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| !Shape and flow
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| !Form<br/>Drag
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| !Skin<br/>friction
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| |-
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| |[[File:Flow plate.svg|94px]]
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| | 0%
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| | 100%
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| |-
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| |[[File:Flow foil.svg|94px]]
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| | ~10%
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| | ~80%
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| |-
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| |[[File:Flow sphere.svg|94px]]
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| | ~90%
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| | ~10%
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| |-
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| |[[File:Flow plate perpendicular.svg|94px]]
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| | 100%
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| | 0%
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| |}
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| In [[fluid dynamics]], '''drag''' (sometimes called '''air resistance''', a type of friction, or '''fluid resistance''', another type of friction) refers to [[force]]s acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers (or surfaces) or a fluid and a [[solid]] surface. Unlike other resistive forces, such as dry [[friction]], which are nearly independent of velocity, drag forces depend on velocity.<ref>French (1970), p. 211, Eq. 7-20</ref><ref name=NASAdrag>{{cite web|title=What is Drag?|url=http://www.grc.nasa.gov/WWW/k-12/airplane/drag1.html}}</ref>
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| Drag forces always decrease fluid velocity relative to the solid object in the fluid's [[Pathline|path]].
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| ==Examples of drag==
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| Examples of drag include the component of the [[Net force|net]] [[Aerodynamic force|aerodynamic]] or [[hydrodynamics|hydrodynamic]] [[force]] acting opposite to the direction of movement of the solid object relative to the Earth as for cars, aircraft<ref name=NASAdrag/> and boat hulls; or acting in the same geographical direction of motion as the solid, as for sails attached to a down wind sail boat, or in intermediate directions on a sail depending on points of sail.<ref name=Eiffel>{{cite book|last=Eiffel|first=Gustave|title=The Resistance of The Air and Aviation|year=1913|publisher=Constable &Co Ltd|location=London}}</ref><ref name=Marchaj1>{{cite book|last=Marchaj|first=C. A.|title=Sail performance : techniques to maximise sail power|year=2003|publisher=Adlard Coles Nautical|location=London|isbn=978-0-7136-6407-2|pages=147 figure 127 lift vs drag polar curves|edition=Rev. ed.}}</ref><ref>{{cite web|title=Forces on sails|url=http://en.wikipedia.org/wiki/Forces_on_sails#Relationship_of_lift_coefficient_to_angle_of_incidence:_polar_diagram|work=Polar diagram after Eiffel|accessdate=16 October 2011}}</ref><ref name=Fossati1>{{cite book|last=Drayton|first=Fabio Fossati ; translated by Martyn|title=Aero-hydrodynamics and the performance of sailing yachts : the science behind sailing yachts and their design|year=2009|publisher=International Marine /McGraw-Hill|location=Camden, Maine|isbn=978-0-07-162910-2|pages=98 Fig 5.17 Chapter five Sailing Boat Aerodynamics}}</ref> In the case of viscous drag of [[Laminar flow|fluid in a pipe]], drag force on the immobile pipe decreases fluid velocity relative to the pipe.<ref name=Fowler>{{cite web|title=Calculating Viscous Flow: Velocity Profiles in Rivers and Pipes|url=http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/RiverViscosity.pdf|accessdate=16 October 2011}}</ref><ref>{{cite web|title=Viscous Drag Forces|url=http://www.ce.utexas.edu/prof/kinnas/319LAB/Applets/Viscous/viscous.html|accessdate=16 October 2011}}</ref>
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| ==Types of drag==
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| Types of drag are generally divided into the following categories:
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| *[[parasitic drag]], consisting of
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| **[[Parasitic_drag#Form_drag|form drag]],
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| **[[Parasitic_drag#Skin_friction|skin friction]],
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| **[[Parasitic_drag#Interference_drag|interference drag]],
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| *[[lift-induced drag]], and
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| *[[wave drag]] ([[aerodynamics]]) or wave resistance (ship hydrodynamics).
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| The phrase ''parasitic drag'' is mainly used in aerodynamics, since for lifting wings drag is in general small compared to lift. For flow around bluff bodies, drag is most often dominating, and then the qualifier "parasitic" is meaningless. Form drag, skin friction and interference drag on bluff bodies are not coined as being elements of "parasitic drag", but directly as elements of drag. <br>
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| Further, lift-induced drag is only relevant when [[wing]]s or a [[lifting body]] are present, and is therefore usually discussed either in the aviation perspective of drag, or in the design of either semi-planing or [[planing hull]]s. [[Wave drag]] occurs when a solid object is moving through a fluid at or near the [[speed of sound]] in that fluid—or in case there is a freely-moving fluid surface with [[ocean surface wave|surface waves]] radiating from the object, e.g. from a ship.
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| [[File:Drag sphere nasa.svg|right|thumb|Drag coefficient ''C''<sub>d</sub> for a sphere as a function of [[Reynolds number]] ''Re'', as obtained from laboratory experiments. The solid line is for a sphere with a smooth surface, while the dashed line is for the case of a rough surface.]]
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| Drag depends on the properties of the fluid and on the size, shape, and speed of the object. One way to express this is by means of the [[drag equation]]:
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| :<math>F_D\, =\, \tfrac12\, \rho\, v^2\, C_D\, A</math>
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| where
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| :''F<sub>D</sub>'' is the drag force,
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| :''ρ'' is the density of the fluid,<ref>Note that for the [[Earth's atmosphere]], the air density can be found using the [[barometric formula]]. It is 1.293 kg/m<sup>3</sup> at 0 °C and 1 [[atmosphere (unit)|atmosphere]].</ref>
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| :''v'' is the speed of the object relative to the fluid,
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| :''A'' is the cross-sectional area, and
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| :''C<sub>D</sub>'' is the [[drag coefficient]] – a [[dimensionless number|dimensionless]] number.
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| The drag coefficient depends on the shape of the object and on the [[Reynolds number]]:
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| :<math>R_e=\frac{vD}{\nu}</math>
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| where ''D'' is some characteristic diameter or linear dimension and ν is the [[kinematic viscosity]] of the fluid (equal to the [[viscosity]] μ divided by the density). At low Reynolds number, the drag coefficient is asymptotically proportional to the inverse of the Reynolds number, which means that the drag is proportional to the speed. At high Reynolds number, the drag coefficient is more or less constant. The graph to the right shows how the drag coefficient varies with Reynolds number for the case of a sphere.
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| For high velocities (or more precisely, at high [[Reynolds number]]) drag will vary as the square of [[velocity]]. Thus, the resultant power needed to overcome this drag will vary as the cube of velocity. The standard equation for drag is one half the coefficient of drag multiplied by the fluid [[mass density]], the [[cross sectional area]] of the specified item, and the square of the velocity.
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| ''Wind resistance'' is a layman's term for drag. Its use is often vague, and is usually used in a relative sense (e.g. a [[badminton]] [[shuttlecock]] has more ''wind resistance'' than a [[squash (sport)|squash]] ball).
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| == Drag at high velocity ==
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| {{main|Drag equation}}
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| [[File:194144main 022 drag.ogg|thumb|320px|Explanation of drag by [[NASA]].]]
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| As mentioned, the [[drag equation]] with a constant drag coefficient gives the force experienced by an object moving through a [[fluid]] at relatively large velocity (i.e. high [[Reynolds number]], ''R<sub>e</sub>'' > ~1000). This is also called ''quadratic drag''. The equation is attributed to [[Lord Rayleigh]], who originally used ''L''<sup>2</sup> in place of ''A'' (''L'' being some length).
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| :<math>F_D\, =\, \tfrac12\, \rho\, v^2\, C_d\, A,</math>
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| <sup>[[Drag_equation#Derivation|see derivation]]</sup>
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| The reference area ''A'' is often [[orthographic projection]] of the object—on a plane perpendicular to the direction of motion—e.g. for objects with a simple shape, such as a sphere, this is the [[cross section (geometry)|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.
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| In case of a wing, comparison of the drag to the [[lift force]] is easiest when the reference areas are the same, since then the ratio of drag to lift force is just the ratio of drag to [[lift coefficient]].<ref>[http://www.grc.nasa.gov/WWW/K-12/airplane/sized.html ''Size effects on drag''], from NASA Glenn Research Center.</ref> Therefore, the reference for a wing often is the [[planform]] (or wing) area rather than the frontal area.<ref>[http://www.grc.nasa.gov/WWW/K-12/airplane/geom.html ''Wing geometry definitions''], from NASA Glenn Research Center.</ref>
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| For an object with a smooth surface, and non-fixed [[flow separation|separation point]]s—like a sphere or circular cylinder—the drag coefficient may vary with Reynolds number ''R<sub>e</sub>'', even up to very high values (''R<sub>e</sub>'' of the [[order of magnitude|order]] 10<sup>7</sup>).
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| <ref>{{cite journal | last=Roshko | first=Anatol | title=Experiments on the flow past a circular cylinder at very high Reynolds number | journal=Journal of Fluid Mechanics | volume=10 | issue=3 | year=1961 | pages=345–356 | doi=10.1017/S0022112061000950 |bibcode = 1961JFM....10..345R }}</ref>
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| <ref name=Batch341>Batchelor (1967), p. 341.</ref>
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| For an object with well-defined fixed separation points, like a circular disk with its plane normal to the flow direction, the drag coefficient is constant for ''R<sub>e</sub>'' > 3,500.<ref name=Batch341/>
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| Further the drag coefficient ''C<sub>d</sub>'' is, in general, a function of the orientation of the flow with respect to the object (apart from symmetrical objects like a sphere).
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| === Power ===
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| The [[power (physics)|power]] required to overcome the aerodynamic drag is given by:
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| ::<math> P_d = \mathbf{F}_d \cdot \mathbf{v} = \tfrac12 \rho v^3 A C_d</math>
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| Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at {{convert|50|mph|km/h|abbr=on}} may require only {{convert|10|hp|kW|lk=in}} to overcome air drag, but that same car at {{convert|100|mph|km/h|abbr=on}} requires {{convert|80|hp|kW|abbr=on}}. With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much [[Mechanical work|work]]. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power. It's important to value the rolling resistance in relation to the drag force.
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| === Velocity of a falling object ===
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| {{main|Terminal velocity}}
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| The velocity as a function of time for an object falling through a non-dense medium, and released at zero relative-velocity ''v'' = 0 at time ''t'' = 0, is roughly given by a function involving a [[hyperbolic tangent]] (tanh):
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| ::<math> v(t) = \sqrt{ \frac{2mg}{\rho A C_d} } \tanh \left(t \sqrt{\frac{g \rho C_d A}{2 m}} \right). \,</math>
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| The hyperbolic tangent has a [[Limit of a function|limit]] value of one, for large time ''t''. In other words, velocity [[asymptotically]] approaches a maximum value called the [[terminal velocity]] ''v<sub>t</sub>'':
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| ::<math>v_{t} = \sqrt{ \frac{2mg}{\rho A C_d} }. \,</math>
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| For a potato-shaped object of average diameter ''d'' and of density ''ρ<sub>obj</sub>'', terminal velocity is about
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| ::<math>v_{t} = \sqrt{ gd \frac{ \rho_{obj} }{\rho} }. \,</math>
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| For objects of water-like density (raindrops, hail, live objects—mammals, birds, insects, etc.) falling in air near the surface of the Earth at sea level, terminal velocity is roughly equal to
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| ::<math>v_{t} = 90 \sqrt{ d }, \,</math>
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| with ''d'' in metre and ''v<sub>t</sub>'' in m/s. For example, for a human body (<math> \mathbf{} d </math> ~ 0.6 m) <math> \mathbf{} v_t </math> ~ 70 m/s, for a small animal like a cat (<math> \mathbf{} d </math> ~ 0.2 m) <math> \mathbf{} v_t </math> ~ 40 m/s, for a small bird (<math> \mathbf{} d </math> ~ 0.05 m) <math> \mathbf{} v_t </math> ~ 20 m/s, for an insect (<math> \mathbf{} d </math> ~ 0.01 m) <math> \mathbf{} v_t </math> ~ 9 m/s, and so on. Terminal velocity for very small objects (pollen, etc.) at low Reynolds numbers is determined by Stokes law.
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| Terminal velocity is higher for larger creatures, and thus potentially more deadly. A creature such as a mouse falling at its terminal velocity is much more likely to survive impact with the ground than a human falling at its terminal velocity. A small animal such as a [[cricket (insect)|cricket]] impacting at its terminal velocity will probably be unharmed. This, combined with the relative ratio of limb cross-sectional area vs. body mass (commonly referred to as the [[Square-cube law]]), explains why very small animals can fall from a large height and not be harmed.<ref>Haldane, J.B.S., [http://irl.cs.ucla.edu/papers/right-size.html "On Being the Right Size"]</ref>
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| == Very low Reynolds numbers: Stokes' drag ==
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| [[File:Inclinedthrow.gif|thumb|400px|[[Trajectory|Trajectories]] of three objects thrown at the same angle (70°). The black object does not experience any form of drag and moves along a parabola. The blue object experiences [[Stokes' law|Stokes' drag]], and the green object [[Newtonian fluid|Newton drag]].]]
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| {{main|Stokes' law}}
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| The equation for '''viscous resistance''' or '''linear drag''' is appropriate for objects or particles moving through a fluid at relatively slow speeds where there is no turbulence (i.e. low [[Reynolds number]], <math>R_e < 1</math>).<ref>[http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Dynamics/Forces/DragForce.html Drag Force<!-- Bot generated title -->]</ref> Note that purely laminar flow only exists up to Re = 0.1 under this definition. In this case, the force of drag is approximately proportional to velocity, but opposite in direction. The equation for viscous resistance is:<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/airfri.html Air friction], from Department of Physics and Astronomy, Georgia State University</ref>
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| :<math>\mathbf{F}_d = - b \mathbf{v} \,</math>
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| where:
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| :<math>\mathbf{} b </math> is a constant that depends on the properties of the fluid and the dimensions of the object, and
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| :<math> \mathbf{v} </math> is the velocity of the object
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| When an object falls from rest, its velocity will be
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| :<math>v(t) = \frac{(\rho-\rho_0)Vg}{b}\left(1-e^{-bt/m}\right)</math>
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| which asymptotically approaches the terminal velocity <math> \mathbf{} v_t = \frac{(\rho-\rho_0)Vg}{b}</math>. For a given <math>\mathbf{} b </math>, heavier objects fall more quickly.
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| For the special case of small spherical objects moving slowly through a [[viscosity|viscous]] [[fluid]] (and thus at small Reynolds number), [[George Gabriel Stokes]] derived an expression for the drag constant:
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| :<math>b = 6 \pi \eta r\,</math>
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| where:
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| :<math>\mathbf{} r </math> is the [[Stokes radius]] of the particle, and <math>\mathbf{} \eta </math> is the fluid viscosity.
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| The resulting expression for the drag is known as [[Stokes' drag]]:<ref>{{Cite book | publisher = Butterworth-Heinemann | isbn = 9780080928593 | last1 = Collinson | first1 = Chris | last2= Roper | first2 = Tom | title = Particle Mechanics | year = 1995 | page = 30 }}</ref>
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| :<math>\mathbf{F}_d = -6 \pi \eta r\, \mathbf{v}.</math>
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| For example, consider a small sphere with radius <math>\mathbf{} r </math> = 0.5 micrometre (diameter = 1.0 µm) moving through water at a velocity <math>\mathbf{} v </math> of 10 µm/s. Using 10<sup>−3</sup> Pa·s as the [[dynamic viscosity]] of water in SI units,
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| we find a drag force of 0.09 pN. This is about the drag force that a bacterium experiences as it swims through water.
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| == Drag in aerodynamics ==
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| {{main|Aerodynamic drag}}
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| === Lift-induced drag ===
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| {{main|Lift-induced drag}}
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| [[File:Induced drag r.svg|thumb|right|150px|Induced drag ''vs.'' lift<ref>Clancy, L.J. (1975) ''Aerodynamics'' Fig 5.24. Pitman Publishing Limited, London. ISBN 0-273-01120-0</ref><ref>Hurt, H. H. (1965) ''Aerodynamics for Naval Aviators'', Figure 1.30, NAVWEPS 00-80T-80</ref>]]
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| '''Lift-induced drag''' (also called '''induced drag''') is drag which occurs as the result of the creation of [[lift (force)|lift]] on a three-dimensional [[lifting body]], such as the [[wing]] or fuselage of an airplane. Induced drag consists of two primary components, including drag due to the creation of vortices ('''vortex drag''') and the presence of additional viscous drag ('''lift-induced viscous drag'''). The vortices in the flow-field, present in the wake of a lifting body, derive from the turbulent mixing of air of varying pressure on the upper and lower surfaces of the body, which is a necessary condition for the creation of [[lift (force)|lift]].
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| With other parameters remaining the same, as the [[lift (force)|lift]] generated by a body increases, so does the lift-induced drag. For an aircraft in flight, this means that as the [[angle of attack]], and therefore the [[lift coefficient]], increases to the point of stall, so does the lift-induced drag. At the onset of [[Stall (flight)|stall]], lift is abruptly decreased, as is lift-induced drag, but viscous pressure drag, a component of parasite drag, increases due to the formation of turbulent unattached flow on the surface of the body.
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| === Parasitic drag ===
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| {{main|parasitic drag}}
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| '''Parasitic drag''' (also called '''parasite drag''') is drag caused by moving a solid object through a fluid. Parasitic drag is made up of multiple components including viscous pressure drag ('''form drag'''), and drag due to surface roughness ('''skin friction drag'''). Additionally, the presence of multiple bodies in relative proximity may incur so called '''interference drag''', which is sometimes described as a component of parasitic drag.
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| In aviation, [[induced drag]] tends to be greater at lower speeds because a high [[angle of attack]] is required to maintain lift, creating more drag. However, as speed increases the induced drag becomes much less, but parasitic drag increases because the fluid is flowing more quickly around protruding objects increasing friction or drag. At even higher speeds in the [[transonic]], [[wave drag]] enters the picture. Each of these forms of drag changes in proportion to the others based on speed. The combined overall drag curve therefore shows a minimum at some airspeed - an aircraft flying at this speed will be at or close to its optimal efficiency. Pilots will use this speed to maximize [[Endurance (aircraft)|endurance]] (minimum fuel consumption), or maximize [[Glide ratio|gliding range]] in the event of an engine failure.
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| === Power curve in aviation ===
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| [[File:Drag Curve 2.jpg|right|thumb|200px|The ''power curve'': form and induced drag ''vs.'' airspeed]]
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| The interaction of parasitic and induced drag ''vs.'' airspeed can be plotted as a characteristic curve, illustrated here. In aviation, this is often referred to as the ''power curve'', and is important to pilots because it shows that, below a certain airspeed, maintaining airspeed counterintuitively requires ''more'' thrust as speed decreases, rather than less. The consequences of being "behind the curve" in flight are important and are taught as part of pilot training. At the subsonic airspeeds where the "U" shape of this curve is significant, wave drag has not yet become a factor, and so it is not shown in the curve.
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| === Wave drag in transonic and supersonic flow ===
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| [[File:Qualitive variation of cd with mach number.png|thumb|right|Qualitative variation in Cd factor with Mach number for aircraft]]
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| {{main|wave drag}}
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| '''Wave drag''' (also called '''compressibility drag''') is drag which is created by the presence of a body moving at high speed through a compressible fluid. In [[aerodynamics]], Wave drag consists of multiple components depending on the speed regime of the flight.
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| In transonic flight (Mach numbers greater than about 0.8 and less than about 1.4), wave drag is the result of the formation of shockwaves on the body, formed when areas of local supersonic (Mach number greater than 1.0) flow are created. In practice, supersonic flow occurs on bodies traveling well below the speed of sound, as the local speed of air on a body increases when it accelerates over the body, in this case above Mach 1.0. However, full supersonic flow over the vehicle will not develop until well past Mach 1.0. Aircraft flying at transonic speed often incur wave drag through the normal course of operation. In transonic flight, wave drag is commonly referred to as '''transonic compressibility drag'''. Transonic compressibility drag increases significantly as the speed of flight increases towards Mach 1.0, dominating other forms of drag at these speeds.
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| In supersonic flight (Mach numbers greater than 1.0), '''wave drag''' is the result of shockwaves present on the body, typically '''oblique shockwaves''' formed at the leading and trailing edges of the body. In highly supersonic flows, or in bodies with turning angles sufficiently large, '''unattached shockwaves''', or '''bow waves''' will instead form. Additionally, local areas of transonic flow behind the initial shockwave may occur at lower supersonic speeds, and can lead to the development of additional, smaller shockwaves present on the surfaces of other lifting bodies, similar to those found in transonic flows. In supersonic flow regimes, '''wave drag''' is commonly separated into two components, '''supersonic lift-dependent wave drag''' and '''supersonic volume-dependent wave drag'''.
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| The closed form solution for the minimum wave drag of a body of revolution with a fixed length was found by Sears and Haack, and is known as the '''Sears-Haack Distribution'''. Similarly, for a fixed volume, the shape for minimum wave drag is the '''Von Karman Ogive'''.
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| [[Busemann's Biplane]] is not, in principle, subject to wave drag at all when operated at its design speed, but is incapable of generating lift.
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| ==d'Alembert's paradox==
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| {{main|d'Alembert's paradox}}
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| In 1752 [[Jean le Rond d'Alembert|d'Alembert]] proved that [[potential flow]], the 18th century state-of-the-art [[inviscid flow]] theory amenable to mathematical solutions, resulted in the prediction of zero drag. This was in contradiction with experimental evidence, and became known as d'Alembert's paradox. In the 19th century the [[Navier–Stokes equations]] for the description of [[viscosity|viscous]] flow were developed by [[Adhémar Jean Claude Barré de Saint-Venant|Saint-Venant]], [[Claude-Louis Navier|Navier]] and [[George Gabriel Stokes|Stokes]]. Stokes derived the drag around a sphere at very low [[Reynolds number]]s, the result of which is called [[Stokes law]].<ref name=Batchelor>Batchelor (2000), pp. 337–343.</ref>
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| In the limit of high-Reynolds numbers the Navier–Stokes equations approach the inviscid [[Euler equations (fluid dynamics)|Euler equations]]; of which the potential-flow solutions considered by d'Alembert are solutions. However, at high Reynolds numbers all experiments showed there is drag. Attempts to construct inviscid [[steady flow]] solutions to the Euler equations, other than the potential flow solutions, did not result in realistic results.<ref name=Batchelor/>
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| The notion of [[boundary layer]]s—introduced by [[Ludwig Prandtl|Prandtl]] in 1904, founded on both theory and experiments—explained the causes of drag at high Reynolds numbers. The boundary layer is the thin layer of fluid close to the object's boundary, where viscous effects remain important when the viscosity becomes very small (or equivalently the Reynolds number becomes very large).<ref name=Batchelor/>
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| == See also ==
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| <div style="-moz-column-count:3; column-count:3;">
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| * [[Added mass]]
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| * [[Aerodynamic force]]
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| * [[Angle of attack]]
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| * [[Boundary layer]]
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| * [[Coandă effect]]
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| * [[Drag crisis]]
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| * [[Drag coefficient]]
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| * [[Drag equation]]
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| * [[Drag-resistant aerospike]]
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| * [[Gravity drag]]
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| * [[Keulegan–Carpenter number]]
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| * [[Morison equation]]
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| * [[Parasitic drag]]
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| * [[Ram pressure]]
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| * [[Reynolds number]]
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| * [[Stall (flight)]]
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| * [[Stokes' law]]
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| * [[Terminal velocity]]
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| </div>
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| ==Notes==
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| {{reflist|2}}
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| == References ==
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| *{{cite book | author=French, A. P. | title=Newtonian Mechanics (The M.I.T. Introductory Physics Series) | edition=1st | publisher=W. W. Norton & Company Inc., New York | year=1970 | isbn=978-0-393-09958-4}}
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| *{{cite book | author=Serway, Raymond A.; Jewett, John W. | title=Physics for Scientists and Engineers | edition=6th | publisher=Brooks/Cole | year=2004 | isbn=978-0-534-40842-8}}
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| *{{cite book | author=Tipler, Paul | title=Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics | edition=5th | publisher=W. H. Freeman | year=2004 | isbn=978-0-7167-0809-4}}
| |
| *{{cite book
| |
| | last = Huntley | first = H. E.
| |
| | year = 1967
| |
| | title = Dimensional Analysis
| |
| | publisher = Dover
| |
| | id = LOC 67-17978
| |
| }}
| |
| *{{cite book
| |
| | author=Batchelor, George
| |
| | authorlink=George Batchelor
| |
| | title=An introduction to fluid dynamics
| |
| | publisher=[[Cambridge University Press]]
| |
| | edition=2nd
| |
| | series=Cambridge Mathematical Library
| |
| | isbn=978-0-521-66396-0
| |
| | mr=1744638
| |
| | year=2000
| |
| }}
| |
| * Clancy, L.J. (1975), ''Aerodynamics'', Pitman Publishing Limited, London. ISBN 978-0-273-01120-0
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| | |
| == External links ==
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| *[http://arxiv.org/abs/physics/0609156 Educational materials on air resistance]
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| *[http://craig.backfire.ca/pages/autos/drag Aerodynamic Drag] and its effect on the acceleration and top speed of a vehicle.
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| *[http://www.apexgarage.com/tech/horsepower_calc.shtml Vehicle Aerodynamic Drag calculator] based on drag coefficient, frontal area and speed.
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| * [http://howthingsfly.si.edu Smithsonian National Air and Space Museum's How Things Fly website]
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| | |
| {{DEFAULTSORT:Drag (Physics)}}
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| [[Category:Aerodynamics]]
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| [[Category:Fluid dynamics]]
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