Drag Coefficient: Does Cd Vary in Different Mediums?

[peterg07]

Hi

Is the drag coefficient for a particular object the same in different mediums? Say we have Cd = 1 in air for one object, is Cd the same for this object in water?

 

[D H]

The drag coefficient isn't even the same at different velocities in the same medium, let alone in different media.

 

[peterg07]

Thanks for the quick feedback, D H. Thread ended.

 

[cjl]

The drag coefficient isn't even the same at different velocities in the same medium, let alone in different media.

That depends. This gets into a discussion of nondimensional parameters - in a low speed flow, the drag coefficient will be the same so long as the reynolds number is similar. The reynolds number describes the relative importance of inertia and viscous forces on the fluid behavior. This is a key principle behind a lot of small scale testing of models in wind/water tunnels - similar reynolds number means similar flow behavior, including drag and lift coefficients and generation of turbulence.

In a high speed flow (greater than mach 0.3 or so, typically), you need to also match the mach number. This can still be done in different media, but it is more difficult to match both the reynolds and mach number properly. Depending on the flow parameters of interest, sometimes only one is matched, and the other is considered to be close enough to get useful data (but if this is the case, the drag and lift coefficient and flow behavior will not be identical between the model and the real situation).

In the case of water and air, with the same object in each and a low speed flow, we have a density ratio of about a thousand (air ~1 kg/m³, water ~1000kg/m³), a viscosity ratio of about 50 (air ~2*10^-5 Pa*s @ 300K, water ~1*10^-3 Pa*s @ 20C), so to match the reynolds number, we need a velocity in water that is 1/20 of the velocity in air. So, the drag coefficient of an object in 20C water at 5 mph should be similar to that of the same object in 300K (27C) air at 100 mph. We can also manipulate the length scale of the object to achieve similar results - a half-scale object in water at 10mph will also have a similar drag coefficient to a full scale in air at 100mph, and a quarter scale at 10mph in water will have a similar flow behavior to a full scale in air at 50mph. You could even manipulate the temperatures of the flows as well (changing the viscosity and density) or the pressure of the air flow (changing the density), and so long as the reynolds number stayed similar (and the flow stayed below mach 0.3 or so), the drag coefficient and flow behavior will be the same.

Basically, what I'm getting at here is that although DH is technically correct, there are parameters you can look at that do allow for comparisons between different media, different velocities, and different size scales, and as a result, you can actually get quite a bit of useful information by testing in a completely different environment than the intended one.