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I am using Engineering Equation Solver, and it has been telling me the units of my distribution are inconsistent.

According to a the book I am reading, I think it should be unitless (as it is a probability). However EES, says enter image description here

$$ h = \frac{k}{c}\cdot \left(\frac{v}{c}\right)^{k-1}\cdot exp\left(-\left(\frac{v}{c}\right)^{k}\right)$$ In theory, v and c have the same units [m/s] and k is unitless. I do not understand why the units are not working out.

Hope you can help me out.

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  • $\begingroup$ The equation solver, sorry about that! $\endgroup$
    – RMS
    Commented Feb 6, 2021 at 22:08

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If you have defined the same units for v and c then the equation should work just fine.

In all likelihood, h is the probability density so you its units should be $\frac{s}{m}$

In order to see where the problem lies, I would suggest breaking up the terms and checking their units independently within the software. I.e. I would find the units in EES for:

  • $\frac{k}{c}$ : the units should be $\frac{s}{m}$
  • $\frac{v}{c}$ : It should be unitless
  • $\left(\frac{v}{c}\right)^{k-1}$ : It should be unitless
  • $\exp\left(\left(\frac{v}{c}\right)^k\right)$ : It should be unitless

Then I would try to build up the equation to see, if the problem continues.

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