[1] The similitude principle was developed by Wallace D. Hayes, a pioneer in hypersonic flow, which is considered to begin at about five times the speed of sound, or Mach 5, and is described in his classic book Hypersonic Flow Theory co-written with Ronald Probstein and first published in 1959.
The behavior of the physical processes in actual problems is affected by so many physical quantities that a complete mathematical description thereof is usually very difficult and sometimes practically impossible due to the complicated nature of the phenomena.
describe, and even predict the behavior of physical processes in real problems in a relatively simple manner.
Dimensional analysis is a method of deducing logical groupings of the variables, through which we can describe similarity criteria of the processes.
(courtesy: Book: Mass transfer : from fundamentals to modern industrial applications, Publisher: Weinheim : WILEY-VCH, 2006.