Rheology — Fluid Obeying Newton’s Law of Viscosity A fluid that obeys Newton’s law of viscosity (shear stress proportional to shear rate with constant viscosity) is termed a:

Introduction:Newton's law of viscosity underpins many engineering calculations: shear stress tau is proportional to velocity gradient du/dy with proportionality mu (dynamic viscosity). Fluids following this linear relation with mu approximately constant are classified as Newtonian.

Given Data / Assumptions:

• Continuum assumption valid; single-phase fluid.
• Shear rates within a range where mu does not depend on shear rate.
• Temperature uniform (to keep mu constant).

Concept / Approach:Newtonian: tau = mu * (du/dy). Non-Newtonian fluids violate this linearity or constancy of mu. ‘‘Ideal’’ fluid is inviscid (mu = 0) — a mathematical abstraction. ‘‘Real’’ includes all actual fluids, Newtonian or not, so it is not specific enough.

Step-by-Step Solution:Match the definition given to the rheological class.Linear stress–strain-rate with constant mu ⇒ Newtonian fluid.Therefore choose ‘‘newtonian fluid’’.

Verification / Alternative check:Water and air behave Newtonian across wide shear-rate ranges, confirming the classification.

Why Other Options Are Wrong:‘‘Real’’ is too broad; ‘‘ideal’’ ignores viscosity; ‘‘non-Newtonian’’ contradicts the constant-mu law.

Common Pitfalls:Assuming any temperature dependence disqualifies Newtonian behavior—Newtonian refers to shear-rate independence, not temperature independence.

Final Answer:newtonian fluid