HYDRAULIC MODELS 681
Re (16.5)(with hf 8 gR/lV^2 ) to avoid viscous effects; this usually requires
10 3.5Re 10 4.5. For models of intakes the Weber number (defined as
V( D/)1/2) should be greater than 11 and the Reynolds number (VD/v)
greater than 3 104 to avoid surface tension and viscous effects. The above
are only approximate guidelines; for further details, see, for example,
Kobus (1980), Novak and Cˇábelka (1981) and Knauss (1987).
It is extremely unlikely that on a standard reduced model problems
associated with the aeration and bulking of flow over spillways can be fully
investigated, although useful results can be obtained for the initiation of
aeration on chutes, the design of artificial aerators, aeration in shaft spill-
ways, etc. The scale effects in, for example, energy dissipation also have to
be carefully analysed (Kobus, 1984).
An ordinary scale model of, say, a spillway will not cavitate where
cavitation would occur in prototype, because the ambient atmospheric
pressure has not been reduced to the model scale. Pressure measurements
taken on the model and converted to prototype would, however, indicate
whether cavitation in prototype is likely. For example, if a model scale
Ml25 exhibits a negative pressure of 0.5 m, cavitation would occur in
prototype because 250.512.5 m below atmospheric pressure, which is
physically not possible, as cavitation would start close to the minimum
possible value of 10 m. If we want to investigate the behaviour of a spill-
way with cavitation occurring on the model, this has to be placed in a cavi-
tation tunnel where we can control and reduce the ambient pressure
(Novak and Cˇábelka, 1981); even in this case we have to take into account
water quality and other scale effects (Kobus, 1984; Burgi, 1988; Eickmann,
1992).
Flow-induced vibrations on model gates with the model operated
according to the Froude law reproducing correctly the flow field are
subject to scale effects which can be overcome by a hybrid rigid model
(simulating the low frequency interaction of the gate with the flow) or by
use of models with an overall reproduction of elasticity (see e.g. Haszpra,
1979 or ICOLD, 1996; refer also to Section 16.2).
Investigations on models of hydraulic structures often require
sophisticated instrumentation for the measurement of discharge, velocity
and pressure fluctuations, air concentration, etc. Models of navigable
waterways and of locks with model barges in particular need specialized
equipment. On some waterway models the steering and propulsion of the
model barge(s) are computer controlled and model tests are used to cali-
brate mathematical simulation models (Mlfor such models is likely to be
smaller than 15). Forces acting on model barges during lock operation are
recorded by special dynamometers eliminating, or at least minimizing, the
inertial forces.
126 R
k1/2