y 0 to obtain the increase, ∆yya y 0 , for the aerated flow. The inception
of aeration occurs at the point where the turbulent boundary layer pene-
trates the full depth of the flow. This position can be calculated by combin-
ing the equations of non-uniform (non-aerated) flow with the equation of
the turbulent boundary layer growth or (sufficient for preliminary design
purposes) from equation (4.23). For aeration to begin the energy of the
turbulent surface eddies must exceed the energy of the surface tension.
Thus in model experiments often no air is actually entrained at all (or its
inception is delayed), because of the disproportionally high surface
tension, although the ‘inception point’ can be clearly distinguished by the
beginning of a rough water surface. Although closely connected with drop
ejection and impact the whole mechanism of self-aeration of supercritical
flow is more complex and subject of further research (Rein, 1998, Fer-
rando and Rico, 2002).
Ackers and Priestley (1985) and Wood (1991) quote a simple equa-
tion for the growth of the boundary layer with distance L:
/L0.0212(L/Hs)0.11(L/k)^ 0.10 (4.37)
whereHsis the potential flow velocity head and kis the equivalent rough-
ness value. Equation (4.37) was derived primarily from field data for con-
crete gravity dam spillways.
Water levels in the non-uniform non-aerated flow can be determined
by standard non-uniform flow calculations. The computation of the par-
216 DAM OUTLET WORKS
Fig. 4.11 Development of flow on a chute spillway (Ackers and Priestley,
1985)