In my research I'm working with river profiles. We always define a concavity index which is a number in the range from 0.2 to 0.6. That index is necessary for the calculation of another indicator called Ksn. The units of Ksn (sort of a gradient that consider also other parameters related to the fluvial system) are in meters when the concavity index is equal to 0.5. When concavity is another value within that range, meters are raised to the power of some number since Ksn units are meters ^(1-2m) been m in this case the concavity index. How can I interpret this unit measure? What is a meter raised to the power of, let's say, 0.72? Thanks in advance.
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I do not think that something like $m^{0.72}$ where "$m$" stands for "meter" , makes any sense. We have $m$ , $m^2$ and $m^3$. That's it. – Peter Sep 15 '23 at 06:50
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If you want to be judicious about the units in your equations, and the equations include terms like "length to the power of 0.72", then I recommend changing the equation so that instead, you're first dividing it by a constant which is set to $=1~\text{m}$. Then, the term would look something like $$ \left( \frac{ \text{length}}{1~\text{m}} \right)^{0.72} $$ for which the output is unitless. It might not be pretty but at least the units are consistent. That's my two cents ... – Matti P. Sep 15 '23 at 07:25