A Glimpse of Dimensional Analysis

There are two classical methods in dimensional analysis, Buckingham s pi theorem and the method of indices by Lord Rayleigh. Here we will briefly explain the more common of the two Buckingham s theorem. 

Buckingham s theorem. This theorem can be divided into three steps as shown below (Sonin 2001). Step 1 define the dependent variable and find all the relevant independent variables. This is a critical and, normally, difficult task. A simple example will be to relate the distance covered (dependent variable) by a body in fi-ee fall before hitting the ground. Assuming that the air resistance is negligible, the two independent variables are time (t) and acceleration of gravity (g)  

Step 2 identify the dimensions of the dependent and independent variables. In our example  

Step 3 If an equation contains n separate variables and dimemional constants and these are given dimensionless formulas in terms of m fundamental dimensions, then the number of dimensionless groups in a complete set is n — m (Johnstone and Thrings 1957). In our example, we have three variables, including g, a dimensional constant (d, t, and g), and we have two fundamental dimensions L and t). Thus, we can form just one dimensionless group. 

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