Question

A Newtonian fluid is defined as one in which the shear stress is:

• A. Independent of rate of shear
• B. Directly proportional to rate of shear
• C. Inversely proportional to viscosity
• D. Proportional to pressure

Hint:

Logic Tip: Think of water (a Newtonian fluid). If you stir it twice as fast (double the shear rate), it resists your spoon twice as hard (double the shear stress). The relationship is direct and linear.

Answer 1

The Correct Option is B

Concept:
Fluid behavior is often categorized by how the fluid deforms under applied forces. A Newtonian fluid follows a simple linear relationship between the applied shear stress and the resulting rate of deformation (shear rate).

Step 1:
For a Newtonian fluid, the shear stress ($\tau$) acting on fluid layers is mathematically defined by Newton's law of viscosity.

Step 2:
The law states that shear stress is equal to the dynamic viscosity ($\mu$) multiplied by the velocity gradient or rate of shear ($du/dy$): $$ \tau = \mu \frac{du}{dy} $$

Step 3:
In the equation above, assuming dynamic viscosity ($\mu$) remains constant for a given temperature and pressure, the shear stress ($\tau$) varies directly with the rate of shear ($du/dy$). Therefore, they are directly proportional.