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I came upon definition of the derivative functions for the cylinder as given below. I can't understand why the derivative with respect to "x/a" is introduced here. Coordinate "x" varies along the cylinder and "a" is the radius of the cylinder, so why is there ratio between these parameteres? enter image description here

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    Let $X:=x/a$, then the prime is a derivative wrt $X$. Why use $X$? Because it is much nicer to work with dimensionless variables. See for instance non dimensionalization – Sal Jul 06 '21 at 12:51
  • Ok. I just don't understand why two completely different parameteters are used here? What radius (which is constant) has to do with the change in length of the cylinder? If we want to nondimensionalize something shouldn't the parameteres relate to each other somehow? –  Jul 06 '21 at 13:08
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    Presumably the radius $a$ is the only length scale in the problem (eg. if the cylinder is of infinite extent) – Sal Jul 06 '21 at 13:10
  • Thank you for help. At least I got an understanding of why. –  Jul 06 '21 at 13:32

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