proposed an equation (applicable to model and prototype) where air
entrainment replaces the effect of H*:
ys3.39 (q0.6(1)0.3y 0 0.16)/(g0.3d0.06) (5.16c)
whereqa/q0,13 (1 vc/v) (H*/t)0.446;tis the jet thickness and vcthe
minimum velocity required for air entrainment (1.1 m/s).
Equation (5.16c) can be approximated by an earlier author’s equa-
tion
ys3.27 (q0.60H*0.05y 0 0.15)/(g0.3d0.10). (5.16d)
Lopardo (1997) proposed the equation
ys/H*2.5 (q/(g H*^3 )0.5)0.5(m) (5.16e)
which translates to :
ys1.41q0.5H*0.25(m) (5.16f)
Equation (5.16e) is based on over 60 laboratory and 17 prototype results
and with a safety factor 1.3 covers all recent field data, e.g. from Tarbela
and several dams in China, Africa and South America; it can give higher
results than (5.16b), (5.16c) or (5.16d) (particularly when the safety factor
1.3 is applied). Equations (5.16c–e) are dimensionally correct and all equa-
tions (5.16) confirm again the decisive influence of the unit discharge in
dam design (see also Sections 4.7.1 and 5.2.1).
For flip bucket spillways Tarajmovich proposed the equation (1978):
ys 6 ycrtan 1 (5.17)
whereysys y 0 (as in equation (5.15)), ycris the critical depth, and 1 is
the upstream angle of the scour hole, which is a function of the flip bucket
exit angle but does not vary widely (14° 1 24° for 10°40°).
The pressure fluctuations on the floor of a plunge pool underneath a
plunging jet can be very considerable; it will be a function of plunge
length, pool depth, jet size and shape and can reach a substantial percent-
age of the head H*(Ervine, Falvey and Withers, 1997). If the plunge pool
is not deep enough to absorp the energy of the jet it may have to be pro-
vided with slabs forming a stilling basin floor (see Section 5.3.1). In this
case slab joints should be located outside the zone affected by the jet
deflection to avoid strong uplift forces in case of a joint waterstop fracture
or if using open joints (which may be advantageous with effective founda-
tion drainage). For further details of forces acting on plunge pool slabs
and their design see Melo et al. (2006).
260 ENERGY DISSIPATION
