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Specific weight

2013-11-22T07:29:43Z

188.4.76.141: /* Fluid mechanics */

In [[physics]], the '''Planck charge''', denoted by <math>q_\text{P}</math>, is one of the base units in the system of [[natural units]] called [[Planck units]]. It is a quantity of [[electric charge]] defined in terms of [[fundamental physical constants]].

The Planck charge is defined as:<ref>{{cite journal
|first1=Michael |last1=Stock
|first2=Thomas J |last2=Witt
|title=CPEM 2006 round table discussion 'Proposed changes to the SI'
|journal=Metrologia
|volume=43
|number=6
|pages=583
|year=2006
|doi=10.1088/0026-1394/43/6/014
|bibcode = 2006Metro..43..583S }}</ref>
<ref>{{cite book|last=Pavšič|first=Matej|title=The Landscape of Theoretical Physics: A Global View|year=2001|publisher=Kluwer Academic|location=Dordrecht|isbn=0-7923-7006-6|pages=347–352|url=http://www.springer.com/physics/theoretical%2C+mathematical+%26+computational+physics/book/978-0-7923-7006-2?otherVersion=978-1-4020-0351-6}}</ref>

:<math>q_\text{P} = \sqrt{4 \pi\epsilon_0 \hbar c} = \sqrt{2 c h \epsilon_0} = \frac{e}{\sqrt{\alpha}} = 1.875\;5459 \times 10^{-18}</math> [[coulomb]]s,

where:

:<math> c \ </math> is the [[speed of light]] in the [[vacuum]],
:<math> h \ </math> is [[Planck's constant]],
:<math> \hbar \equiv \frac{h}{2 \pi} \ </math> is the [[reduced Planck constant]],
:<math> \epsilon_0 \ </math> is the [[permittivity of free space]]
:<math> e \ </math> is the [[elementary charge]]
:<math> \alpha \ </math> = (137.03599911)−1 is the [[fine structure constant]].

The Planck charge is <math>\alpha^{-1/2} \approx 11.706</math> times greater than the [[elementary charge]] ''e'' carried by an [[electron]].

The [[Gaussian units|Gaussian cgs units]] are defined so that <math>4 \pi\epsilon_0 = 1</math>, in which case <math>q_\text{P}</math> has the following simple form:

:<math>q_\text{P} = \sqrt{ \hbar c}.</math>

It is customary in theoretical physics to adopt the [[Lorentz–Heaviside units]] (also known as rationalized cgs). When made natural (<math>c=1</math>) they are like the SI system with <math>\epsilon_0 = \mu_0 = 1</math>. Therefore it is more appropriate to define the Planck charge as

:<math>q'_\text{P} = \sqrt{\epsilon_0 \hbar c} = \frac{e}{\sqrt{4\pi\alpha}} = 5.291 \times 10^{-19}</math> [[coulomb]]s,

When charges are measured in units of <math>q'_\text{P}</math>, i.e., when <math>q'_\text{P}</math> is set equal to 1, we obtain <math>\alpha = e^2/(4\pi)</math>, which is commonly used in theoretical physics. In contrast, in (non-rationalized) natural cgs units where <math>q_\text{P}=1</math> we have <math>\alpha = e^2</math>.

==See also==
*[[Orders of magnitude (charge)]]

== Notes and references==
{{Reflist|2}}

{{Planck's natural units}}
{{Portal bar|Physics}}

{{DEFAULTSORT:Planck Charge}}
[[Category:Natural units|charge]]
[[Category:Electromagnetism]]
[[Category:Units of electrical charge]]

Error diffusion

2013-09-16T16:49:46Z

188.4.175.109: Added external link to matlab implementation

'''Airway resistance''' is a concept in [[respiratory physiology]] that describes the resistance of the [[respiratory tract]] to airflow during inspiration and expiration.

Airway resistance can be measured using [[body plethysmography]].

==Definition==
Analogously, to [[Ohm's Law]]:
:<math>R_{AW} = \frac {{\Delta}P}{\dot V}</math>

Where:
:<math>{\Delta P} = P_{ATM} - P_A</math>

So:
:<math>R_{AW} = \frac {P_{\mathrm{ATM}} - P_{\mathrm{A}}}{\dot V}</math>

Where:
*<math>R_{AW}</math> = Airway Resistance
*<math>{\Delta}P</math> = Pressure Difference driving airflow
*<math>P_{ATM}</math> = Atmospheric Pressure
*<math>P_A</math> = Alveolar Pressure
*<math>\dot V</math> = Volumetric Airflow (not [[minute ventilation]] which confusingly maybe represented by the same symbol)

N.B. PA and <math>\dot V</math> change constantly during the respiratory cycle.

==Determinants of Airway Resistance==
There are several important determinants of airway resistance including:
*The diameter of the airways
*Whether airflow is laminar or turbulent

===Hagen–Poiseuille Equation===
In [[fluid dynamics]], the [[Hagen–Poiseuille equation]] is a [[physical law]] that gives the [[pressure]] drop in a fluid flowing through a long cylindrical pipe. The assumptions of the equation are that the flow is laminar [[viscous]] and [[incompressible]] and the flow is through a constant circular cross-section that is substantially longer than its diameter. The equation is also known as the '''Hagen–Poiseuille law''', '''Poiseuille law''' and '''Poiseuille equation'''.

:<math> {\Delta P} = \frac{8 \mu l {\dot V}}{ \pi r^4} </math>

Where:
*<math>\Delta P</math> = Pressure difference between the ends of the pipe
*<math>l</math> = Length of pipe
*<math> \mu </math> = the [[dynamic viscosity]]
*<math>\dot V</math> = the [[volumetric flow rate]] (Q is usually used in fluid dynamics, however in [[respiratory physiology]] it denotes [[cardiac output]])
*<math>r</math> = the [[radius]] of the pipe

Dividing both sides by <math>\dot V</math> and given the above definition shows:-
:<math> R = \frac{8 \mu l}{\pi r^{4}} </math>

While the assumptions of the Hagen–Poiseuille equation are not strictly true of the respiratory tract it serves to show that, because of the fourth power, relatively small changes in the radius of the airways causes large changes in airway resistance.

An individual small airway has much greater resistance than a large airway, however there are many more small airways than large ones. Therefore resistance is greatest at the [[bronchi]] of intermediate size, in between the fourth and eighth bifurcation.<ref>{{GeorgiaPhysiology|4/4ch2/s4ch2_51}}</ref>

===[[Laminar flow]] versus [[Turbulent flow]]===
Where air is flowing in a laminar manner it has less resistance than when it is flowing in a turbulent manner. If flow becomes turbulent, and the pressure difference is increased to maintain flow, this response itself increases resistance. This means that a large increase in pressure difference is required to maintain flow if it becomes turbulent.

Whether flow is laminar or turbulent is complicated, however generally flow within a pipe will be laminar as long as the [[Reynolds number]] is less than 2300.<ref name="Engineering Toolbox">{{cite web|title=Reynolds Number|url=http://www.engineeringtoolbox.com/reynolds-number-d_237.html}}</ref>

:<math>Re = {{\rho {\mathrm v} d} \over \mu}</math>

where:
*<math>Re</math> is the Reynolds number
*<math>d</math> is the diameter of the pipe.
*<math>{\bold \mathrm v}</math> is the mean velocity.
*<math>{\mu}</math> is the [[dynamic viscosity]].
*<math>{\rho}\,</math> is the [[density]].

This shows that larger airways are more prone to turbulent flow than smaller airways. In cases of upper airway obstruction the development of turbulent flow is a very important mechanism of increased airway resistance, this can be treated by administering [[Heliox]] which is much less dense than air and consequently more conductive to laminar flow.

==Changes in Airway Resistance==
Airway resistance is not constant. As shown above airway resistance is markedly affected by changes in the diameter of the airways, therefore diseases affecting the respiratory tract can increase airway resistance. Airway resistance can change over time, for example, in asthma during an attack the airways constrict causing an increase in airway resistance. Airway resistance can also vary between inspiration and expiration, for example, in [[emphysema]] there is destruction of the elastic tissue of the lungs which help hold the small airways open, therefore during expiration, particularly forced expiration, these airways may collapse causing increased airway resistance.

==Derived Parameters==

===Airway Conductance (GAW)===
This is simply the mathematical inverse of airway resistance.
:<math>G_{AW} = \frac{1}{R_{AW}}</math>

===Specific Airway Resistance (sRaw)<ref name=EPA>{{cite web|title=US EPA Glossary of Terms|url=http://www.epa.gov/apti/ozonehealth/glossary.html#S}}</ref><ref name="Kirkby et al">{{cite journal|last=Kirkby|first=J.|author2=et al|title=Reference equations for specific airway resistance in children: the Asthma UK initiative|journal=European Respiratory Journal|year=2010|volume=36|issue=3|pages=622–629|doi=10.1183/09031936.00135909|url=http://erj.ersjournals.com/content/36/3/622.full.pdf|accessdate=9 April 2012}}</ref> ===
:<math>sR_{AW} = {R_{AW}}{V}</math>

:Where V is the lung volume at which RAW was measured.

Also called volumic airway resistance. Due to the elastic nature of the tissue that supports the small airways airway resistance changes with lung volume. It is not practically possible to measure airway resistance at a set absolute lung volume, therefore specific airway resistance attempts to correct for differences in lung volume at which different measurements of airway resistance were made.

Specific airway resistance is often measured at FRC, in which case:

:<math>sR_{AW} = {R_{AW}}\times{FRC}</math>

===Specific Airway Conductance (sGaw)<ref name=EPA/>===
:<math>sG_{AW} = \frac{G_{AW}}{V} = \frac{1}{R_{AW}V} = \frac{1}{sR_{AW}}</math>

:Where V is the lung volume at which GAW was measured.

Also called volumic airway conductance. Similarly to specific airway resistance, specific airway conductance attempts to correct for differences in lung volume.

Specific airway conductance is often measured at FRC, in which case:

:<math>sG_{AW} = \frac{G_{AW}}{FRC}</math>

==See also==
* [[turbulent flow]]
* [[laminar flow]]
* [[Reynolds number]]
* [[Upper airway resistance syndrome]] (UARS)

==References==
<references/>

==External links==
* [http://oac.med.jhmi.edu/res_phys/Encyclopedia/AirwayResistance/AirwayResistance.HTML Overview at med.jhmi.edu]
* [http://www.medstudents.com.br/calculat/airrest.htm Calculator at medstudents.com.br]

{{Respiratory physiology}}

[[Category:Respiratory therapy]]
[[Category:Respiratory physiology]]
[[Category:Mathematics in medicine]]

Flashsort

2012-05-12T16:04:11Z

188.4.162.31: minor typo

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