Limitations of Dimensional Analysis

Ashmeeta Bhattarai asked:

“What are limitations of principle of homogeneity of dimensional analysis?”

The dimensional analysis has the following limitations

  1. It fails while using it to derive a relation among physical quantities, if there are more than 3 unknown variables on which a given physical quantity depends
  2. It does not tell whether a given Physical quantity is a scalar or a vector.
  3. It does not tell us the value of constants involved
  4. It does not always tell us the exact FORM of a relation
  5. It cannot be used for deriving logarithmic, trigonometric or exponential relations
  6. A dimensionally correct equation may not always be the correct relation. (Because there are more than one physical quantity having the same dimensions)

Know some more? Write them as comments to this post


  1. Numbers are the Supreme Court of science. However Godel proved that we may not prove everything using numbers. Physics needs numbers. There must be Physics Foibles. Always more to prove.