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Power_of_Dimensional_Analysis - dimensions of the variables...

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The Power of Dimensional Analysis In some cases of dimensional analysis, particularly when there is only one nondimensional Π parameter, you can predict the trend of one variable as a function of the other variables – often to within a single constant. Example: For a soap bubble, P = function( σ s , R ). Dimensional analysis yields constant s P R ∆= We obtain this without knowing any physics of the problem; we need to know only the
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Unformatted text preview: dimensions of the variables involved in the problem. Compare this to the exact result, 4 s P R ∆ = In other words, an exact analysis tells us that the constant is equal to 4. However, the relationship between ∆ P , s , and R is known to within a single constant by the process of dimensional analysis. Dimensional analysis is very powerful indeed! Never underestimate the power of dimensional analysis!...
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