The combined energy loss in the first three phases of energy dissipa-
tion can be expressed from a velocity coefficient !1–3, which can be deter-
mined in model tests from the theoretical supercritical flow depth
conjunctive to the subcritical depth needed to form a stable jump down-
stream of a (ski-jump) spillway. Even if this value of !may be subject to
scale effects (the prototype !is likely to be smaller because of increased
aeration), the model studies give a very good indication of the relative
merits of various designs.
Generally (Fig. 5.1),
!1–3f(S/S,q, geometry) (5.5)
whereSis the height of the ‘take-off’ point above the reference datum.
A comparison of !1–3for three designs is shown in Fig. 5.2: curve a, a
normal spillway ending in a stilling basin; curve b, a ski-jump spillway
without baffles at the take-off edge; curve c, a spillway with baffles which
split the jet so that the air entrainment and energy dissipation is enhanced
and the pressures on the stilling basin floor are reduced. The increase of!
(and decrease of relative energy loss) with qis again demonstrated. By
using a suitable design, the values of !have been reduced throughout by a
factor about 0.7; this results in substantial energy losses, e.g. for !1–30.5,
e/E75% (equation (5.3)). The optimum (lowest) value of !1–3is attained
forS/S0.6; at this value the overall nappe gains a sufficient velocity and
degree of turbulence while flowing over the upper part of the overall spill-
way to disperse effectively on the baffles at the take-off edge, and has a
sufficiently long free fall through air to aerate intensively and to break up
the jet core (Novak and Cˇábelka, 1981).
The disintegration of a falling circular jet of diameter Dwas studied
by Ervine and Falvey (1987), who showed that a complete decay of the
solid inner core occurs after a length of fall L, with L/Din the range
50–100. For flat jets, which are more relevant to spillway design, Horˇení
(1956) established experimentally that the length of fall from the crest
required for total jet disintegration (for qin m^2 s^1 ) is
L5.89q0.3196(q)1/3(m). (5.6)
5.2.3 Flip bucket
The flip bucket (Fig. 5.3) is a version of a ski-jump spillway that is usually
used as an end to a chute or tunnel spillway whenever the geological and
topographical conditions are suitable. Flip buckets (just as ski-jump spill-
ways) are usually tailor-made for a given project, and the designs are
developed with the aid of scale models.
248 ENERGY DISSIPATION
