Newtonian fluid: Difference between revisions

Latest revision as of 06:19, 16 February 2025

Newtonian Fluid[edit]

A Newtonian fluid is a fluid in which the viscous stresses arising from its flow, at every point, are linearly proportional to the local strain rate—the rate of change of its deformation over time. This relationship is described by Isaac Newton's law of viscosity, which states that the shear stress between adjacent fluid layers is proportional to the velocity gradients between the two layers.

File:Dilatant-pseudoplastic.svg

Graph showing the behavior of different types of fluids, including Newtonian fluids.

Characteristics[edit]

The defining characteristic of a Newtonian fluid is its constant viscosity, regardless of the stress applied to it. This means that the fluid's viscosity does not change with the rate of flow or shear rate. Common examples of Newtonian fluids include water, air, and mineral oil.

Viscosity[edit]

Viscosity is a measure of a fluid's resistance to deformation at a given rate. For Newtonian fluids, this property remains constant, which simplifies the mathematical modeling of their flow. The viscosity of a Newtonian fluid is only dependent on temperature and pressure, not on the forces acting upon it.

Mathematical Description[edit]

The relationship between shear stress (_) and shear rate (du/dy) in a Newtonian fluid is given by:

_ = _ (du/dy)

where:

_ is the shear stress,
_ is the dynamic viscosity,
du/dy is the velocity gradient perpendicular to the direction of shear.

Comparison with Non-Newtonian Fluids[edit]

Unlike Newtonian fluids, non-Newtonian fluids have a viscosity that changes with the rate of shear or stress. These fluids can be further classified into several types, such as pseudoplastic, dilatant, Bingham plastic, and thixotropic fluids.

Pseudoplastic Fluids[edit]

Pseudoplastic fluids, also known as shear-thinning fluids, decrease in viscosity with an increase in shear rate. An example of a pseudoplastic fluid is ketchup.

Dilatant Fluids[edit]

Dilatant fluids, or shear-thickening fluids, increase in viscosity with an increase in shear rate. An example of a dilatant fluid is a mixture of cornstarch and water.

Applications[edit]

Newtonian fluids are often used as a baseline in fluid dynamics studies due to their simple behavior. Understanding the flow of Newtonian fluids is crucial in various engineering applications, including aerodynamics, hydraulics, and lubrication.

Related pages[edit]

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-'''Newtonian fluid''' is a category of [[fluid]]s that maintain a constant [[viscosity]] regardless of the applied [[shear stress]]. Named after [[Sir Isaac Newton]], who first described this behavior in his work ''Philosophiæ Naturalis Principia Mathematica'', Newtonian fluids are characterized by their predictable and constant flow behavior. Common examples of Newtonian fluids include [[water]], [[air]], and simple [[organic solvents]].
+{{DISPLAYTITLE:Newtonian Fluid}}
+==Newtonian Fluid==
+A '''Newtonian fluid''' is a fluid in which the viscous stresses arising from its flow, at every point, are linearly proportional to the local strain rate—the rate of change of its deformation over time. This relationship is described by [[Isaac Newton]]'s law of viscosity, which states that the shear stress between adjacent fluid layers is proportional to the velocity gradients between the two layers.
+[[File:Dilatant-pseudoplastic.svg|thumb|right|300px|Graph showing the behavior of different types of fluids, including Newtonian fluids.]]
 ==Characteristics==
-The primary characteristic of a Newtonian fluid is its constant viscosity, which means that its flow behavior or [[rheology]] does not change, regardless of the forces acting upon it. This is in contrast to [[non-Newtonian fluid]]s, whose viscosity can change when under force or over time. In mathematical terms, the relationship between the shear stress (\(\tau\)) and the shear rate (\(\dot{\gamma}\)) in a Newtonian fluid is linear and passes through the origin, represented by the equation \(\tau = \eta\dot{\gamma}\), where \(\eta\) is the dynamic viscosity, a constant.
+The defining characteristic of a Newtonian fluid is its constant viscosity, regardless of the stress applied to it. This means that the fluid's viscosity does not change with the rate of flow or shear rate. Common examples of Newtonian fluids include [[water]], [[air]], and [[mineral oil]].
-==Applications==
+===Viscosity===
-Newtonian fluids play a crucial role in various industries and applications due to their predictable behavior. In [[engineering]], understanding the flow of Newtonian fluids is essential for the design of [[pipelines]], [[pumps]], and other systems involving fluid transport. In the [[food industry]], many liquids (such as water and simple syrups) are treated as Newtonian fluids for processing and quality control purposes.
+Viscosity is a measure of a fluid's resistance to deformation at a given rate. For Newtonian fluids, this property remains constant, which simplifies the mathematical modeling of their flow. The viscosity of a Newtonian fluid is only dependent on temperature and pressure, not on the forces acting upon it.
+===Mathematical Description===
+The relationship between shear stress (_) and shear rate (du/dy) in a Newtonian fluid is given by:
+: _ = _ (du/dy)
-==Viscosity==
+where:
-Viscosity is a measure of a fluid's resistance to gradual deformation by shear or tensile stress. For Newtonian fluids, this property is constant at a given temperature and pressure, which simplifies calculations and models related to flow dynamics. The [[SI unit]] for measuring viscosity is the Pascal-second (Pa·s), though the centipoise (cP) is also commonly used, especially in the [[chemical industry]].
+* _ is the shear stress,
+* _ is the dynamic viscosity,
+* du/dy is the velocity gradient perpendicular to the direction of shear.
 ==Comparison with Non-Newtonian Fluids==
-Unlike Newtonian fluids, non-Newtonian fluids have a viscosity that changes under stress or over time. Examples include [[ketchup]], [[custard]], and [[slime]], which can behave more like a solid or a liquid depending on the forces applied to them. Understanding the difference between these fluid types is crucial for applications requiring precise control over fluid behavior.
+Unlike Newtonian fluids, [[non-Newtonian fluid|non-Newtonian fluids]] have a viscosity that changes with the rate of shear or stress. These fluids can be further classified into several types, such as [[pseudoplastic]], [[dilatant]], [[Bingham plastic]], and [[thixotropic]] fluids.
-==Mathematical Description==
+===Pseudoplastic Fluids===
-The behavior of Newtonian fluids is governed by the [[Navier-Stokes equations]], a set of nonlinear partial differential equations that describe the motion of viscous fluid substances. These equations are a cornerstone of [[fluid mechanics]] and are used to model the flow of Newtonian fluids in various contexts.
+Pseudoplastic fluids, also known as shear-thinning fluids, decrease in viscosity with an increase in shear rate. An example of a pseudoplastic fluid is [[ketchup]].
-==See Also==
+===Dilatant Fluids===
+Dilatant fluids, or shear-thickening fluids, increase in viscosity with an increase in shear rate. An example of a dilatant fluid is a mixture of cornstarch and water.
+==Applications==
+Newtonian fluids are often used as a baseline in fluid dynamics studies due to their simple behavior. Understanding the flow of Newtonian fluids is crucial in various engineering applications, including [[aerodynamics]], [[hydraulics]], and [[lubrication]].
+==Related pages==
 * [[Fluid dynamics]]
 * [[Viscosity]]
-* [[Reynolds number]]
+* [[Non-Newtonian fluid]]
-* [[Laminar flow]]
+* [[Rheology]]
-* [[Turbulent flow]]
 [[Category:Fluid dynamics]]
-[[Category:Physical chemistry]]
-[[Category:Materials science]]
-{{Physics-stub}}
-{{Chemistry-stub}}