Hydraulic Structures: Fourth Edition

STRUCTURAL MODELS 683

rion (equations (8.19) or (8.20)) we obtain another equation for M∆, (∆

( (^) s )/ ):

M∆ . (16.12)

We have now nine variables and seven equations, and again only two
degrees of freedom for choice of scales. For similarity of sediment
transport, additional boundary conditions may be required and similarity
of bedforms also has to be investigated.
To model tidal motion on estuary and coastal engineering models
similar considerations apply; however, we must remember that for the ver-
tical motion of the water surface (or the sediment fall velocity) the corre-
sponding velocity scale is given by

MwMh/MtMh3/2/Ml (16.13)

(asMtMl/MvMlMh^ 1/2). For studies of wave refraction, which depends
only on depth, the wave celerity scale McMh1/2; we can also obtain the
same result from the long shallow-water wave equation (equation (14.15)).
As for short deep-water waves, McML1/2(equation (14.14)) and ML
McMT(equation (14.1)), where MTis the wave period scale and MLthe
wavelength scale, this results in

Mc(ML1/2Mh1/2)MT. (16.14)

Thus we can have in this case a distorted model Mh-Ml. For reproducing
wave diffraction, the wave height along the obstacle must be correctly
reproduced and, therefore, MLMl, i.e. an undistorted model is required
if major scale effects are to be avoided.
Again, only the outline approach to river and coastal engineering
models has been discussed; for further detailed treatment of the subject
the reader is referred to, for example, Allen (1947), Yalin (1971), Kobus
(1980) or Novak and Cˇábelka (1981).

16.2 Structural models

16.2.1 General

Structural models of hydraulic structures are mainly models of dams and
their foundations – but see also models of gates (Section 16.1.3). Con-
ceived as a technique for verifying and developing the theoretical analysis
of more complex structures, physical modelling offers the advantage of a

MRMh



MlMd

MRMS



Md

MU^2 *



Md