What are the limitations of dimensional analysis?

Explanation

1. This method gives to information about the dimensionaless constants in the formula like 1,2 …………., `pi` ,e, etc.
2. This method cannot decide whether the given quantity is a vector or a scalar.
3. This method is not suitable to derive relations involving trigonometric, exponential and logarithmic functions.
4. It cannot be applied to an equation involving more than three physical quantities.
5. It can only check on whether a physical relation is dimensionally correct but not the correctness of the relation. for example using dimensional analysis , `s = ut + 1/3 at^2 ` is dimensionally correct whereas the correct relation is `s = ut + 1/2 at^2`