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Could someone please explain me how to derive the mathematical relationship between the two?

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    $\begingroup$ If you look at the wikipedia pages, en.wikipedia.org/wiki/Drag_coefficient and en.wikipedia.org/wiki/Reynolds_number you will see it depends on the physical conditions, airfoils, pipes, flat plates, you name it.....I mean that literally , what object have you got in mind? What have you tried yourself? $\endgroup$ – user108787 Sep 12 '16 at 23:09
  • $\begingroup$ @CountTo10 Suppose you have an object travelling in a fluid (for example an object in free fall in the atmosphere) how could I relate the drag coefficient to the reynolds in that case? $\endgroup$ – mickkk Sep 13 '16 at 9:14
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I was a drilling fluid engineer many decades ago and we then calculated by hand daily the pressure drop through our drill bits, equivelant circulating densities Etc.. Oh the good old days, Try the link www.drillinghandbook.com/category/engineering-calculations Mostly under the section drilling pressure losses. This might help.

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