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I am having problems with understanding the scaling process of the N-S equations in fluid dynamics.

From textbooks, I see that each quantity say velocity, time, length...etc are all divided some some reference values in order to obtain some dimensionaless quantity V*, t*, p*, g* etc..

And the N-S equations are then rewrite into a dimensionless form, the coefficients beceome the Reynolds number, Froude number etc...

And the writer says after having this dimensionless equation, we can know the importance of the terms by just looking at the coefficients.

That's what the textbook said, and I don't really understand. I can't catch the reason for making it in a dimensionless form. Can't I still judge the importance of the terms by looking at the coefficients of the terms when the equation have dimensions? Why must we transform it to be dimensionless?

Can anyone help me out?

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# Scaling of the N-S equations

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