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.

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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