This document presents the derivation of the Navier-Stokes equations in cylindrical coordinates. I have searched on the web for something similar (and I have seen that a lot of other people search for the steps of such a derivation), but I have been unsuccessful. For this reason I have thought to write a document describing step-by-step how to obtain the equations, starting from the Cauchy momentum equation. It is quite tedious but it helps in the understanding of differential calculus and derivation of conservation equations in cylindrical coordinates. As a corollary, the equations for axisymmetric and Hagen-Poiseulle flows are derived from the general Navier-Stokes equations in cylindrical coordinates. If you find any error of typo, please send me an email.
You can download here a pdf of the document, or read it online at:
https://demichie.github.io/NS_cylindrical/
2023-09-27. Fixed an error in Eq.22 (Thanks to Abdallah Daddi-Moussa-Ider)