It is a common practice when examining a fluids viscous behavior to plot the shear rule (velocity gradient) d/dy = on the abscissa versus

It is a common practice when examining a fluid’s viscous behavior to plot the shear rule (velocity gradient)

dυ/dy = γ

on the abscissa versus shear sires (τ) on the ordinate. When a fluid has a straight-line behavior between these two variables it is called a Newtonian fluid, and the resulting relationship is

τ = μγ

where μ is the fluid viscosity. Many common fluids follow this behavior such as water, milk, and oil. Fluids that do not behave in this way are called non-Newtonian. Some examples of non-Newtonian fluids are shown in Figure.

For Bingham plastics, there is a yield stress τ_y that must be over-come before flow will begin,

τ = τ_y + μγ

A common example is toothpaste.

For pseudoplastics,  the shear stress is raised to the power n,

τ = μγⁿ

Common examples are yogurt and shampoo.

The following data shows the relationship between the shear stress τ and the shear strain rate γ for a Bingham plastic fluid. The yield stress τ_y is the amount of stress that must be exceeded before flow begins. Find the viscosity μ (slope), τ_y and the r² value using a regression method.

Bingham Pseudoplastic Newtonian Shear strain ly) (4) ssas Jeoys