Coefficient of Drag

  1. Hello,

    I understood that in low velocities the standrad drag equation:
    [tex]F_d=\frac{ρv^2C_dA}{2}[/tex]
    Could linearized to something like:
    [tex]F_d=γv[/tex]
    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
     
    Last edited: Jan 12, 2013
  2. jcsd
  3. 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
    [itex]\mathrm{C_d}=\frac{24}{\mathrm{Re}}[/itex]
    With the Reynolds number
    [itex]\mathrm{Re}=\frac{\rho v D}{\mu}[/itex]

    Because A is the cross-sectional surface of the sphere, the force can be written as:
    [itex]F_d=3\pi \mu D v[/itex], 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
    [itex]F_d=1.2\pi \mu (4+E) a v[/itex].

    Note that when E=1, then 2a=D and Stokes' result is recovered. The derivation is for instance in Happel and Brenner's book.
     
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