Environmental Engineering Reference
In-Depth Information
As shown before
v
0; also
v
2
is always larger than zero and
∗
A
=
v
3
A
can be ignored as it is very small. Hence, the coefficient of
Coriolis can be presented as:
∗
3
v
2
∗
A
α
=
1
+
(2.26)
¯
v
2
∗
A
Another example of the effect of the velocity distribution on a hydraulic
equation is the application of the second law of Newton in some hydraulic
problems. The law states that the sum of all external forces is equivalent
to the rate of change of momentum:
P
=
m
v
=
(
m
v
)
out
−
(
m
v
)
in
(2.27)
The mass of water flowing with a velocity
v
a
through an area
A
is
ρv
a
A
.
The momentum passing that area per unit of time is the product of the
mass and the velocity:
ρv
a
A
. The momentum for the whole cross
section with area
A
is:
ρv
A
A
. The total momentum for the whole
cross section can also be expressed by the average velocity
v
2
A
.
¯
v
as:
βρ
¯
Equating this quantity with
ρv
A
A
results in
v
A
∗
A
β
=
(
v
2
¯
∗
A
)
(
(
v
)
2
A
v
2
v
2
)
A
¯
v
±
¯
±
2
v
¯
∗
v
+
β
=
=
v
2
¯
∗
A
v
2
¯
∗
A
where
v
∗
A
=
0
v
2
A
¯
β
=
1
+
(2.28)
v
2
A
where
β
=
coefficient of Boussinesq (
α
is always larger than
β
).
2.6 UNIFORM FLOW
Uniform flow in open channels is characterized by:
•
the depth, cross section, velocity and discharge are constant in every
section;
•
the lines that represent the energy, water surface and channel bottom
are parallel; the slopes are
S
o
=
S
w
.
It is assumed that uniform flow in open channels is steady and
turbulent (meaning that Re
>>
600). Flow in open channels encounters
S
f
=
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