Editing Laminar flow

{{short description|Flow where fluid particles follow smooth paths in layers}}
[[File:Laminar flow profile.gif|thumb|The velocity profile associated with laminar flow resembles a deck of [[playing cards]]. This flow profile of a fluid in a pipe shows the fluid acting in layers that slide over one another.]]

'''Laminar flow''' ({{IPAc-en|ˈ|l|æ|m|ɪ|n|ər}}) is the property of fluid particles in [[fluid dynamics]] to follow smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing.<ref>Streeter, V.L. (1951-1966) ''Fluid Mechanics'', Section 3.3 (4th edition). McGraw-Hill</ref> At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another smoothly. There are no cross-currents perpendicular to the direction of flow, nor [[eddies]] or swirls of fluids.<ref name="Geankoplis, Christie John 2003">{{cite book
 |title       = Transport Processes and Separation Process Principles
 |last        = Geankoplis
 |first       = Christie John
 |year        = 2003
 |publisher   = Prentice Hall Professional Technical Reference
 |isbn        = 978-0-13-101367-4
 |url         = http://www.pearsonhighered.com/educator/product/Transport-Processes-and-Separation-Process-Principles-Includes-Unit-Operations/9780131013674.page
 |url-status     = live
 |archive-url  = https://web.archive.org/web/20150501122109/http://www.pearsonhighered.com/educator/product/Transport-Processes-and-Separation-Process-Principles-Includes-Unit-Operations/9780131013674.page
 |archive-date = 2015-05-01
}}</ref> In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface.<ref>{{cite web
 |url         = http://www.efm.leeds.ac.uk/CIVE/CIVE1400/Section4/laminar_turbulent.htm
 |title       = Real Fluids
 |last1       = Noakes
 |first1      = Cath
 |last2       = Sleigh
 |first2      = Andrew
 |date        = January 2009
 |work        = An Introduction to Fluid Mechanics
 |publisher   = University of Leeds
 |access-date  = 23 November 2010
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20101021003853/http://www.efm.leeds.ac.uk/CIVE/CIVE1400/Section4/laminar_turbulent.htm
 |archive-date = 21 October 2010
}}</ref>
Laminar flow is a flow regime characterized by high [[momentum diffusion]] and low momentum [[convection]].

When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of two types of flow may occur depending on the velocity and [[viscosity]] of the fluid: laminar flow or [[Turbulence|turbulent flow]]. Laminar flow occurs at lower velocities, below a threshold at which the flow becomes turbulent. The threshold velocity is determined by a dimensionless parameter characterizing the flow called the [[Reynolds number]], which also depends on the viscosity and density of the fluid and dimensions of the channel. Turbulent flow is a less orderly flow regime that is characterized by [[eddies]] or small packets of fluid particles, which result in lateral mixing.<ref name="Geankoplis, Christie John 2003"/> In non-scientific terms, laminar flow is ''smooth'', while turbulent flow is ''rough''.

==Relationship with the Reynolds number==
[[Image:Stokes sphere.svg|thumb|upright|A [[sphere]] in Stokes flow, at very low [[Reynolds number]]. An object moving through a fluid experiences a [[drag force]] in the direction opposite to its motion.]]

The type of flow occurring in a fluid in a channel is important in fluid-dynamics problems and subsequently affects [[heat transfer|heat]] and [[mass transfer]] in fluid systems. The [[dimensionless number|dimensionless]] [[Reynolds number]] is an important parameter in the equations that describe whether fully developed flow conditions lead to laminar or turbulent flow. The Reynolds number is the ratio of the [[inertial force]] to the [[Shear stress|shearing force]] of the fluid: how fast the fluid is moving relative to how [[viscosity|viscous]] it is, irrespective of the scale of the fluid system. Laminar flow generally occurs when the fluid is moving slowly or the fluid is very viscous. As the Reynolds number increases, such as by increasing the flow rate of the fluid, the flow will transition from laminar to turbulent flow at a specific range of Reynolds numbers, the [[laminar–turbulent transition]] range depending on small disturbance levels in the fluid or imperfections in the flow system. If the Reynolds number is very small, much less than 1, then the fluid will exhibit [[Stokes flow|Stokes]], or creeping, flow, where the viscous forces of the fluid dominate the inertial forces.

The specific calculation of the Reynolds number, and the values where laminar flow occurs, will depend on the geometry of the flow system and flow pattern. The common example is [[flow conditioning|flow through a pipe]], where the Reynolds number is defined as

:<math> \mathrm{Re} = \frac{\rho u D_\text{H}}{\mu} = \frac{u D_\text{H}}{\nu} = \frac{Q D_\text{H}}{\nu A}, </math>

where:
: {{math|''D''<sub>H</sub>}} is the [[hydraulic diameter]] of the pipe <!--; its characteristic travelled length, {{math|''L''}}, – what is this?--> (m);
: {{math|''Q''}} is the [[volumetric flow rate]] (m<sup>3</sup>/s);
: {{math|''A''}} is the pipe's cross-sectional area (m<sup>2</sup>);
: {{math|''u''}} is the mean speed of the fluid ([[SI units]]: m/s);
: {{math|''μ''}} is the [[dynamic viscosity]] of the fluid (Pa·s = N·s/m<sup>2</sup> = kg/(m·s));
: {{math|''ν''}} is the [[kinematic viscosity]] of the fluid, {{math|''ν'' {{=}} ''{{sfrac|μ|ρ}}''}} (m<sup>2</sup>/s);
: {{math|''ρ''}} is the [[density]] of the fluid (kg/m<sup>3</sup>).

For such systems, laminar flow occurs when the Reynolds number is below a critical value of approximately 2,040, though the transition range is typically between 1,800 and 2,100.<ref name=Recrit>{{cite journal|last1=Avila|first1=K.|first2=D.|last2=Moxey|first3=A.|last3=de Lozar|first4=M.|last4=Avila|first5=D.|last5=Barkley|first6=B.|last6=Hof|title=The Onset of Turbulence in Pipe Flow|journal=Science|date=July 2011|volume=333|issue=6039|pages=192–196|doi=10.1126/science.1203223|pmid=21737736|bibcode=2011Sci...333..192A|s2cid=22560587}}</ref>

For fluid systems occurring on external surfaces, such as flow past objects suspended in the fluid, other definitions for Reynolds numbers can be used to predict the type of flow around the object. The particle Reynolds number Re<sub>p</sub> would be used for particle suspended in flowing fluids, for example. As with flow in pipes, laminar flow typically occurs with lower Reynolds numbers, while turbulent flow and related phenomena, such as [[vortex shedding]], occur with higher Reynolds numbers.

==Examples==
[[Image:Laminar flow.gif|thumb|right|In the case of a moving plate in a liquid, it is found that there is a layer (lamina) that moves with the plate, and a layer of stationary liquid next to any stationary plate.]]

A common application of laminar flow is in the smooth flow of a viscous liquid through a tube or pipe. In that case, the velocity of flow varies from zero at the walls to a maximum along the cross-sectional centre of the vessel. The flow profile of laminar flow in a tube can be calculated by dividing the flow into thin cylindrical elements and applying the viscous force to them.<ref>{{cite web
 |url         = http://hyperphysics.phy-astr.gsu.edu/hbase/pfric.html
 |title       = Laminar Flow
 |last        = Nave
 |first       = R.
 |year        = 2005
 |work        = HyperPhysics
 |publisher   = Georgia State University
 |access-date  = 23 November 2010
 |url-status     = live
 |archive-url  = https://web.archive.org/web/20110219090625/http://hyperphysics.phy-astr.gsu.edu/hbase/pfric.html
 |archive-date = 19 February 2011
}}
</ref>

Another example is the flow of air over an aircraft [[wing]]. The [[boundary layer]] is a very thin sheet of air lying over the surface of the wing (and all other surfaces of the aircraft). Because air has [[viscosity]], this layer of air tends to adhere to the wing. As the wing moves forward through the air, the boundary layer at first flows smoothly over the streamlined shape of the [[airfoil]]. Here, the flow is laminar and the boundary layer is a laminar layer. [[Ludwig Prandtl|Prandtl]] applied the concept of the laminar boundary layer to airfoils in 1904.<ref>{{cite book
 |title=A History of Aerodynamics and Its Impact on Flying Machines
 |last=Anderson
 |first=J. D.
 |year=1997
 |publisher=Cambridge University Press
 |isbn=0-521-66955-3
 |url=https://books.google.com/books?isbn=0521669553
}}</ref><ref>{{cite book
 |title=Laminar flow analysis
 |last=Rogers
 |first=D. F.
 |year=1992
 |publisher=Cambridge University Press
 |isbn=0-521-41152-1
 |url=https://books.google.com/books?isbn=0521411521
}}</ref>

An everyday example is the slow, smooth and optically transparent flow of shallow water over a smooth barrier.<ref>{{cite web |author=((sovereign578)) |title=Laminar Flow in Nature |url=https://www.youtube.com/watch?v=uaqKFeqRLik |website=YouTube |date=5 November 2016 |access-date=17 December 2019 |language=en}}</ref>

When water leaves a [[faucet|tap]] without an aerator with little force, it first exhibits laminar flow, but as acceleration by the force of gravity immediately sets in, the Reynolds number of the flow increases with speed, and the laminar flow of the water downstream from the tap can transition to turbulent flow. Optical transparency is then reduced or lost entirely.

==Laminar flow barriers==
[[File:Experimental chamber for studying chemotaxis in response to laminar flow.ogv|thumb|right|Experimental chamber for studying [[chemotaxis]] in response to laminar flow]]

Laminar airflow is used to separate volumes of air, or prevent airborne contaminants from entering an area. [[Laminar flow cabinet|Laminar flow hoods]] are used to exclude contaminants from sensitive processes in science, electronics and medicine. [[Air door|Air curtains]] are frequently used in commercial settings to keep heated or refrigerated air from passing through doorways. A [[laminar flow reactor]] (LFR) is a [[Chemical reactor|reactor]] that uses laminar flow to study chemical reactions and process mechanisms. A laminar flow design for [[animal husbandry]] of [[rat]]s for disease management was developed by Beall et al. 1971 and became a standard around the world<ref name="Suckow-2006">{{cite book | editor-last1=Suckow | editor-first1=Mark A. | editor-first2=Steven H. | editor-last2=Weisbroth | editor-first3=Craig L. | editor-last3=Franklin | title=The Laboratory Rat | publisher=[[American College of Laboratory Animal Medicine]] ([[Academic Press|AP]]) | publication-place=Amsterdam Boston | year=2006 | isbn=978-0-08-045432-0 | oclc=162569241 | page=304/pp.{{spaces}}304{{ndash}}337/xvi+912 | edition=2 | chapter=10. Housing and Environment | first1=Robert E. | last1=Faith | first2=Jack R. | last2=Hessler}} {{ISBN|9780120749034}} {{ISBN|0120749033}}</ref> including in the then-[[Eastern Bloc]].<ref name="Travnicek-Mandel-1979">{{cite journal | last1=Trávníček | first1=J. | last2=Mandel | first2=L. | title=Gnotobiotic techniques | journal=[[Folia Microbiologica]] | publisher=[[Czechoslovak Society for Microbiology]] ([[Springer Netherlands|Springer]]) | volume=24 | issue=1 | year=1979 | issn=0015-5632 | doi=10.1007/bf02927240 | pages=6–10 | pmid=374207 | s2cid=6421827}}</ref>

==See also==
{{Portal|Physics}}
* [[Hagen–Poiseuille equation]]
* [[Shell balance]]
* [[Wake turbulence]]
* [[Water current]]

==References==
{{Reflist}}

==External links==
{{Wiktionary|laminar}}
* {{YouTube|Brvkwq-6oFo|3mtr High laminar Flow Waterfall, 1:01 m:s, 2016}}
* {{YouTube|OV-IazRk0sU|Build a laminar flow nozzle for $15, 8:07 m:s, 2008}}
* {{YouTube|uaqKFeqRLik|Laminar flow of a small stream, 2016}}
* {{YouTube|1zw5h5IYlic|A fountain in Chicago, 2014}}
* {{YouTube|p08_KlTKP50|Reversible laminar flow demonstrated with blue and green corn syrup, 2007}}
* {{YouTube|KqqtOb30jWs|Laminar flow in a pipe, 2006}}

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[[Category:Aerodynamics]]
[[Category:Flow regimes]]
[[Category:Cleanroom technology]]
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