Newtonian Fluids:
A Newtonian fluid is a type of fluid that follows Newton's law of viscosity, which states that the shear stress acting on a fluid is directly proportional to the velocity gradient of the fluid. In simpler terms, the rate of deformation of a Newtonian fluid is directly proportional to the shear stress applied to it.

Shear Stress and Velocity Gradient:
Shear stress is the force per unit area that acts parallel to the surface of an object when there is a deformation or flow of material. Velocity gradient, on the other hand, is the change in velocity per unit distance in a fluid flow. It represents how the velocity of the fluid changes across a given distance.

Direct Proportionality:
When a fluid is said to be Newtonian, it means that the shear stress acting on the fluid is directly proportional to the velocity gradient. This can be mathematically expressed as:

Shear Stress ∝ Velocity Gradient

This relationship implies that as the velocity gradient increases, the shear stress also increases proportionally. Similarly, if the velocity gradient decreases, the shear stress decreases proportionally.

Explanation:
In the context of the given question, the correct answer is option 'A' because a Newtonian fluid exhibits a direct proportionality between shear stress and velocity gradient. This means that as the velocity gradient increases or decreases, the shear stress acting on the fluid will increase or decrease accordingly.

It is important to note that not all fluids behave as Newtonian fluids. Non-Newtonian fluids, such as viscoelastic fluids or thixotropic fluids, do not follow Newton's law of viscosity. These fluids exhibit different behaviors, such as shear-thinning (decreasing viscosity with increasing shear rate) or shear-thickening (increasing viscosity with increasing shear rate).

Conclusion:
In summary, a fluid is classified as a Newtonian fluid when the shear stress acting on it is directly proportional to the velocity gradient. This relationship is a fundamental characteristic of Newtonian fluids and allows for the prediction and analysis of fluid behavior in various engineering applications.