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In [[dimensional analysis]], the '''Strouhal number''' ('''St''') is a [[dimensionless number]] describing oscillating flow mechanisms. The parameter is named after [[Vincenc Strouhal]], a Czech physicist who experimented in 1878 with wires experiencing [[vortex shedding]] and singing in the wind.<ref>{{cite book |last=White |first=Frank M. |title=Fluid Mechanics |edition=4th |year=1999 |location= |publisher=McGraw Hill |isbn=0-07-116848-6 }}</ref> The Strouhal number is an integral part of the fundamentals of [[fluid mechanics]].
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The Strouhal number is often given as
 
:<math> \mathrm{St}= {f L\over V}, </math>
 
where ''f'' is the frequency of [[vortex shedding]], ''L'' is the characteristic length (for example [[hydraulic diameter]], or [[chord]] length) and ''V'' is the velocity of the fluid. In certain cases like heaving (plunging) flight, this characteristic length is the amplitude of oscillation. This selection of characteristic length can be used to present a distinction between Strouhal number and Reduced Frequency. 
 
:<math> \mathrm{St}= {k a\over \pi c}, </math>
 
where ''k'' is the [[reduced frequency]] and ''a'' is amplitude of the heaving oscillation.  
 
[[Image:Srrrpd.png|thumb|right|300px|Strouhal number as a function of the Reynolds number for a long cylinder]]
 
For large Strouhal numbers (order of 1), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid "plug". For low Strouhal numbers (order of 10<sup>−4</sup> and below), the high-speed, quasi steady state portion of the movement dominates the oscillation. Oscillation at intermediate Strouhal numbers is characterized by the buildup and rapidly subsequent shedding of vortices.<ref>{{cite journal |first=Ian J. |last=Sobey |year=1982 |title=Oscillatory flows at intermediate Strouhal number in asymmetry channels |journal=[[Journal of Fluid Mechanics]] |volume=125 |issue= |pages=359–373 |doi=10.1017/S0022112082003371 |bibcode = 1982JFM...125..359S }}</ref>
 
For spheres in uniform flow in the [[Reynolds number]] range of 800 < Re < 200,000 there co-exist two values of the Strouhal number. The lower frequency is attributed to the large-scale instability of the wake and is independent of the [[Reynolds number]] Re and is approximately equal to 0.2. The higher frequency Strouhal number is caused by small-scale instabilities from the separation of the shear layer.<ref name="Kim and Durbin, 1988">{{cite journal |last=Kim |first=K. J. |last2=Durbin |first2=P. A. |year=1988 |title=Observations of the frequencies in a sphere wake and drag increase by acoustic excitation |journal=[[Physics of Fluids]] |volume=31 |issue=11 |pages=3260–3265 |doi=10.1063/1.866937 |bibcode = 1988PhFl...31.3260K }}</ref><ref name="Sakamoto and Haniu, 1990">{{cite journal |last=Sakamoto |first=H. |last2=Haniu |first2=H. |year=1990 |title=A study on vortex shedding from spheres in uniform flow |journal=Journal of Fluids Engineering |volume=112 |issue=December |pages=386–392 |doi= |bibcode=1990ATJFE.112..386S }}</ref>
 
== Applications ==
In [[metrology]], specifically axial-flow turbine meters, the '''Strouhal number''' is used in combination with the [[Roshko number]] to give a correlation between flow rate and frequency. The advantage of this method over the freq/viscosity versus K-factor method is that it takes into account temperature effects on the meter. 
 
:<math> \mathrm{St}= {f\over U}{C^3} </math>
 
f = meter frequency,
U = flow rate,
C = linear coefficient of expansion for the meter housing material
 
This relationship leaves Strouhal dimensionless, although a dimensionless approximation is often used for C<sup>3</sup>, resulting in units of pulses/volume (same as K-factor).
 
In animal flight or swimming, propulsive efficiency is high over a narrow range of Strouhal constants, generally peaking in the 0.2 < St < 0.4 range.<ref name="tnt">{{Harv|Taylor|Nudds|Thomas|2003}}</ref> This range is used in the swimming of dolphins, sharks, and bony fish, and in the cruising flight of birds, bats and insects.<ref name="tnt" /> However, in other forms of flight other values are found.<ref name="tnt" /> Intuitively the ratio measures the steepness of the strokes, viewed from the side (e.g., assuming movement through a stationary fluid) – ''f'' is the stroke frequency, ''L'' is the amplitude, so the numerator ''fL'' is half the vertical speed of the wing tip, while the denominator ''V'' is the horizontal speed. Thus the graph of the wing tip forms an approximate sinusoid with aspect (maximum slope) twice the Strouhal constant.<ref>See illustrations at {{Harv|Corum|2003}}</ref>
 
== See also ==
* [[Froude number]]
* [[Mach Number]]
* [[Rossby number]]
* [[Weber Number]]
* [[Aeroelastic_flutter#Flutter|Aeroelastic Flutter]]
* [[Kármán vortex street]]
 
==References==
{{Reflist}}
{{refbegin}}
* {{cite doi|10.1038/nature02000}}
* {{cite web|url=http://style.org/strouhalflight/ | title = The Strouhal Number in Cruising Flight | work = ''[http://13pt.com 13pt],'' | first = Jonathan | last = Corum | year = 2003 | postscript = – depiction of Strouhal number for flying and swimming animals | accessdate = 2012-11-13}}
{{refend}}
 
==External links==
*[http://www.weltderphysik.de/intern/upload/annalen_der_physik/1878/Band_241_216.pdf Vincenc Strouhal, Ueber eine besondere Art der Tonerregung]
 
{{NonDimFluMech}}
 
[[Category:Dimensionless numbers of fluid mechanics]]
[[Category:Fluid dynamics]]

Latest revision as of 05:30, 9 January 2015

This article will now explain stretching exercises that will strengthen and thicken your cartilage, which results in an increase of your stature by at least 2-3 inches. Any time you install or adjust an antenna, perform a channel scan with your digital converter to see if you have improved reception and perhaps more channels available to you. During the day, your spine gets pulled downward a lot when you are standing, so it is good to counteract this at night. Although some studies have shown that calcium and vitamins A and D do not help in increasing the height of an adult, they all agree that they are extremely important when it comes to preserving height. Most importantly, you will need the terrarium itself.

All of a sudden it made perfect sense that this is exactly what I wanted to do. If you have not yet set up your digital TV converter, consider foregoing the automatic channel scan that most converters feature. They will help you get taller by elongating your spine. In understanding the genetics of Mosaic Turner syndrome, we know it is usually caused by nondisjunction. You should stretch as far as it is possible to without irritation, but make sure you keep your pelvic region on the ground.

Nowadays I have found the funny side and I can even laugh at myself for being that clumsy bloke, this is fine now but through my younger years it was not so easy. Hence it must be noted that trying to get taller fast requires a lot of dedication and hard work which will eventually help you finally grow taller. Simply height increase can show a significant change in anyone's life. That means each tree will get the moisture from a 5 foot diameter ground area without competition from the tree beside it. They will work with their shoulders hunched above their computer monitor and walk with their head low and shoulders to the fore.

Every average person spends two-third of his or her lifetime sleeping. The village of Cochise is named, as is the county, for the famous Apache Indian chief. If it takes you more than thrity seconds before you are out of breath, then build up the intensity. Doing thus can let it produce the human growth hormone healthily and normally. As you function throughout the day, gravity compresses it back down.

Also, sleep allows the body to grow and develop itself naturally. Some of the most effective intense exercises that can help in growing taller naturally are yoga and swimming. HGH causes us to grow taller and develop into our adult bodies. Trousers that are too long look untidy and can make you appear shorter whilst trousers that are too short give the. Bring on the unusual, from humble beginnings in a scotch whisky distillery.

If you have any inquiries concerning exactly where and how to use how to grow taller overnight, you can make contact with us at our own webpage.

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