Fluid classification by constitutive relation: a fluid in which shear stress is directly proportional to the velocity gradient (rate of shear) is called a

Introduction:
Engineering correlations for pressure drop and heat/mass transfer depend on the constitutive behavior of the working fluid. This question checks recognition of the Newtonian model, the simplest and most widely used relation between shear stress and rate of shear.

Given Data / Assumptions:

• Shear stress τ is proportional to velocity gradient du/dy.
• Constant proportionality (dynamic viscosity μ) independent of shear rate.

Concept / Approach:
A Newtonian fluid obeys τ = μ (du/dy). Examples include water, air, and many light oils at moderate conditions. Non-Newtonian fluids deviate from linearity or exhibit yield stress/time dependence (e.g., Bingham plastics, pseudoplastics, dilatants, thixotropic fluids). A perfect (inviscid) fluid has τ = 0 regardless of shear rate, an idealization not realized in practice.

Step-by-Step Solution:
Match definition: linear τ–(du/dy) with constant μ → Newtonian.Exclude models with yield stress (Bingham: τ = τ_y + μ_p du/dy), or shear-dependent μ (dilatant/pseudoplastic).Exclude inviscid: τ ≡ 0, not proportional to du/dy.

Verification / Alternative check:
Plotting τ versus du/dy gives a straight line through origin for Newtonian fluids; other models show offsets (yield) or curvature (shear-thinning/thickening).

Why Other Options Are Wrong:

• Bingham plastic: needs a yield stress before flow begins.
• Perfect fluid: no viscous stresses at all.
• Dilatant/thixotropic: non-linear or time-dependent behavior.

Common Pitfalls:
Assuming all common liquids are Newtonian at all conditions; many slurries, polymer solutions, and pastes are non-Newtonian.

Final Answer:
Newtonian fluid