Dimensional analysis and law of similarity

The method of dimensional analysis is used in every field of engineering. This method derives from the condition that each term summed in an equation depicting a physical relationship must have the same dimension. By constructing non-dimensional quantities expressing the relationship among the variables, it is possible to summarize the experimental results and to determine their functional relationship. To determine the characteristics of a full-scale device through model tests, besides geometrical similarity, similarity of dynamical conditions between the two is also necessary. When the dimensions of all terms of an equation are equal, the equation is dimensionally correct. In this case, whatever unit system is used, the equation holds its physical meaning. If the dimensions of all terms of an equation are not equal, dimensions must be hidden in coefficients so that only the designated units can be used. Such an equation would be void of physical interpretation. Utilizing the principle that the terms of physically meaningful equations have equal dimensions, the method of obtaining dimensionless groups of which the physical phenomenon is a function is called dimensional analysis.