2.2. PRINCIPLES OF DIMENSIONAL ANALYSIS
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material properties are the properties of the fluid, such
as density, dynamic viscosity, surface tension, etc. When
the system response includes interaction with solid, permeable, or movable boundaries, then variables related to these
boundary characteristics must also be selected. Common
parameters might include breakwater permeability, sediment grain size and density, or surface roughness.
• External Effects. This category contains variables that
characterize any external effects that produce a change in
the physical system being considered. For coastal hydrodynamics, typical parameters of this type include pressures,
velocities, accelerations (gravity), wind shear stress, etc.
Most physical variables will fall into one of the above broad categories.
Munson, et al. (1990) offered six points to consider when selecting
variables for use in dimensional analysis:
1. Clearly define the problem and determine the main variables of interest.
2. Consider the basic laws governing the physical process,
even if only a crude theory can be formulated.
3. List variables into the three broad categories of geometric,
material properties, and external effects.
4. Consider other variables that do not fit into one of the three
broad variable categories. Time is an important parameter
in many situations.
5. Include physical parameters that are considered constant,
such as acceleration of gravity. These parameters are useful
in forming dimensionless parameters.
6. Make certain all variables are independent by looking for
functional relationships among the selected variables within
each broad category. For example, fluid specific weight (7),
fluid density (p), and gravity ( known expression 7 = p g, therefore, only two of the three
variables can be considered independent.
In summary, it is best to have some theory about the process, what the
major variables are, and how these variables are affecting the process. If
differential equations describing a process have been derived, they immediately give the significant variables of the problem. Although dimensional
analysis can be complicated in cases where there are a large number of
variables, there are many situations, both analytical and experimental, in
which the procedure is a useful tool.
29
material properties are the properties of the fluid, such
as density, dynamic viscosity, surface tension, etc. When
the system response includes interaction with solid, permeable, or movable boundaries, then variables related to these
boundary characteristics must also be selected. Common
parameters might include breakwater permeability, sediment grain size and density, or surface roughness.
• External Effects. This category contains variables that
characterize any external effects that produce a change in
the physical system being considered. For coastal hydrodynamics, typical parameters of this type include pressures,
velocities, accelerations (gravity), wind shear stress, etc.
Most physical variables will fall into one of the above broad categories.
Munson, et al. (1990) offered six points to consider when selecting
variables for use in dimensional analysis:
1. Clearly define the problem and determine the main variables of interest.
2. Consider the basic laws governing the physical process,
even if only a crude theory can be formulated.
3. List variables into the three broad categories of geometric,
material properties, and external effects.
4. Consider other variables that do not fit into one of the three
broad variable categories. Time is an important parameter
in many situations.
5. Include physical parameters that are considered constant,
such as acceleration of gravity. These parameters are useful
in forming dimensionless parameters.
6. Make certain all variables are independent by looking for
functional relationships among the selected variables within
each broad category. For example, fluid specific weight (7),
fluid density (p), and gravity ( known expression 7 = p g, therefore, only two of the three
variables can be considered independent.
In summary, it is best to have some theory about the process, what the
major variables are, and how these variables are affecting the process. If
differential equations describing a process have been derived, they immediately give the significant variables of the problem. Although dimensional
analysis can be complicated in cases where there are a large number of
variables, there are many situations, both analytical and experimental, in
which the procedure is a useful tool.