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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 formula is accurate only under certain conditions: the objects must have a blunt form factor and the fluid must have a large enough [[Reynolds number]] to produce [[turbulence]] behind the object. The equation is
:<math>F_D\, =\, \tfrac12\, \rho\, v^2\, C_D\, A</math>
where
:''F<sub>D</sub>'' is the [[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>
:''ρ'' 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 0°C and 1  [[atmosphere (unit)|atmosphere]]</ref>
:''v'' is the [[velocity]] of the object relative to the fluid,
:''A'' is the reference [[area]], and
:''C<sub>D</sub>'' is the [[drag coefficient]] – a [[dimensionless number|dimensionless]] [[coefficient]] related to the object's geometry and taking into account both [[skin friction]] and [[form drag]].
 
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 a [[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|Airships]] 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 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 -->]</ref> For smooth bodies, like a circular 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>
 
== 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 [[Pressure#Stagnation pressure|stagnation pressure]] over the whole area. No real object exactly corresponds to this behavior. ''C<sub>D</sub>'' 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<sub>D</sub>'' around 1, more or less. Smoother objects can have much lower values of ''C<sub>D</sub>''. The equation is precise – it simply provides the definition of ''C<sub>D</sub>'' ([[drag coefficient]]), which varies with the [[Reynolds number]] and is found by experiment.
 
Of particular importance is the <math>u^2</math> dependence on velocity, meaning that fluid drag increases with the square of velocity. When velocity is doubled, for example, not only does the fluid strike with twice the velocity, but twice the [[mass]] of fluid strikes per second. Therefore the change of [[momentum]] per second is multiplied by four. [[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.
 
== Derivation == <!-- [[Drag (physics)]] links here -->
The '''drag equation''' may be derived to within a multiplicative constant by the method of [[dimensional analysis]]. If a moving fluid meets an object, it exerts a force on the object. Suppose that the variables involved – under some conditions – are the:
* speed ''u'',
* fluid density ''ρ'',
* viscosity ''ν'' of the fluid,  
* size of the body, expressed in terms of its frontal area ''A'', and
* drag force ''F<sub>D</sub>''.  
Using the algorithm of the [[Buckingham π theorem]], these five variables can be reduced to two dimensionless parameters:
* [[drag coefficient]] ''C<sub>D</sub>'' and
* [[Reynolds number]] ''R''<sub>e</sub>.
 
Alternatively, the dimensionless parameters via direct manipulation of the underlying differential equations.
 
That this is so becomes apparent when the drag force ''F<sub>D</sub>'' is expressed as part of a function of the other variables in the problem:
 
:<math>
  f_a(F_D,\, u,\, A,\, \rho,\, \nu)\, =\, 0. \,
</math>
 
This rather odd form of expression is used because it does not assume a one-to-one relationship. Here, ''f<sub>a</sub>'' is some (as-yet-unknown) function that takes five arguments. Now the right-hand side is zero in any system of units; so it should  be possible to express the relationship described by ''f<sub>a</sub>'' in terms of only dimensionless groups.
 
There are many ways of combining the five arguments of ''f<sub>a</sub>'' to form dimensionless groups, but the [[Buckingham π theorem]] states that there will be two such groups.  The most appropriate are the Reynolds number, given by
 
:<math>
  \mathrm{Re}\, =\, \frac{u\,\sqrt{A}}{\nu}
</math>
 
and the drag coefficient, given by
 
:<math>
  C_D\, =\, \frac{F_D}{\frac12\, \rho\, A\, u^2}.
</math>
 
Thus the function of five variables may be replaced by another function of only two variables:
 
:<math>
  f_b\left( \frac{F_D}{\frac12\, \rho\, A\, u^2},\, \frac{u\, \sqrt{A}}{\nu} \right)\, =\, 0.
</math>
 
where ''f<sub>b</sub>'' is some function of two arguments.
The original law is then reduced to a law involving only these two numbers.
 
Because the only unknown in the above equation is the drag force ''F<sub>D</sub>'', it is possible to express it as
 
:<math>
  \frac{F_D}{\frac12\, \rho\, A\, u^2}\, =\, f_c\left( \frac{u\, \sqrt{A}}{\nu} \right)
</math>
 
or
 
:<math>
  F_D\, =\, \tfrac12\, \rho\, A\, u^2\, f_c(R_e), \,
</math> &nbsp; &nbsp; and with &nbsp; &nbsp; <math> C_D\, =\, f_c(R_e).</math>
 
Thus the force is simply ½ ''ρ'' ''A'' ''u<sup>2</sup>'' times some (as-yet-unknown) function ''f<sub>c</sub>'' of the Reynolds number ''R''<sub>e</sub> – a considerably simpler system than the original five-argument function given above.
 
Dimensional analysis thus makes a very complex problem (trying to determine the behavior of a function of five variables) a much simpler one: the determination of the drag as a function of only one variable, the Reynolds number.
 
The analysis also gives other information for free, so to speak.  The analysis shows that, other things being equal, the drag force will be proportional to the density of the fluid. This kind of information often proves to be extremely valuable, especially in the early stages of a research project.
 
To empirically determine the Reynolds number dependence, instead of experimenting on huge bodies with fast-flowing fluids (such as real-size airplanes in wind-tunnels), one may just as well experiment on small models with more viscous and higher velocity fluids, because these two systems are [[Similitude (model)|similar]].
 
== See also ==
* [[Aerodynamic drag]]
* [[Angle of attack]]
* [[Morison equation]]
* [[Stall (flight)]]
* [[Terminal velocity]]
 
==Notes==
{{Reflist}}
 
== References ==
*{{cite book
| first=G.K.
| last=Batchelor
| authorlink=George Batchelor
| title=An Introduction to Fluid Dynamics
| year=1967
| publisher=Cambridge University Press
| isbn=0-521-66396-2 }}
*{{cite book
| last = Huntley | first = H. E.
| year = 1967
| title = Dimensional Analysis
| publisher = Dover
| id = LOC 67-17978
}}
 
[[Category:Aerodynamics]]
[[Category:Equations of fluid dynamics]]
[[Category:Aircraft wing design]]

Latest revision as of 23:40, 6 January 2015

These are only a limited of countless categories individuals are put into based on their weight. So how do we know where we fit? There are virtually hundreds of charts to measure by, sow that one functions best?

Free resource that you do not need to cognise how to puzzle out the bmi chart. The online tool does it for you. In purchase to do which you can choose some of the charts on this page. It won't take much time.

Strength Training: There is a great deal of info out there on lifting weights plus strength training, yet bmi chart men being thoughtful to commence this inside the "right" way is important because you receive older. Running Planet has performed a good job w/ laying out "The 8 rules of Strength Training". We have several good videos on the Resources page.

The above stated research is not the only one that have studied Playboy playmates with all the assumption that the women selected for this title reflect the societal norm for beauty. For instance Singh had earlier noted that, whereas changes inside body structure had been found among Playboy Playmates, the total Waist-to-Hip ratio had only improved somewhat from .68 to .71. What is the significance of this? A healthy WHR range for a female is considered between .67 and .80, where a high ratio is associated with decreased fertility (Rempala & Garvey, 2007). The ratio also increases during menopause plus pregnancy, both, naturally, associated with decreased fertility.

There are numerous causes that cause weight. Let's have a look at a few of these factors. Food that is wealthy in fats plus carbohydrates results inside accumulation of excessive cholesterols in the body. This fat, if not completely absorbed by the body, tends to make 1 fatty over time. Saturated fatty acids that are found in butter, oil, meat etc. can create one's weight abnormal. Heredity factors also play a big part. Obesity commonly runs in families. Snacks, soft refreshments, fast food like burgers, pizzas, hotdogs, and different calorie-rich foods makes one's body weight go from proportion.

The waist-to-hip ratio is a worthwhile measure for determining wellness bmi chart women risk due to the site of fat storage. It is calculated by dividing the ratio of ab girth by cool measuring.

That is to not say which the changes in preference were large, with all the age of the female models seldom being above 25 years. Same applied to the additional measurements. During the 40 years inside query the lowest Body Mass Index was 16 plus highest was 20, with the average being regarding middle inside between (to calculate BMI visit this BMI Calculator). Same used to Waist-to-Hip ratio which stayed in the range of .57 to .73.

In addition to weight training and aerobic exercise, overcoming a taste for fat can assist we slim down. Your perfect women's clothing size could depend on whether you may be small, medium or big frame; whether you may be a pear or hourglass shape and whether we have excess skin/fat from pregnancies or being obese. Maintain good exercise plus eating habits and we may discover a fresh skinny jean size which proves it's not all in your genes!