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

4-2. Air Entrainment

a. General. Air enlrainment should be considered in
the design of rapid- flow channels. The enlrainment of
air may result in bulking of the now and necessitate in-
Cre:lSCd wall heights. Presently available data indicate
that appreciable air entrainment should not occur with
Froude numbers less than about 1.6.

b. Early design crileria. The USAED, Sacramento,
developed !he following equation based on data reported
by Hall (1943):

m=

v2
..uuga

(4-1)

where

m = air-water ratio

Y = theoretical average flow velOCity
without air

d = now depth including air

The term y2/gd is the Fronde number squared. Equa-
tion 4-1 with minor differences in the definition of terms
has been published by Gumensky (1949), The basic
equation has been used extensively for design purposes in
the past.

c. Modern i1lVesligaliollS. The mechanics of
self-aerated now in open channels with sand grain sur-
faces has been studied at the University of Minnesota by
Straub and Anderson (1960). The results of the
Minnesota tests have been combined with selected Kittitas
chute prototype data (Hall 1943) and published as HDC
050.3. The chart includes the following suggested design
equation:

C sO. 70110910

~)+ 0.971
(q-'

(4-2)

where

C = ratio of experimentally determined
air volume to air plus water volume

EM 1110-2.1601
1 Jul 91

S = sine of angle of chute inclination

q = discharge per unit width of channel

d. Design crileria. Use of EqUation 4-2 or HDC
050-3 requires the assumption that the experimenlal water
!low depth d.", in the term
C = dj(d. + d.",) where d. is depth of air-Water mix.
ture, fl. is the same as the theoretically computed flow
dep!h. The Minnesota data indicate that this assumption
is valid only for small Froude numbers. For large Froude
numbers, the theoretically computed depths for nonaerated
now were found to be SO to 75 percent greater than the
observed experimental flow depth. For this reason and
for convenience of design. the Minnesota and Kittitas data
have been computed and plotted in terms of the observed
tolal now depth (air plus water) and the theoretical flow
depth and Froude number for nonaerated flow (plate 50a).
The resulting design curve has been extrapolated for low
Froude numbers and replotted as Plate SOb. This plate
should be used for air-enlrained nows in flood conlrOl
channels. A comparison of HDC 050.3 and Plate SOb
indicates that this plate results in more conservative
design for low Froude numbers.

4-3. Hydraulic Jump In Open Channels

a. General. Flow changes from the rapid to lranquil
state will usually occur in the form of a hydraulic jump.
The hydraulic jump consists of an abrupt rise of the water
surface in the region of impact between rapid and lranquil
flows. Flow depths before and after the jump are less
than and greater than critical depth, respectively. The
zone of impact of the jump is accompanied by large-scale
turbulence, surface waves, and energy dissipation. The
hydr:wlic jump in a channel may occur at locations such
as:

(I) The vicinity of a break in grade where the chan.
nel slope decre:lses from steep to mild.

(2) A short distance upStre:lm from channel consnic.
tions such as those caused by bridge piers.

(3) A relatively abrupt converging transition.

(4) A channel junction where rapid now occurs in a
nibutary channel and tranquil flow in the main channel.

(5) Long channels where high velocities can no
longer be sustained on a mild slope.

4-3