Editing Drag coefficient (section)

== Definition ==
[[File:Hoerner fluid dynamic drag coefficients.svg|thumb|Table of drag coefficients in increasing order, of 2D shapes between walls (right column) and 3D shapes (left column), depicted with the same projected frontal area, at Reynolds numbers between 10<sup>4</sup> and 10<sup>6</sup> with flow from the left
<ref>{{cite book |last1=Hoerner |first1=Sighard F. |date=1965 |title= Fluid-Dynamic Drag : Practical Information on Aerodynamic Drag and Hydrodynamic Resistance |page=3–17 |edition=2 |url=https://archive.org/details/FluidDynamicDragHoerner1965}}</ref>]]
The drag coefficient <math>c_\mathrm d</math> is defined as

<math display=block>c_\mathrm d = \dfrac{ 2F_\mathrm d}{ \rho u^2 A}</math>

where:
* <math>F_\mathrm d</math> is the [[drag (physics)|drag force]], which is by definition the force component in the direction of the [[flow velocity]];<ref>See [[lift force]] and [[vortex induced vibration]] for a possible force components transverse to the flow direction</ref>
* <math>\rho</math> is the [[mass density]] of the fluid;<ref>Note that for the [[Earth's atmosphere]], the air density can be found using the [[barometric formula]]. Air is 1.293 kg/m<sup>3</sup> at {{convert|0|°C}} and 1 [[atmosphere (unit)|atmosphere]].</ref>
* <math>u</math> is the [[flow speed]] of the object relative to the fluid;
* <math>A</math> is the reference [[area]]

The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross-sectional area of the vehicle, depending on where the cross-section is taken. For example, for a sphere <math>A = \pi r^2</math> (note this is not the surface area = <math>4 \pi r^2</math>).

For [[airfoil]]s, the reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low, much lower than for a car with the same drag, frontal area, and speed.

[[Airship]]s and some [[Solid of revolution|bodies of revolution]] use the volumetric drag coefficient, in which the reference area is the [[square (algebra)|square]] of the [[cube root]] of the airship volume (volume to the two-thirds power). Submerged streamlined bodies use the wetted surface area.

Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less.

As a caution, note that although the above is the conventional definition for the drag coefficient, there are other definitions that one may encounter in the literature. The reason for this is that the conventional definition makes the most sense when one is in the Newton regime, such as what happens at high Reynolds number, where it makes sense to scale the drag to the momentum flux into the frontal area of the object. But, there are other flow regimes. In particular at very low Reynolds number, it is more natural to write the drag force as being proportional to a drag coefficient multiplied by the speed of the object (rather than the square of the speed of the object). An example of such a regime is the study of the mobility of aerosol particulates, such as smoke particles. This leads to a different formal definition of the "drag coefficient," of course.