ABSTRACT
When we have a complete understanding of physics and have no difficulty with formulation but are mathematically stuck before solution, dimensional analysis provides a functional (implicit) form of solution. Actually, there exists three distinct methods for dimensional analysis: formulation, Π- theorem, and physical similitude. Whenever a formulation is readily available, term-by-term nondimensionalization of this formulation leads directly to the related dimensionless numbers. The procedure is not suitable to problems which cannot be readily formulated. If a formulation is not readily accessible but all physical and geometric quantities which characterize a physical situation are clearly known, we write an implicit relation among these quantities. Ratios established from the individual terms of appropriate general principles gives the dimensionless numbers. The great convenience of this method is that there is no need to worry about an explicit formulation, except for a clear understanding of terms comprising a general principle.
