# Scaling of the N-S equations

by hanson
Tags: equations, scaling
 Sci Advisor HW Helper PF Gold P: 4,119 Certainly, you don't have to use dimensionless variables. However, using dimensionless variables can simplify the analysis of a problem. First, it cuts down the number of symbols in the equation. (Less writing!) This often highlights the "[standard] form" of an equation. It may be easier to recognize the mathematics, and possibly draw analogies between different physical systems. (For example, it may help you recognize that the mass-spring system is analogous to an inductor-capacitor system.) Additionally, one can't compare A with B (i.e. one can't say A>B) if they carry different dimensions. However, if $$\alpha$$ and $$\beta$$ are dimensionless, then one can compare them. In particular, it may useful to know that $$\alpha\gg\beta$$ so that the $$\beta$$-term in an expression like $$\alpha \blacksquare + \beta \blacksquare +\ldots$$ may be neglected. Implicit in the above is the idea of "scaling". For example, if you know how a problem scales, you can experimentally model it less expensively. (For example, wind tunnel tests for airplanes. Another example: special effects using miniatures and slow-motion.)