Theory of Dimensional Analysis

Dimensions of Commonly Used Physical Quantities in Engineering 

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The theory of dimensional analysis indicates that the dimensionless variables are formed by the products of powers of certain of the original dimensional variables. For this reason, the generalized dimensionless variables are often termed dimensionless products and are denoted by the symbox 77. The four dimensionless variables required in the present problem will, therefore, be denoted by 77. 772, 773, and 7r4. Eq. (1.23) can, therefore, be reduced to the following form ... 

The theory of dimensional analysis shows that each of these tt s must contain one prime dimensional variable which does not occur in any of the other tt s, together with other dimensional variables which occur in all the 77 s. In the present problem there are, of course, eight dimensional variables and four 77 s so four prime variables must be selected and there will also be four other dimensional variables which occur in all the 7r s. 

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