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

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

Step 1: Understand what a Newtonian fluid is. A Newtonian fluid is a type of fluid that has a constant viscosity, meaning it flows the same way regardless of how much force is applied to it.
Step 2: Learn about shear rate. Shear rate is a measure of how fast layers of fluid are sliding past each other. It is usually expressed in units like 1/second.
Step 3: Know what shear stress is. Shear stress is the force applied to the fluid divided by the area over which the force is applied. It is measured in units like Pascals (Pa).
Step 4: Understand the relationship. In a Newtonian fluid, when you increase the shear rate (how fast the layers are moving), the shear stress increases in a linear way. This means that if you double the shear rate, the shear stress also doubles.
Step 5: Conclude that in a Newtonian fluid, viscosity (which is shear stress divided by shear rate) remains constant, regardless of the shear rate. This is why we say shear stress is directly proportional to shear rate.

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