A fluid which has a linear relationship between the magnitude of applied shear-stress and the resulting rate of deformation is called a/an __________ fluid.

ANS:A - Newtonion

A fluid which has a linear relationship between the magnitude of applied shear stress and the resulting rate of deformation is called a Newtonian fluid. Here's why:

• Newtonian Fluid: A Newtonian fluid is defined by Newton's law of viscosity, which states that the shear stress (τ\tauτ) between adjacent fluid layers is directly proportional to the velocity gradient (dudy\frac{du}{dy}dydu​). Mathematically, this relationship is expressed as: τ=μdudy\tau = \mu \frac{du}{dy}τ=μdydu​ where μ\muμ is the dynamic viscosity of the fluid.
• Linear Relationship: In a Newtonian fluid, the rate of deformation (velocity gradient) is directly proportional to the applied shear stress. This linear relationship holds true across a wide range of shear rates and stresses for Newtonian fluids.