Editing Drag coefficient (section)

== Blunt and streamlined body flows ==

=== Concept ===
The force between a fluid and a body, when there is relative motion, can only be transmitted by normal pressure and tangential friction stresses. So, for the whole body, the drag part of the force, which is in-line with the approaching fluid motion, is composed of frictional drag (viscous drag) and pressure drag (form drag). The total drag and component drag forces can be related as follows:

<math display="block">\begin{align}
c_\mathrm d &= \dfrac{2 F_\mathrm d}{\rho v^2 A}\\
&= c_\mathrm p + c_\mathrm f \\
&= \underbrace{ \dfrac{2}{\rho v^2 A} \displaystyle \int_{S} \mathrm{d}S  (p-p_o) \left(\hat{\mathbf{n}} \sdot \hat{\mathbf{i}}\right) }_{ c_\mathrm p }+ \underbrace{ \dfrac{2}{\rho v^2 A} \displaystyle \int_{S} \mathrm{d}S  \left(\hat{\mathbf{t}} \sdot \hat{\mathbf{i}}\right) T_{\rm w} }_{ c_\mathrm f}
\end{align}</math>

where:
*<math>A</math> is the planform area of the body,
*<math>S</math> is the wet surface of the body,
*<math>c_\mathrm p</math> is the [[pressure]] drag coefficient,
*<math>c_\mathrm f</math> is the [[friction]] drag coefficient,
*<math>\hat \mathbf{t} </math> is the unit vector in the direction of the shear stress acting on the body surface d''S'',
*<math>\hat \mathbf{n} </math> is the unit vector in the direction perpendicular to the body surface d''S'', pointing from the fluid to the solid,
*<math>T_\mathrm w</math> magnitude of the [[shear stress]] acting on the body surface d''S'',
*<math>p_\mathrm o</math> is the pressure far away from the body (note that this constant does not affect the final result),
*<math>p</math> is pressure at surface d''S'',
*<math>\hat{\mathbf{i}}</math> is the unit vector in direction of free stream flow

Therefore, when the drag is dominated by a frictional component, the body is called a '''streamlined body'''; whereas in the case of dominant pressure drag, the body is called a '''blunt''' or '''bluff body'''. Thus, the shape of the body and the angle of attack determine the type of drag. For example, an airfoil is considered as a body with a small angle of attack by the fluid flowing across it. This means that it has attached [[boundary layer]]s, which produce much less pressure drag.
[[File:Drag curves for aircraft in flight.svg|thumb|Trade-off relationship between zero-lift drag and lift induced drag]]
The [[Wake (physics)|wake]] produced is very small and drag is dominated by the friction component. Therefore, such a body (here an airfoil) is described as streamlined, whereas for bodies with fluid flow at high angles of attack, boundary layer separation takes place. This mainly occurs due to adverse [[pressure gradient]]s at the top and rear parts of an [[airfoil]].

Due to this, wake formation takes place, which consequently leads to eddy formation and pressure loss due to pressure drag. In such situations, the airfoil is [[Stall (flight)|stalled]] and has higher pressure drag than friction drag. In this case, the body is described as a blunt body.

A streamlined body looks like a fish ([[tuna]]), [[Oropesa (minesweeping)|Oropesa]], etc. or an airfoil with small angle of attack, whereas a blunt body looks like a brick, a cylinder or an airfoil with high angle of attack. For a given frontal area and velocity, a streamlined body will have lower resistance than a blunt body. Cylinders and spheres are taken as blunt bodies because the drag is dominated by the pressure component in the wake region at high [[Reynolds number]].

To reduce this drag, either the flow separation could be reduced or the surface area in contact with the fluid could be reduced (to reduce friction drag). This reduction is necessary in devices like cars, bicycle, etc. to avoid vibration and noise production.