What is the relationship between shear stress and shear rate in a Newtonian fluid?

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Q: What is the relationship between shear stress and shear rate in a Newtonian fluid?

Solution: In a Newtonian fluid, shear stress is directly proportional to shear rate, which defines its viscosity.

Steps: 6

Step 1: Understand what a Newtonian fluid is. A Newtonian fluid is a type of fluid that flows in a consistent manner, meaning its viscosity remains constant regardless of the shear rate.
Step 2: Define shear stress. Shear stress is the force applied per unit area that causes the fluid to deform or flow.
Step 3: Define shear rate. Shear rate is the rate at which the fluid is deformed or the speed at which different layers of the fluid move relative to each other.
Step 4: Learn the relationship. In a Newtonian fluid, when you increase the shear rate (how fast the fluid is being deformed), the shear stress (the force causing the deformation) also increases.
Step 5: Understand proportionality. This means that shear stress is directly proportional to shear rate. If you double the shear rate, the shear stress also doubles.
Step 6: Connect to viscosity. The constant of proportionality between shear stress and shear rate is called viscosity, which is a measure of a fluid's resistance to flow.