Limitation of dimensions analysis
There are several limitations of dimensional analysis, including:
1. It assumes that the physical relationship between variables can be expressed solely based on their dimensions. However, this assumption may not hold true in all cases as there may be other factors affecting the relationship.
2. It cannot determine the presence of dimensionless quantities or dimensionless constants, which are often encountered in physics and engineering problems.
3. It does not provide any information about the numerical values or coefficients associated with the variables under consideration. It only focuses on the relationship between the variables based on their dimensions.
4. It is not applicable to all types of physical phenomena. For example, it is not well suited for analyzing complex systems or systems with multiple variables and interactions.
5. It may lead to erroneous conclusions if the variables involved have different units or if there are differences in the units chosen for analysis.
6. It is only valid for linear relationships between variables. Non-linear relationships between variables cannot be accurately analyzed using dimensional analysis alone.
7. It does not consider the effects of non-dimensionalization, which involves normalizing the variables to a certain scale. Non-dimensionalization can provide further insights into the physical relationship between variables but is not accounted for in dimensional analysis alone.