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State and explain Newton’s law of viscosity.

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Newton's law of viscosity, also known as Newton's law of fluid friction, is a fundamental principle in fluid mechanics that describes the relationship between the shear stress and the velocity gradient in a flowing fluid. It states that the shear stress (τ) between adjacent layers of a fluid is directly proportional to the velocity gradient (du/dy), where du is the change in velocity and dy is the change in the distance perpendicular to the flow direction. Mathematically, it can be represented as τ = μ * (du/dy), where μ is the dynamic viscosity of the fluid.

According to Newton's law of viscosity, the proportionality constant μ, known as the dynamic viscosity, determines the resistance of the fluid to shear deformation. A fluid with high viscosity, such as honey or molasses, will resist flow and have a higher resistance to shear stress. In contrast, a fluid with low viscosity, like water, flows easily and has a lower resistance to shear stress.

This law helps explain the behavior of fluids under different conditions and is applicable to both liquids and gases. It is a fundamental concept in various fields, including engineering, physics, and chemistry, and is crucial in understanding fluid flow, designing hydraulic systems, and predicting the behavior of fluids in various applications, such as in pipelines, pumps, and lubrication systems. Newton's law of viscosity provides a quantitative framework to study and analyze fluid behavior, enabling engineers and scientists to make informed decisions in fluid dynamics and related disciplines.

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