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Homework Help: Relating the Reynolds number to the Drag Coeffient

  1. Oct 21, 2006 #1
    How does one relate the Reynolds number to the Drag Coeffient?

    It seems the drag coefficient for different velocities must be determined experimentally per set. I know the Reynolds number is a method to determine laminar or turbulent flow, but can it be used to determine the drag coefficient?
  2. jcsd
  3. Oct 21, 2006 #2


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    See discussion on drag coeffient and the relationship between drag force and velocity here.

    In addition, Reynolds number is a function of velocity, and density, characteristic dimension (length), and viscosity.

    One can relate Re and Cd through velocity.
  4. Oct 22, 2006 #3
    Thank you for your response.

    The Drag coefficient is given by,

    [tex]\mbox{C}d\; =\; \frac{1}{2}\mbox{C}d\left( v \right)Apv^{2}[/tex]

    And the Reynolds number is given by,

    [tex]\mbox{Re}\; =\; \frac{vpl}{\mu }[/tex]

    I'm failing to see how to solve Cd in terms of the Reynolds number since the Reynolds number doesnt contain a drag force.
  5. Oct 24, 2006 #4
    Anyone? The clock is ticking :(
  6. Oct 25, 2006 #5


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    Taking [tex]Re\, =\, \frac{\rho vl}{\mu }[/tex], then

    [tex]Re^2\, =\, \frac{(\rho vl)^2}{\mu^2 }[/tex], or

    [tex]Re^2(\frac{\mu}{l})^2\, =\,(\rho v)^2}[/tex]

    The one looks at Cd

    [tex]C_d\; =\; \frac{1}{2}C_d\left( v \right)A\frac{(\rho v)^{2}}{\rho}[/tex]

    then do appropriate substitution.
  7. May 26, 2011 #6
    Does it matter if the medium has a very high viscosity? We were looking at a calculation in sea water with a Poise of 1.025. Some gents said that the calculation that we used should use v2 instead of v. What do the gurus think?
  8. May 26, 2011 #7


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    Unless you have some special kind of Cd, the drag force is usually proportional to v^2 rather than v. Without knowing what specific calculation you are talking about, deponent further sayeth not.
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