Editing Laminar flow (section)

==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.