Editing Drag equation (section)

{{Short description|Equation for the force of drag}}
{{Use mdy dates |date=June 2022}}

In [[fluid dynamics]], the '''drag equation''' is a formula used to calculate the force of [[drag (physics)|drag]] experienced by an object due to movement through a fully enclosing [[fluid]]. The equation is:
<math display="block">F_{\rm d}\, =\, \tfrac12\, \rho\, u^2\, c_{\rm d}\, A</math>
where
*<math>F_{\rm d}</math> is the drag [[force]], which is by definition the force component in the direction of the flow velocity,
*<math>\rho</math> is the [[mass density]] of the fluid,<ref>For the [[Earth's atmosphere]], the air density can be found using the [[barometric formula]]. Air is {{cvt|1.293|kg/m3|lb/cuft}} at {{cvt|0|C|F|0}} and 1  [[atmosphere (unit)|atmosphere]]</ref>
*<math>u</math> is the [[flow velocity]] relative to the object,
*<math>A</math> is the reference [[area]], and
*<math>c_{\rm d}</math> is the [[drag coefficient]] – a [[dimensionless number|dimensionless]] [[physical coefficient|coefficient]] related to the object's geometry and taking into account both [[skin friction]] and [[form drag]]. If the fluid is a liquid, <math>c_{\rm d}</math> depends on the [[Reynolds number]]; if the fluid is a gas, <math>c_{\rm d}</math> depends on both the Reynolds number and the [[Mach number]].

The equation is attributed to [[Lord Rayleigh]], who originally used ''L''<sup>2</sup> in place of ''A'' (with ''L'' being some linear dimension).<ref>See Section 7 of Book 2 of Newton's [[Principia Mathematica]]; in particular Proposition 37.</ref>

The reference area ''A'' is typically defined as the area of the [[orthographic projection]] of the object on a plane perpendicular to the direction of motion. For non-hollow objects with simple shape, such as a sphere, this is exactly the same as the maximal [[cross section (geometry)|cross sectional]] area. For other objects (for instance, a rolling tube or the body of a cyclist), ''A'' may be significantly larger than the area of any cross section along any plane perpendicular to the direction of motion. [[Airfoils]] use the square of the [[chord (aircraft)|chord length]] as the reference area; since airfoil chords are usually defined with a length of 1, the reference area is also 1. Aircraft use the wing area (or rotor-blade area) as the reference area, which makes for an easy comparison to [[lift (force)|lift]]. [[Airship]]s and [[Solid of revolution|bodies of revolution]] use the volumetric coefficient of drag, in which the reference area is the square of the [[cube root]] of the airship's volume. Sometimes different reference areas are given for the same object in which case a drag coefficient corresponding to each of these different areas must be given.

For sharp-cornered [[bluff body|bluff bodies]], like square cylinders and plates held transverse to the flow direction, this equation is applicable with the drag coefficient as a constant value when the [[Reynolds number]] is greater than 1000.<ref>[http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Dynamics/Forces/DragForce.html Drag Force<!-- Bot generated title -->] {{webarchive |url=https://web.archive.org/web/20080414225930/http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Dynamics/Forces/DragForce.html |date=April 14, 2008 }}</ref> For smooth bodies, like a cylinder, the drag coefficient may vary significantly until Reynolds numbers up to 10<sup>7</sup> (ten million).<ref>See Batchelor (1967), p. 341.</ref>