What are the Defects of Dimensional Analysis ?

Defects of Dimensional Analysis (i) While deriving a formula the proportionality constant cannot be found. (ii) The formula for a physical quantity depending on more than three other physical quantities cannot be derived. It can be checked only. (iii) The equations of the type $v=u \pm$ at cannot be derived. They can be checked only. (iv) The equations containing trigonometrical functions ( $\sin \theta, \cos \theta$, etc), logarithmic functions ( $\log x, \log x^{3}$ etc) and exponential functi...