Question

The Newton's law of viscosity and a simple dashpot represent rheological model for

• A. St. Venant body
• B. Hookean body
• C. Non Newtonian liquid
• D. Newtonian liquid

Hint:

A Newtonian liquid obeys Newton's law of viscosity, where shear stress is proportional to rate of shear strain.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Rheology is the study of the flow of matter. Rheological models are used to describe the relationship between stress and strain (or rate of strain) in materials. The question asks what kind of material is described by Newton's law of viscosity, which is mechanically modeled by a dashpot.
Step 2: Detailed Explanation:
1. Newton's Law of Viscosity: This law states that for a fluid, the shear stress ($\tau$) is directly proportional to the rate of shear strain (or velocity gradient, $\frac{du}{dy}$). The constant of proportionality is the viscosity ($\mu$). \[ \tau = \mu \frac{du}{dy} \] A fluid that obeys this linear relationship is called a Newtonian liquid. Examples include water, air, and mineral oil. 2. Rheological Models: - A dashpot is a mechanical device that resists motion via viscous friction. The force it exerts is proportional to the velocity. This is the mechanical analogue of a viscous fluid, where stress is proportional to the rate of strain. Therefore, a dashpot represents an ideal Newtonian liquid. - A Hookean body (or Hookean solid) is an ideal elastic solid. It obeys Hooke's law, where stress is proportional to strain. Its mechanical model is a perfect spring. - A St. Venant body represents an ideal plastic solid. It does not deform until a certain yield stress is reached, after which it flows without any increase in stress. Its mechanical model is a friction block. - A Non-Newtonian liquid is a fluid that does not obey Newton's law of viscosity. The relationship between shear stress and rate of shear strain is non-linear. Examples include ketchup, paint, and blood. Step 3: Final Answer:
Newton's law of viscosity and its mechanical model, the dashpot, both describe the behavior of a Newtonian liquid. Therefore, option (D) is correct.