- #1
jimmy1066
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Homework Statement
A function [tex]f(x)[/tex] has dimensions of length, [tex]L[/tex].
I need to non-dimensionalize [tex]f(x)[/tex] using the substitution [tex]x=zL[/tex] and then differentiate it with respect to [tex]z[/tex].
Homework Equations
[tex]x=zL[/tex]
The Attempt at a Solution
First I made the substitution:
[tex]f(x) \Rightarrow f(zL)[/tex]
[tex]\frac{\partial f(zL)}{\partial z}[/tex] = L f '(z L)
Is this correct? I'm not sure because this now has dimensions of length.
What happens if I write: f(x) = f(zL) = f(x(z)) = F(z) and then differentiate w.r.t. z?