Environmental Engineering Reference
In-Depth Information
The shear stress of the banks will not be considered unless the bed and
sides are covered by coarse, non-cohesive material; in that case the angle
of repose should be included.
The boundary shear stress at the bottom is:
S
(N
/
m
2
)
τ
max
=
c
∗
ρ
∗
g
∗
y
∗
(C.24)
where:
c
=
correction factor for various b/y ratios
density of water (kg/m
3
)
ρ
=
acceleration due to gravity (9.81 m/s
2
)
g
=
y
=
water depth (m)
S
=
bottom slope (m/m)
The correction factor c is a function of the
b
/
y
ratio:
e
(
b
/
y
)
∗
0
.
065
c
=
0
.
77
∗
for 1
< b/y <
4
(C.25)
c
=
1
for
b/y
≥
4
(C.26)
Field studies on very coarse material have shown that the “critical
shear stress”, above which motion of particles will start, is approximately
0.94
D
75
(N/m
2
), where
D
is in mm. For the design a boundary shear
stress of 0.80
∗
D
75
is recommended.
The maximum boundary shear stress
in normal soils in normal canals
and under normal conditions
can be between 3 and 5 N/m
2
. The USBR
recommendations for fine material are given in Table C.3. In case that
the shear stress is too high the most sensitive factor to reduce the stress
is a gentler bottom slope.
∗
D
75
or 0.75
∗
Recommended critical boundary shear stress (N/m
2
).
Table C.3.
D
50
(mm)
Clear water
Light load
Heavy load
0.1
1.20
2.40
3.60
0.2
1.25
2.49
3.74
0.5
1.44
2.64
3.98
1.0
1.92
2.87
4.31
2.0
2.88
3.83
5.27
5.0
6.71
7.90
8.87
The design values of critical boundary shear stress are established for
straight canals, and should be reduced for sinuous canals. See Table C.4
for the reduction in percentage.
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