response to development for complex situations are usually made using a physical model. The
physical model is designed to achieve similar behavior as that of the prototype. The
relationship of the governing physical processes and parameters must then be the same for
the model as for the prototype.
5.6.1 Physical Modeling
Physical models are used to test the performance of a design or to study the details of a
phenomenon. The performance tests of proposed structures can be made at moderate costs
and small risks on small-scale (physical) models. Similarly, the interaction of a structure and
the river environment can be studied in detail. In this regard, HEC-23 (Lagasse et al. 2001)
discusses the use of physical modeling in bridge scour and stream instability countermeasure
design.
The natural phenomena are governed by appropriate sets of governing equations. If these
equations can be integrated, the prediction of a given phenomena in time and space domains
can be made mathematically. In many cases related to river engineering, all the governing
equations are not known. Also, the known equations cannot be directly treated mathematically
for the geometries involved. In such cases, physical models are used to physically represent
solutions to the governing equations.
The similitude required between a prototype and a model implies two conditions:
1. To each point, time and process in the prototype, a uniquely coordinated point, time and
process exists in the model; and
2. The ratios of corresponding physical magnitudes between prototype and model are
constant for each type of physical quantity.
Rigid Boundary Models. To satisfy the preceding conditions in clear water, geometric,
kinematic, and dynamic similarities must exist between the prototype and the model.
Geometric similarity refers to the similarity of form between the prototype and its model.
Kinematic similarity refers to similarity of motion, while dynamic similarity is a scaling of masses
and forces. For kinematic similarity, patterns or paths of motion between the model and the
prototype should be geometrically similar. If similarity of flow is maintained between the model
and prototype, mathematical equations of motion will be identical for the two. Considering the
equations of motion, the dimensionless ratios of V / gy (Froude number) and Vy/ν (Reynolds
number) are both significant parameters in models of rigid boundary clear water open channel
flow. The Froude number represents the ratio of inertial to gravity forces in the system being
modeled, while the Reynolds number represents the ratio of inertial to friction (viscosity) forces.
It is seldom possible to achieve kinematic, dynamic and geometric similarity all at the same
time in a model. For instance, in open channel flow, gravitational forces predominate, and
hence, the effects of the Froude number are more important than those of the Reynolds
number. Therefore, the Froude criterion is used to determine the geometric scales, but only
with the knowledge that some scale effects, that is, departure from strict similarity, exists in the
model.
Ratios (or scales) of velocity, time, force and other characteristics of flow for two systems are
determined by equating the appropriate dimensionless number which applies to a dominant
force. If the two systems are denoted by the subscript m for model and p for prototype, then
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