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The 'drag equation' is a practical formula used to calculate the force of drag experienced by an object due to a fluid that it is moving through. The equation is attributed to Lord Rayleigh, who originally used $L^2$ in place of $A$ (L being some linear dimension). The force on a moving object due to a fluid is:
:$mathbf\{F\}\_d\; =\; \{1\; over\; 2\}$
ho mathbf{v}^2 C_d A^{see derivation}
where
:'F'_d is the force of drag,
:ρ is the density of the fluid (''Note that for the Earth's atmosphere, the density can be found using the barometric formula. (Air is 1.293 kg/m³ at 0°C and 1 atmosphere''),
:'v' is the velocity of the object relative to the fluid,
:''A'' is the reference area, and
:''C_d'' is the drag coefficient (a dimensionless constant, e.g. 0.25 to 0.45 for a car).
The reference area ''A'' is the area of the projection of the object on a plane perpendicular to the direction of motion (ie cross-sectional area). 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. The reference for a wing would be the plane area rather than the frontal area.

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Discussion

The equation is based on an idealized situation where all of the fluid impinges on the reference area and comes to a complete stop, building up stagnation pressure over the whole area. No real object exactly corresponds to this behavior. ''C_d'' is the ratio of drag for any real object to that of the ideal object. In practice a rough unstreamlined body (a bluff body) will have a ''C_d'' around 1, more or less. Smoother objects can have much lower values of ''C_d''. The equation is precise--it simply provides the definition of ''C_d'' (drag coefficient), which varies with the Reynolds number and is found by experiment.
Of particular importance is the ''v''² dependence on velocity, meaning that fluid drag increases with the square of velocity.
Force is equivalent to the change of momentum divided by time. This is in contrast with solid-on-solid friction, which generally has very little velocity dependence.

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See also

★ angle of attack

★ stall

★ terminal velocity