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Limitations of Dimensional Analysis

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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)

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