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

less than 20 percent (less than 10 percent in important
instances) change in velocity between steps. Adjustments
in the aransition should be made. if necessary, to obtain a
water-surface profile that is as nearly straight as
practical>le.

(2) Rapid flow. In rapid flow, stationary waves
result with changes in channel alignment. These disrur.
bances may necessitate increased wall heighL thereby
appreciably increasing conslrUction costs. USAED, Los
Angeles. uses the criterion in Table 2-2 for the design of
straight-line or wedge-type transitions to coniine flow
disturbances within the normal channel freeboard
allowance:

Table 2-2
Recommended Convergence and Divergence Transition Rat..

Mean channel
velocity, Ips

Wall ftllAl for each
wall (horizontal to
longitudinal)

10.1

1:10

15.30

1:15

30.40

1:20

(a) Rectangular contractions. Ippen (1950), Ippen
and Dawson (1951), and Ippen and Harleman (1956) ap-
plied the wave theory to the design of rectangular channel
transitions for rapid flow and developed the following
equations for computing flow depths in and downSlre:lm
from the convergence:

ean 9 .

tan p,t (v1 ... SF:- Sill~'1 - 3)
" :an: "1 ... -/1 ... SFi un';:' ~t - 1

(2-22)

~~ = 4 ({1 + 8Ff sin2 ~l - 1)

(2-23 )

and

F2 = Yl fF2
2 Y2 [ 1

_ 1 Yl (Y2 _ 1)
"7 Y2 CY~

(2-24)

t~~ + 1 J ]

2.9

EM '110-2-1601
1 Jul91

where

a = wall deflection angle

F = Froude number

~ = wave front angle

y = flow depth

The subscripts I. 2, and 3 refer to the flow are:lS indic:ued
on the sketches in Plate 21. For straight.line ccnvergence
(plate 2Ib). the maximum flow disturbance results when
the initial wave front intersection. point B. occurs at the
downstre:lm transition CC: When the reflected waves BD
and B D' intersect the channel walls below or above sec.
tion CC: diamond-shaped cross waves develop in the
channel. However, the change in wall alignment at sec-
tion CC' results in negative wave disturllances that should
tend to decre:lSe the downstre:lm effects of positive wave
fronts. This should result in somewhat lower depths
where the waves meet the downsa-e:lm walls. The mini-
mum disturbance occurs when the reflected waves BD and
BD' meet the channel walls at section CC: This. theoreti-
cally, results in the flow filaments again becoming parallel
to the channel center line. If the renected waves meet the
walls UpStre:lm from section CC: the waves would be
deflected again with a resultin g increase in depth.
Graphic plots of Equations 2.22 through 2-24 have been
published (Ippen 1950. Ippen and Dawson 1951, and
Ippen and Harleman 1956). Plate 22 presents design
curves based on these equations. The extent of the curves
has been limited to flow conditions normally occurring in
rapid-flow flood conlrOl channels. The required length of
the lransition is a function of the wall deflection angle e
and the channel cona-action b1 - b3 . or

b1 - bJ
L 2
4. can tj

(2-25)

where

bl = upslream channel width. ft

~ = downstre:lm channel width. ft

The theory indicates th:u the surface disturllanc~s are
minimized when L = Ll + l.:! (plate 21). The equations
for Ll and L2 are