Environmental Engineering Reference
In-Depth Information
The Reynolds number gives the ratio between the inertia force and the
viscous force and is represented by:
ρv
2
L
2
µvL
=
vL
ν
Re
=
(2.4)
where:
v
=
mean velocity (m/s)
L
=
a characteristic length, e.g. water depth (m)
kinematic viscosity (m
2
/s)
ν
=
For low Reynolds numbers the flow is laminar and for large numbers
the flow is turbulent. An additional form of the Reynolds number is the
number using the shear velocity:
ρu
∗
R
µ
u
∗
R
ν
Re
∗
=
=
(2.5)
where:
u
∗
=
√
gRS
o
=
shear velocity (m/s)
g
=
acceleration due to gravity (m/s
2
)
R
=
hydraulic radius (m)
S
o
=
bottom slope (m/m)
kinematic viscosity (m
2
/s)
ν
=
2.3 GEOMETRY
Canals are man-made channels and their cross-section can be prismatic
(when
A
and
S
o
are constant) or non-prismatic. Moreover, the cross-
section can be either regular (e.g. circular, triangular, rectangular or
trapezoidal) or irregular. Figure 2.5 gives the main characteristics within a
cross section and a longitudinal section of a canal.
B
s
y
(1)
(m)
b
Cross section
y
(1)
(S
f
)
(1)
(S
0
)
Figure 2.5. Main
characteristics of a canal.
Longitudinal section
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