# Is Drag Coefficient Constant for same shape, different size?

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1. Sep 28, 2015

### Typhon4ever

I've read that drag coefficient depends on the shape of the object but I am confused as to what shape means. Does it mean geometric shape or is area included in that? Say I have one sphere of radius r and keep fluid velocity, density, and viscosity constant and find its drag coefficient. Would its drag coefficient be different if I measured the drag coefficient of a sphere of radius R assuming again all other parameters are constant?

2. Sep 28, 2015

### Staff: Mentor

It can matter if you change the Reynolds number, e. g. if you change from laminar flow to turbulent flow or vice versa. If that doesn't happen, it is approximately constant if you scale the system up. Wind tunnels usually change more parameters (speed, temperature, ...) to simulate scaled models more accurately.

3. Sep 28, 2015

### Typhon4ever

If velocity, density, and viscosity are kept constant, would Reynolds number change? It shouldn't as long as the diameters of the testing pipe stay the same right?

4. Sep 28, 2015

### SteamKing

Staff Emeritus
Shape means the physical geometry of a body. All spheres have the same shape, just different radii.

The drag coefficient is a non-dimensional quantity which relates drag force with other key variables, like fluid velocity, density, and some physical characteristic of the body in question. Different bodies can have different physical characteristics selected for computing drag coefficient. For most simple shapes, like spheres, usually the characteristic chosen is the projected area of the body normal to the flow of the fluid. For other shapes, there may not be such a simple or obvious choice to be made.

Here is a plot of the drag coefficient of a sphere at different Reynold's numbers:

The study of drag coefficients is pretty involved, much too much to be covered in a forum post.

See this article for more discussion:

http://www.thermopedia.com/content/546/?tid=104&sn=1159

5. Sep 28, 2015

### boneh3ad

If you are doing the test correctly, the diameter Reynolds number of the test section (usually a wind tunnel, not a simple pipe) doesn't matter because it's not a fully-developed duct flow. It's a free stream with thin boundary layers on the walls.

The important parameter here is the Reynolds number based on diameter of the sphere, and that will change with the size. As long as you don't change flow regimes, though, the drag coefficient is essentially constant over several orders of magnitude of $Re_d$.

6. Sep 28, 2015

### Typhon4ever

Just so I am understanding this, by changing the radius of the sphere I am essentially changing the Reynolds number and thus the associated drag force? Are same shaped objects scale-able in terms of their drag force and drag coefficient or would I have to do separate experiments for both?

7. Sep 28, 2015

### SteamKing

Staff Emeritus
The Reynolds number is a means to determine what sort of flow regime in which you are performing your test and in which the real article operates. Drag coefficients, as shown in the sketch above, change depending on the Reynolds number of the flow experienced.

The drag of some simple objects, like spheres and cylinders, can be scaled up from model size to full size without too much hassle. Other objects with more complex shapes, like aircraft and ships, can be tested in model form and have their drag scaled up using special empirical techniques, because the Reynolds numbers for the model tests will often be several orders of magnitude smaller than the Reynolds numbers for the full-size article in operation.

It all depends on the shape you are testing and the flow conditions for which you want the full-size drag force.

8. Sep 29, 2015

### Staff: Mentor

If you scale your model down, you want to keep the Reynolds number similar to the original model. You can reduce the wind speed - but then you increase the Euler number, another relevant dimensionless parameter. In additin, you cannot test supersonic airflow with that approach.
Cryogenic wind tunnels like this one cool down the air to make the tests more realistic in terms of both dimensionless quantities.

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