Homework Help: Relating the Reynolds number to the Drag Coeffient

1. Oct 21, 2006

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?

2. Oct 21, 2006

Astronuc

Staff Emeritus
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.

3. Oct 22, 2006

Noone1982

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 doesnt contain a drag force.

4. Oct 24, 2006

Noone1982

Anyone? The clock is ticking :(

5. Oct 25, 2006

Astronuc

Staff Emeritus
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 Cd

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

then do appropriate substitution.

6. May 26, 2011

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?

7. May 26, 2011

SteamKing

Staff Emeritus
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.