Classify the fluid as Newtonian or non Newtonian on the...

Classify the fluid as Newtonian or non Newtonian on the basis of two measurements of shear stress on a surface and the rate of change in shear strain at the surface for a fluid have been determined by experiment to be $\tau_{1}=0.18$ $\mathrm{N} / \mathrm{m}^{2},(d u / d y)_{1}=17.5 \mathrm{~s}^{-1}$ and $\tau_{2}=0.64 \mathrm{~N} / \mathrm{m}^{2},(d u / d y)_{2}=184 \mathrm{~s}^{-1}$.

Key Concepts

Shear Rate

Shear rate is a measure of the rate at which adjacent layers of fluid move relative to each other, typically expressed in reciprocal seconds (s?¹). It is a critical parameter in characterizing fluid flow and is directly proportional to the deformation rate experienced by the fluid. The concept helps in distinguishing between Newtonian and non-Newtonian fluids based on how the fluid's viscosity responds to changes in the shear rate.

Shear Stress

Shear stress is the force per unit area exerted parallel to the surface of a material or fluid. In the context of fluid dynamics, it describes the internal frictional forces that arise when layers of fluid move relative to each other. Proper understanding of shear stress is essential for analyzing flow behavior and pressure losses in fluid systems.

Newtonian Fluids

Newtonian fluids are those that exhibit a constant viscosity regardless of the shear rate. The relationship between shear stress and shear rate in a Newtonian fluid is linear, typically described by the equation ? = ?(du/dy), where ? is the shear stress, ? is the viscosity, and du/dy is the shear rate. This concept is fundamental in fluid mechanics as it simplifies the analysis and design of systems involving fluid flow by assuming a constant coefficient of viscosity under different flow conditions.

Non-Newtonian Fluids

Non-Newtonian fluids do not follow a linear relationship between shear stress and shear rate, meaning their viscosity can change with the rate of shear. These fluids can exhibit behaviors such as shear thinning (reduction in viscosity with an increase in shear rate) or shear thickening (increase in viscosity with an increase in shear rate). Understanding non-Newtonian behavior is crucial in many practical applications where fluid properties can change under different flow conditions.

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