Dimensional Analysis and Physical Laws
  Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and those for the arguments of functions. In particular, it is shown that there are three types of functions from a viewpoint of dimensional analysis. Relationships between Planck's constant and dimensional analysis are also considered. 
Shinji Tanimoto