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CHAPTER 3. PRINCIPLES OF SIMILITUDE
3.1 The Concept of Similitude
Ideally, a properly designed laboratory model should behave in all respects
like a controlled (usually miniature) version of the prototype. In a fluid flow
model this similar behavior includes the velocity, acceleration, and mass
transport of the fluid and the resultant forces that the fluid flow exerts on
solid bodies and boundaries.
Similitude is achieved when all major factors influencing reactions are
in proportion between prototype and model, while those factors that are
not in proportion throughout the modeled domain are so small as to be
insignificant to the process.
Requirements for similarity in coastal hydraulic models are established
on the basis of dynamical considerations, dimensional analysis, and differential equations. These requirements can be either criteria of similitude or
conditions of similarity. The difference between the two is significant.
Criteria of similitude are imposed by physical relationships between
parameters. They are mathematical conditions that must be met by the
ratios of certain parameters between prototype and model, and they cannot
be altered without altering the underlying physical assumptions. Similitude
criteria are also referred to as scale laws.
Conditions of similarity, on the other hand, are conditions that the
experimenter chooses in order to make the physical model reproduce satisfactory results. These conditions may include one or more similitude criteria
along with several conditions determined by observation or intuition.
A fundamental truth in analytical, physical, or numerical modeling is:
You cannot design a suitable model unless you understand1 the
basic underlying physics/theory of what you are studying.
Langhaar (1951).
The importance of the above quote cannot be overstated. Because selection
of criteria and conditions of similitude requires physical insight, a poor
understanding of the system’s physics can still lead to a functioning model
that produces incorrect (but often believable) results.
Model similitude can be established by a number of different methods.
• Similitude by Calibration. This is the oldest method,
dating back to physical models of the aqueducts of Rome.
Similitude conditions are obtained by calibrating a scale
model until it achieves reasonable reproduction of conditions known to have existed in the past. Calibration is
Understand in this context means that we are aware of the primary physical
mechanisms and their interaction in the phenomenon, but we lack knowledge of the
details of the interaction.
CHAPTER 3. PRINCIPLES OF SIMILITUDE
3.1 The Concept of Similitude
Ideally, a properly designed laboratory model should behave in all respects
like a controlled (usually miniature) version of the prototype. In a fluid flow
model this similar behavior includes the velocity, acceleration, and mass
transport of the fluid and the resultant forces that the fluid flow exerts on
solid bodies and boundaries.
Similitude is achieved when all major factors influencing reactions are
in proportion between prototype and model, while those factors that are
not in proportion throughout the modeled domain are so small as to be
insignificant to the process.
Requirements for similarity in coastal hydraulic models are established
on the basis of dynamical considerations, dimensional analysis, and differential equations. These requirements can be either criteria of similitude or
conditions of similarity. The difference between the two is significant.
Criteria of similitude are imposed by physical relationships between
parameters. They are mathematical conditions that must be met by the
ratios of certain parameters between prototype and model, and they cannot
be altered without altering the underlying physical assumptions. Similitude
criteria are also referred to as scale laws.
Conditions of similarity, on the other hand, are conditions that the
experimenter chooses in order to make the physical model reproduce satisfactory results. These conditions may include one or more similitude criteria
along with several conditions determined by observation or intuition.
A fundamental truth in analytical, physical, or numerical modeling is:
You cannot design a suitable model unless you understand1 the
basic underlying physics/theory of what you are studying.
Langhaar (1951).
The importance of the above quote cannot be overstated. Because selection
of criteria and conditions of similitude requires physical insight, a poor
understanding of the system’s physics can still lead to a functioning model
that produces incorrect (but often believable) results.
Model similitude can be established by a number of different methods.
• Similitude by Calibration. This is the oldest method,
dating back to physical models of the aqueducts of Rome.
Similitude conditions are obtained by calibrating a scale
model until it achieves reasonable reproduction of conditions known to have existed in the past. Calibration is
Understand in this context means that we are aware of the primary physical
mechanisms and their interaction in the phenomenon, but we lack knowledge of the
details of the interaction.