Newtonian Fluid Definition

A real fluid exhibits resistance to flow due to internal friction, which is quantified by viscosity. When a real fluid is subjected to shear stress, it deforms continuously. The rate at which it deforms is called the rate of shear strain (or velocity gradient).

Different types of fluids behave differently under shear stress. The question asks about a specific type of real fluid where a direct proportionality exists between the applied shear stress and the resulting rate of shear strain.

Shear Stress and Shear Strain Rate Relationship

For many common fluids like water, air, and oil, the relationship between shear stress ($\tau$) and the rate of shear strain ($\frac{du}{dy}$) is linear. This relationship is given by Newton's law of viscosity:

$$\tau = \mu \frac{du}{dy}$$

Where:

• $\tau$ is the shear stress
• $\mu$ is the dynamic viscosity of the fluid (a constant for a given fluid at a specific temperature and pressure)
• $\frac{du}{dy}$ is the rate of shear strain (or velocity gradient)

This equation shows that the shear stress is directly proportional to the rate of shear strain, with the constant of proportionality being the dynamic viscosity ($\mu$).

Identifying the Fluid Type

A real fluid that follows Newton's law of viscosity, meaning the shear stress is directly proportional to the rate of shear strain, is known as a Newtonian fluid.

Analyzing the Options

• Newtonian fluid: This matches the description provided in the question. The shear stress is directly proportional to the rate of shear strain.
• real fluid: This is a broad category that includes all fluids with viscosity. It encompasses both Newtonian and non-Newtonian fluids, so it is not specific enough to describe the given proportionality.
• ideal plastic fluid: Also known as a Bingham plastic fluid. This type of fluid requires a certain minimum shear stress (yield stress) before it starts to flow. After yielding, the shear stress might be linearly related to the shear strain rate, but the relationship includes the yield stress, making it not a direct proportionality from zero stress.
• ideal fluid: This is a hypothetical fluid with zero viscosity. In an ideal fluid, there is no shear stress because there is no internal friction, except possibly in situations involving surface tension. It does not fit the description of a fluid where shear stress is proportional to shear strain rate (as there would be no shear stress to begin with due to viscosity).

Therefore, the fluid in which the shear stress is directly proportional to the rate of shear strain is specifically called a Newtonian fluid.