E
e
1 !^2. (5.3)
For a ratio of the height Sof the spillway crest above its toe (or in case of a
spillway with a free-falling jet as in Fig. 5.1 (S–S) above the take-off point)
and the overfall head H, with S/H30 (or 30), and for smooth
spillways (Novak and Cˇábelka, 1981),
! 1 1 0.0155S/H. (5.4)
For a given S,! 1 increases as Hincreases, i.e. if for a given discharge Qthe
spillway width bdecreases and thus qincreases (equation (4.19)). Thus,
for S/H5,! 1 0.92 and the relative head loss is 15%, whereas for
S/H25,! 1 0.61 and the loss is 62%.
The value of could be increased (and !decreased) by using a rough
spillway or by placing baffles on the spillway surface. However, unless aer-
ation is provided at these protrusions, the increased energy dissipation
may be achieved only by providing an opportunity for cavitation damage
(Section 4.6).
Stepped spillways mayprovide an opportunity for additional energy
dissipation (when compared with smooth spillways) pending on the value
of the unit discharge (q) (see also Section 4.7.6). E.g. Rice and Kadavy
(1994) compared (using models) the energy loss on a smooth and stepped
spillway for a 17 m high dam; the result agreed broadly with equation (5.4)
for the smooth spillway and showed a 2–3 times higher energy loss for the
stepped alternative (steps 0.61 m high and 1.52 m deep). Stephenson (1991)
confirms the importance of the unit discharge on the efficiency of energy
dissipation on cascade spillways and Boes and Hager (2003) give a
detailed analysis of the friction factor for the skimming flow regime
demonstrating the effect of the chute slope (friction factor decreases with
the slope) which is much larger than that of the relative roughness (see
also equation (4.68)).
5.2.2 Ski-jump spillways
In many modern spillway designs, increased energy dissipation is achieved
by using free-falling jets, either at the end of a ‘ski-jump’ or downstream of
a flip bucket (Figs 5.2 and 5.3).
The ski-jump spillway was first used by Coyne (1951), and was later
further developed by detailed model studies. Its use brings substantial
S S
H
1
V^2
2 g
V^2
2 g
V^2
2 g
246 ENERGY DISSIPATION
