Hydraulic Structures: Fourth Edition

SPILLWAYS 219

For small values of K, equation (4.50) results in

V

S

n

1/

V

(^2) q
2/
2
3
/3
 1 c (^1) 
2/3

. (4.51)

Equations (4.50) and (4.51) are implicit equations for the velocity which,
when solved, give 1 (equation (4.49)) and thus the depth of the uniform
aerated flow ya(Worked example 4.4).
Wood (1991) recalculated Straub’s data and plotted the average con-
centration (%) as a function of the chute slope . The result can be
approximated as follows:

for 0°40°, C(3/2);

for 40°70°, C 45 0.36. (4.52)

Together with equation (4.43) this permits the computation of ya(see
worked example).
An even simpler way of finding C(ICOLD, 1992b and Vischer and
Hager, 1998) is given by

C0.75(sin)0.75 (4.53)

with the concentration at the chute surface given by

C 0 1.25^3 (4.54)

within radians for 0°40 and

C 0 0.65 sin (4.54a)

for40°.
It must be appreciated that uniform aerated flow is reached only at a
very considerable distance from the spillway crest, and in many chute spill-
ways may never be reached at all, particularly if the specific discharge qis
large (q50 m^2 s^1 ). From the point of view of cavitation protection also a
minimum air concentration is required in contact with the spillway (about
7%); equations (4.41)–(4.53) yield only the average concentration, which
should probably exceed 35% to provide the minimum necessary concen-
tration of air at the spillway surface (see, for example, Wood, 1991).
In order to provide cavitation protection in cases where there is no
air in contact with the spillway, or the air concentration is insufficient and
the velocities high enough to make cavitation damage a real possibility,
‘artificial’ aeration by aerators has been developed (Pinto, 1991; Volkart
and Rutschmann, 1991). These aerators have the form of deflectors

V^3



gq