Newtonian fluid

Newtonian fluid is a category of fluids 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.

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 fluids, 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.

Applications

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

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.

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.

Mathematical Description

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.

See Also

• Fluid dynamics
• Viscosity
• Reynolds number
• Laminar flow
• Turbulent flow