set used is related to a sediment load of less
than 500 ppm (Raudkivi, 1990). The set of regime equations of Simons
and Albertson (1963) is:
K
1
Q
P
=
(4.5)
B
=
0
.
9
P
=
0
.
92
B
s
−
0
.
61
(4.6)
K
2
Q
0
.
36
R
=
(4.7)
h
=
1
.
21
R
for
R <
2
.
1 m
(4.8)
h
=
0
.
61
+
0
.
93
R
for
R >
2
.
1 m
(4.9)
K
3
(
R
2
S
)
n
v
=
(4.10)
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