Relating the Reynolds number to the Drag Coeffient

[Noone1982]

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?

 

[Astronuc]

See discussion on drag coeffient and the relationship between drag force and velocity here.
http://www.grc.nasa.gov/WWW/K-12/airplane/dragco.html

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

One can relate Re and Cd through velocity.

 

[Noone1982]

Thank you for your response.

The Drag coefficient is given by,

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

And the Reynolds number is given by,

\mbox{Re}\; =\; \frac{vpl}{\mu }

I'm failing to see how to solve Cd in terms of the Reynolds number since the Reynolds number doesn't contain a drag force.

 

[Noone1982]

Anyone? The clock is ticking :(

 

[Astronuc]

Taking Re\, =\, \frac{\rho vl}{\mu }, then

Re^2\, =\, \frac{(\rho vl)^2}{\mu^2 }, or

Re^2(\frac{\mu}{l})^2\, =\,(\rho v)^2}

The one looks at C_d

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

then do appropriate substitution.

 

[kurtdtn]

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?

 

[SteamKing]

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.