Environmental Engineering Reference
In-Depth Information
Main equations of the regime theory as given by Lacey
(Henderson, 1966)
SI-units
foot-second units
f
=
√
2520
d
f
=
8
√
d
(D.1)
P
=
4
.
836
√
Q
P
=
2
.
67
√
Q
(D.2)
v
=
0
.
6459
fR
1
.
17
fR
V
=
(D.3)
S
o
=
0
.
000315
f
5
/
3
Q
1
/
6
f
5
/
3
1750
Q
1
/
6
S
o
=
(D.4)
f
=
silt factor for a sediment
f
=
silt factor for a sediment
size
d
size
d
d
=
sediment size (m)
d
=
sediment size (inch)
Q
=
discharge (m
3
/s)
Q
=
discharge (cusec)
P
=
wetted perimeter (m)
P
=
wetted perimeter (foot)
v
=
mean velocity (m/s)
v
=
mean velocity (foot/s)
R
=
hydraulic radius (m)
R
=
hydraulic radius (foot)
S
o
=
bottom slope
S
o
=
bottom slope
According to Lacey (1958) these equations are applicable within the
following range of parameters:
•
Bed material size
0.15-0.40 mm
•
Discharge
0.15-150 m
3
/s (5-5000 cfs)
•
Bed load
small
•
Bed material
non-cohesive
•
Bed form
ripples
The Lacey equations for the design of canals for given d and Q follow
the next steps:
1.
f
d
)
0
.
5
=
(2520
∗
(equation D.1);
4.836(
Q
)
1
/
2
(equation D.2);
2. Determine
P
=
0.6459(
fR
)
1
/
2
(equation D.3),
R
3. From
v
=
=
A/P
and
A
=
Q/v
follows
((
P/f
)
0
.
5
Q
)
2
/
3
the area of the cross section
A
=
1
.
3383
∗
∗
0
.
000315
f
5
/
3
/
Q
1
/
6
(equation D.4);
5. From the given
P
and
A
the channel section is found as a trapezoidal
channel with assumed side slope (
m
)of1
V
:2
H
.
6.
y
4. Next, find the bottom slope
S
=
(
P
2
m
2
)
0
.
5
))
0
.
5
/
(2(
m
m
2
)))
=
P
+
+
4
A
(
m
−
2(1
+
−
2(1
+
m
2
)
0
.
5
B
=
P
−
2
y
∗
(1
+
R
=
A/P
Table D.1 gives some examples of the design of earthen canals
for two sediment diameters (
d
=
0.0004 m and
d
=
0.00015 m) and two
=
=
side slopes (
m
1
.
5) and several discharges
Q
according
to the Lacey method. The results are also presented in the Figure D.1
and D.2.
2 and
m
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