Civil Engineering Reference
In-Depth Information
where
g
is the acceleration due to gravity and
d
is the effective depth of the channel
under the bridge and is equal to
A
/
b
, where
b
is the net or effective width of the
bridge opening.
The theoretical determination of
C
c
is difficult and numerical values are estab-
lished experimentally. Published values of
C
c
for various constriction geometries are
available in the literature on open channel hydraulics (Chow, 1959).
One commonly used hydraulic analysis
∗
is the U.S. Geological Survey (USGS)
method, which is based on extensive research. It determines a base coefficient of
discharge,
C
, for four opening types in terms of the opening ratio,
N
, and constriction
length ratio,
L
/
b
. The coefficient of discharge,
C
, is further modified by adjustment
factors based on the opening ratio, Froude number,
F
, and detail abutment geometry
to obtain the discharge coefficient,
C
. In terms of the USGS method, the coefficient
of contraction is
2
g
h
f
,
+
α
u
V
u
C
V
u
C
c
=
Δ
h
2
g
−
(3.7)
where
C
is the USGC discharge coefficient, which depends on
N
,
L
,
b
,
F
, and other
empirical adjustment factors based on skew angle of the crossing, the conveyance,
K
, details the geometry and flow depth at the constriction;
N
is the bridge opening
ratio and is equal to
Q
c
/
Q
, where
Q
c
is the undisturbed flow that can pass the bridge
constriction and
Q
is the flow in the not constricted channel;
L
is the length of channel
at the constricted bridge crossing;
K
AR
2
/
3
/n
;
d
d
, where
d
u
is the depth
of the channel upstream of the bridge and
d
d
is the depth of the channel downstream
of the bridge;
h
f
is the friction loss upstream and through the constricted opening,
which is
=
Δ
h
=
d
u
−
Q
2
K
u
K
d
L
Q
K
d
2
h
f
=
L
u
+
,
(3.8)
where
L
u
is the length of upstream reach (from the uniform flow to the beginning
of constriction);
K
u
is the upstream conveyance and is equal to
A
u
R
2
/
u
/
n
u
;
K
d
is the
downstream conveyance and is equal to
A
d
R
2
/
d
/n
d
;
A
u
and
A
d
are the upstream and
downstream channel cross-sectional areas, respectively;
R
u
and
R
d
are the upstream
and downstream hydraulic radii, respectively and are equal to area,
A
u
or
A
d
, divided
by the channel wetted perimeter;
n
u
and
n
d
are the upstream and downstream
Manning's roughness coefficients, respectively.
3.2.3.2.1.2 ObstructedDischargeHydraulics
Due to the large live loads, long
railway bridges are often composed of many relatively short spans where the topo-
graphy allows such construction. In these cases, many piers are required that may
create an obstruction to the flow and consideration of the contraction effects due to
obstructionisalsonecessary(Equation3.5with
C
c
beingthecoefficientofcontraction
of the new channel cross section at the obstruction). The flow past an obstruction is
∗
Other methods such as the U.S. Bureau of Public Roads, Biery and Delleur, and the U.K. Hydraulic
Research methods are also used.
