HYDRAULIC MODELS 677
16.1.3 Scale modelsAscale modelin hydraulic engineering (as opposed to analogue and math-
ematical models) (ASCE, 1982) uses the method of direct (physical) simu-
lation of (hydraulic) phenomena, (usually) in the same medium as in the
prototype. Models are designed and operated according to scaling laws,
i.e. conditions that must be satisfied to achieve the desired similarity
between model and prototype. The ratio of a variable in prototype to the
corresponding variable in the model is the scale factor (scale); in the liter-
ature the reciprocal of this ratio is sometimes used. In the following text
the scale factor is denoted by Mx.
Distortion is a conscious departure from a scaling law (e.g. geometric
distortion – discussed later). Non-similarity between model and prototype,
resulting from the fact that not all pertinent dimensionless numbers (phys-
ically meaningful ratios of parameters used in determining scaling laws)
are the same in the model and prototype, is called the scale effect. In other
words, the scale effect is the error caused by using the model according to
the main determining law and neglecting others, e.g. errors resulting from
modelling the prototype on the basis of scales chosen to suit the dominant
force action and allowing the other forces to be out of scale.
The analysis of flow often leads to the use of geometrically distorted
models; indeed, even a geometrically similar model almost inevitably intro-
duces some degree of distortion of flow and some scale effects. The mod-
eller has to be aware of these effects and, in relation to hydraulic structures
design, of model–prototype conformity. He or she has to relate this particu-
larly to the required precision of the answer and, most importantly, must be
aware of whether the model answer enhances or reduces the safety of the
prototype structure. For example, a model of a ski-jump spillway will
produce a jet with less air entrainment than would be the case in prototype;
because of this, and because of the reduced velocity of the jet on the model
and hence the reduced air resistance, when interpreting the distance of the
jet impact on the river bed downstream of the structure one obtains from
the model a distance (when scaled up according to model scale) that is
greater than is likely to be the case in prototype but possibly with a deeper
scour hole. The scale effect in this case means that the actual scour is likely
to be somewhat nearer the dam but shallower than indicated by the model
tests. Does this matter? Does it increase or decrease the safety of the struc-
ture? The answers will depend, amongst other factors, on geological con-
ditions, operational rules, etc.; the interpretation of the scale-model result
thus requires knowledge, and also intuition and experience, both of the
modeller and the design engineer.
Only a few aspects of physical scale models as used in hydraulic
engineering can be touched upon here, and for more detailed treatment
the reader is referred to specialized texts (e.g. Kobus, 1980; Novak and
Cˇábelka, 1981; Novak, 1984).