Editing Newtonian fluid (section)

{{Short description|Type of fluid}}
{{continuum mechanics|cTopic=fluid}}
A '''Newtonian fluid''' is a [[fluid]] in which the [[viscous stress tensor|viscous stresses]] arising from its [[Fluid dynamics|flow]] are at every point linearly correlated to the local [[strain rate]] — the [[derivative (mathematics)|rate of change]] of its [[deformation (mechanics)|deformation]] over time.<ref>{{cite book |first=Ronald L. |last=Panton |title=Incompressible Flow |edition=Fourth |year=2013 |publisher=John Wiley & Sons |location=Hoboken |page=114 |isbn=978-1-118-01343-4 }}</ref><ref name=Batchelor>{{cite book |first= G. K. |last=Batchelor |author-link=George Batchelor |title= An Introduction to Fluid Dynamics |publisher= Cambridge Mathematical Library series, Cambridge University Press |year=2000 |orig-year= 1967 |url= https://books.google.com/books?id=Rla7OihRvUgC&pg=PP1 |isbn=978-0-521-66396-0}}</ref><ref name=Kundu>{{cite book |last1= Kundu |first1=P. |last2=Cohen |first2=I. |title= Fluid Mechanics |page= (page needed)}}</ref><ref name=Kirby>{{cite book |last= Kirby |first=B. J. |title= Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices |url= http://www.kirbyresearch.com/textbook | year= 2010| publisher=Cambridge University Press |isbn=978-0-521-11903-0| via= kirbyresearch.com}}</ref> Stresses are proportional to the rate of change of the fluid's [[velocity|velocity vector]].

A fluid is Newtonian only if the [[tensor]]s that describe the viscous stress and the strain rate are related by a constant [[viscosity|viscosity tensor]] that does not depend on the stress state and velocity of the flow. If the fluid is also [[isotropic]] (i.e., its mechanical properties are the same along any direction), the viscosity tensor reduces to two real coefficients, describing the fluid's resistance to continuous [[Shearing (physics)|shear deformation]] and continuous [[compression (physical)|compression]] or expansion, respectively.

Newtonian fluids are the easiest [[mathematical model]]s of fluids that account for viscosity. While no real fluid fits the definition perfectly, many common liquids and gases, such as water and air, can be assumed to be Newtonian for practical calculations under ordinary conditions. However, [[non-Newtonian fluid]]s are relatively common and include [[Non-newtonian fluid#Oobleck|oobleck]] (which becomes stiffer when vigorously sheared) and non-drip [[paint]] (which becomes [[shear thinning|thinner when sheared]]). Other examples include many [[polymer]] solutions (which exhibit the [[Weissenberg effect]]), molten polymers, many solid suspensions, blood, and most highly viscous fluids.

Newtonian fluids are named after [[Isaac Newton]], who first used the [[differential equation]] to postulate the relation between the shear strain rate and [[shear stress]] for such fluids.