A fluid is termed as the Newtonion fluid, when the shear stress is __________ the velocity gradient.

ANS:C - directly proportional to

A fluid is termed as Newtonian fluid when the shear stress is directly proportional to the velocity gradient. In a Newtonian fluid, the relationship between shear stress (τ) and velocity gradient (dy/du​) is described by Newton's law of viscosity: τ=μ dy/du​ Where:

• τ is the shear stress.
• μ is the dynamic viscosity (constant for a Newtonian fluid).
• dy/du​ is the velocity gradient (rate of change of velocity with respect to distance).

This equation shows that the shear stress experienced by a Newtonian fluid is directly proportional to the velocity gradient. As the velocity gradient increases, the shear stress experienced by the fluid also increases proportionally, maintaining a linear relationship between shear stress and velocity gradient. Therefore, the correct statement is: the shear stress is directly proportional to the velocity gradient.