Condensed Matter


Analytical Derivation of the Drag Curve $C_{D}=C_{D}\left(\mathcal{R}\right)$

Authors: Armando V.D.B. Assis

Through a convenient mathematical approach for the Navier-Stokes equation, we obtain the quadratic dependence $v^{2}$ of the drag force $F_{D}$ on a falling sphere, and the drag coefficient, $C_{D}$, as a function of the Reynolds number. Viscosity effects related to the turbulent boundary layer under transition, from laminar to turbulent, lead to the tensorial integration related to the flux of linear momentum through a conveniently choosen control surface in the falling reference frame. This approach turns out to provide an efficient route for the drag force calculation, since the drag force turns out to be a field of a non-inertial reference frame, allowing an arbitrary and convenient control surface, finally leading to the quadratic term for the drag force.

Comments: 5 pages. English.

Download: PDF

Submission history

[v1] 2011-12-20 08:13:04
[v2] 2012-01-29 22:54:30
[v3] 2012-01-30 11:37:16

Unique-IP document downloads: 247 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus