FLOOD03351

• County: Statewide
• Basin: Statewide
• Title: Engineering and Design Hydraulic Design of Flood Control Channels
• Date: 7/1/1991
• Prepared By: US Army Corps of Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

(a) Prismatic channels. A prismatic channel is ch3r-
acterized by unvarying cross section. constant bottom
slope, and relatively straight a1i gnmenl. There are three
general methods of derennining flow proftles in this type
of channel: direct integrnlion. direct step. and standard
step, as discussed in Chow (1959, pp 252-268). The
direct integration and direct step methods apply exclu-
sively to prismatic channels, whereas the standard step
method applies not only to prismatic channels but is the
only method to be applied to nonprismatic channels. The
direct integrnlion method (with certain restrictions as to
the consWlCY of hydraulic exponents) solves the varied
flow equation to detennine the length of re:lCh between
successive depths. Use is made of varied-flow-function
tables to reduce the amount of computations. This
method is not nonnally employed unless sufficient
profiles and length of channel are involved to warr.mt the
amount of precomput:ltional preparation. The direct step
method detennines the length of reach between successive
depths by solution of the energy and friction equations
written for end sections of the reach. The stand:1rd step
method is discussed in (b) below.

(b) Nonprismatic channels. When the cross section,
alignment. and/or bottom slope changes along the channel,
the standard step method (Chow 1959. P 265) is applied.
This method detennines the water-surface elevation
(depth) at the reach extremity by successive approxima-
tions. Trial water-surfuce elevations are assumed until an
elevation is found that satisfies the energy and friction
equations written for the end sections of the reach. Cross
sections for this method should. in general, be selected so
that velocities are increasing or decreasing continuously
throughout the reach, EM 1110-2-1409 contains further
infonnation on this method. Pl3le 8 shows a sample
computation for a gradually contracting trapezoidal chan-
nel where bOth bottom width and side slope vary. Suc-
cessive approximations of water,surface elevations are
made until a balance of energy is obtained. Friction
losses hr are based on the Manning equation.

Sf ~

n2V2
2.21R,10

~

v2
C"R

(2-1 and 2-2 bis)

For the sample computation a mild slope upstream and
Sleep slope downstream of sta 682+40 have been
assumed. Critical depth would occur in the vicinity of
sta 682+40 and has been assumed as the starting condi-
tion. Initially, column 21 has the same value as column
10. The computations proceed downstre:lll\ as the flow is
rapid. The length of re:JCh is chosen such that the change
in velocity between the ends of the reach is less than

EM 111()"2-1SJ1
1 Jul 31

10 percenl. The energy equation is balanced when
column 21 checks column 10 for the trial water surt:JCe of
column 5. PI3le 9 repeats the computation, substituting k
= 0.002 ft for n = 0.014. For rough channel conditions

C = 32.6 log10 (12/R)

(2-6 bis)

2.3. Flow Through Bridges

Bridge piers 10000ted in channels result in energy losses in
the flow and create disturbances at the bridge section and
in the channel sections immediately upstre:un and down-
stream. As bridge pier losses materially affect W3ler.
surface elevations in the vicinity of the bridge, their
careful determination is important Submergence of
bridge members is not desirable.

a. AbUtment losses. Bridge abutments should not
extend into the flow = in rapid, flow channels. In
tranquil-flow channels they should be so designed that the
flow depth between abutments or between the abutment
and an intennedi3le pier is greater than critical depth.
The Bureau of Public Roads (BPR) (Bradley 1978) has
published design charts for computing backwarer for
various abutment geometries and degrees of conlraCtion.
The design procedure and charts developed by BPR are
recommended for use in channel designs involving bridge
abuunents. For preliminary designs. a step b:JCkwaler
computation using abrupt expansion and conlraCtion head
losses of 1.0 and 0.5. respectively, times the change in
velocity head may be used. This method under the s:une
circumstances may be applied to bridge openings contain-
ing piers.

b. Pier losses, Rapid, tranquil. or a combination of
rapid- and tranquil-flow conditions may occur where only
bridge piers are located in the flow area. Flow through
bridge piers for this condition is classified as class A. B,
or C. according to the depth of flow in relation to critical
depth occurring upstream, between piers. and downstream.
Plate 10 is a graphic description of these cbsses, which
are discussed below. Plate 11 is useful in determining the
class of flow in rectangular channels.

(1) Class A flow (energy method). Chow (1959.
paragraph 17,10) presents a discussion and several energy
Joss fonnulae with appropriate coefficients lhm may be
used for computing bridge pier losses for tranquil flow
(class A). While the momentum method presented below

2-5