SPILLWAYS 221
qa/q0.29(Fr 1)0.62(D/y)0.59 (4.55)where Fr is the Froude number just upstream of the aerator, and
DcA/b, with Athe aerator control orifice area, cthe discharge coeffi-
cient and bthe chute width. The total air flow for an average negative
pressure under the nappe at the aerator ∆pis then
QaqabcA(2∆p/ (^) a)1/2. (4.56)
For further discussion and details of aerators see ICOLD (1992b).
Self-aerated flow in steep partially filled pipes and tunnels resembles
flow in steep rectangular channels (chutes) but the effect of the geometry
of the conveyance and the enclosed space results in differences in air
entrainment and concentration.
Thus Volkart (1982) on the basis of laboratory and field measure-
ments proposed for the air concentration C:
C 1 1/(0.02(Fr 6)1.51) (4.57)
or for C0.3
C0.044Fr 0.3 (4.58)
(whereFrV/(gR)1/2with both the velocity and hydraulic radius applying
to the water component only).
Equation (4.57) defines also Fr6 as a limiting value for the begin-
ning of air entrainment; this in turn can be translated into a limiting slope
S(using the Manning–Strickler equation)
S(36.4/D)1/3gn^2. (4.59)
ForFr17 and S1 the air concentration for flow in partially filled pipes
is smaller than for open rectangular channels (for further details see
Volkart (1982)).
The air supply to the flow must also take into account the air demand
for the air flow above the air–water ‘interface’; (see also Sections 4.7.4, 4.8
and 6.6).
4.7.4 Shaft spillways
A shaft (‘morning glory’) spillway consists of a funnel-shaped spillway,
usually circular in plan, a vertical (sometimes sloping) shaft, a bend, and a
tunnel terminating in an outflow. Shaft spillways can also be combined
with a draw-off tower; the tunnel may also be used as part of the bottom