SPILLWAYS 217
tially and fully aerated non-uniform flow is beyond the scope of this text
but various approaches can be found in, for example Haindl (1984),
Ackers and Priestley (1985), Naudascher (1987), Falvey (1990), ICOLD
(1992b) and Wilhelms and Gulliver (2005). As a very rough estimate, it is
possible to take the distance from the inception of aeration to the point
where air reaches the spillway (and thus may provide some cavitation pro-
tection) to be given also by equation (4.23).
The important depth of the uniform aerated flow, ya, can be esti-
mated in several ways. Writing the average air concentration as
CQa/(QaQ), (Qais the discharge of air), the ratio of the water dis-
chargeQ to the total discharge of the mixture of air and water as
1 Q/(QaQ) and the ratio of air to water discharge as Qa/Q,
C 1 1 /(1). (4.38)For a rectangular chute:
1 Q/(QaQ)y 0 /ya (4.39)wherey 0 is the depth of the non-aerated (uniform) flow.
Wood (1991) defines Cby using the depth, y, where the air concen-
tration is 90%, as
C 1 y 0 /y. (4.40)For a quick assessment of yawe may use the approximate equations
yac 1 ycc 1 (q^2 /g)1/3 (4.41)with the coefficient c 1 in the range 0.32c 1 0.37, or
(ya y 0 )/y 0 0.1(0.2Fr^2 1)1/2. (4.42)Experiments by Straub and Anderson (1958) have shown that the ratio of
the aerated spillway friction factor, a, to the non-aerated one, , decreases
with an increase of air concentration approximately according to (Ackers
and Priestley, 1985)
a/ 1 1.9C^2 (4.43)forC0.65. For C0.65,a/remains constant at 0.2.
Anderson’s data (Anderson, 1965) for rough and smooth
spillways after curve fitting and recalculation to SI units give the following
equations for air concentration. For rough spillways (equivalent roughness
1.2 mm),
C0.72260.743 logS/q1/5 (4.44)