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

Armando V.D.B. Assis (1)

1 Departamento de Física [Universidade Federal de Santa Catarina]

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.

Mots clés: Drag coefficient; Drag force; drag crisis; quadratic force derivation; drag force on sphere; Reynolds number; turbulence

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Dynamique des Fluides [physics.flu-dyn]

Armando V.D.B. Assis. Analytical Derivation of the Drag Curve $C_{D}=C_{D}\left(\mathcal{R}\right)$. 2011. ⟨hal-00653695⟩