Dimensional Analysis (DA)
Posted on September 21, 2021 Physical Modeling
Dimensional analysis (DA) is a method used to reduce the number and complexity of variables which affect physical phenomena of interest in our experiments and studies.
A simplified explanation of DA is to start with writing down all of the independent dimensional variables that affect the dependent performance of a process (e.g. physical dimensions, velocities, flow rates, material properties, temperatures, etc.).
Then, using a variety of methods including background knowledge and more formal techniques such as the Buckingham pi theorem, the independent dimensional parameters are grouped into a reduced set of dimensionless variables.
The result is a set of geometric variables that are physical size ratios, kinematic variables that are ratios of velocities, and dynamic variables that are ratios of forces.
While DA does not a priori reveal the details of the functional relationship between each independent dimensionless variable and dependent result, it provides the framework for analysis, scaling and experimental design.
Experiments correctly scaled to match the important dimensionless variables allow us to develop those functional relationships to solve client’s challenging problems.