Coefficient of Drag

by omertech
Tags: coefficient, drag
 P: 13 Hello, I understood that in low velocities the standrad drag equation: $$F_d=\frac{ρv^2C_dA}{2}$$ Could linearized to something like: $$F_d=γv$$ I am looking for the drag coefficient(either γ or Cd) for either a prolate or a tri-axial ellipsoid at low velocities (less than 0.5 m/s) in water. I found some papers providing drag coefficients for relatively high velocities but none with drag coefficients for low velocities. Best regards
 P: 293 For spheres, the drag coefficient at low velocities can be determined analytically, see e.g. the book of Clift, Grace and Weber - Bubbles, Drops and Particles or Happel and Brenner, Low Reynolds number hydrodynamics. It is $\mathrm{C_d}=\frac{24}{\mathrm{Re}}$ With the Reynolds number $\mathrm{Re}=\frac{\rho v D}{\mu}$ Because A is the cross-sectional surface of the sphere, the force can be written as: $F_d=3\pi \mu D v$, which is known as Stokes' law. The drag of a nonspherical particle depends on its orientation with respect to the mean flow. For a prolate with aspect ratio E=b/a and oriented such that that the short axis with length a (from center to edge) is in the direction of the flow, the drag component is approximately $F_d=1.2\pi \mu (4+E) a v$. Note that when E=1, then 2a=D and Stokes' result is recovered. The derivation is for instance in Happel and Brenner's book.