Question

Which of the following fluids have a linear relationship between shear stress and velocity gradient ?

• A. Newtonian fluids
• B. Non-Newtonian fluids
• C. Plastic fluids
• D. Ideal fluid

Hint:

Plotting a rheological curve (shear stress vs. shear rate) yields: - A straight line through the origin for Newtonian fluids (constant viscosity).
- A curved line for Non-Newtonian fluids (viscosity changes with shear rate).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Fluids are classified into different categories based on their flow behavior and how their viscosity changes under applied shear stress.

Step 2: Detailed Explanation:
A Newtonian fluid is a fluid that obeys Newton's law of viscosity:
\[ \tau = \mu \left(\frac{du}{dy}\right) \]
Where \(\tau\) is the shear stress, \(\mu\) is the viscosity (which remains constant), and \(\frac{du}{dy}\) is the velocity gradient (shear rate).
In these fluids, there is a direct, linear relationship between the applied shear stress and the resulting velocity gradient.
If you plot shear stress against shear rate, it forms a straight line passing through the origin.
Examples of Newtonian fluids include water, air, alcohol, and thin liquid milk.
Non-Newtonian and plastic fluids (such as cream, yogurt, or condensed milk) do not follow this linear relationship.
An ideal fluid is a theoretical fluid with zero viscosity, which does not experience shear stress.

Step 3: Final Answer:
Fluids that exhibit a linear relationship between shear stress and velocity gradient are Newtonian fluids.