Choose the correct statement about fluid behavior and rheology:
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AFluids that follow τ = μ * (du/dy) are called Newtonian fluids
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BFluids that do not follow a linear shear stress–rate of strain relation are called non-Newtonian fluids
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CMaterials that do not flow until a yield stress or yield strain is exceeded are often termed plastics (or viscoplastic)
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DAll of the above
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ENone of the above
Answer
Correct Answer: All of the above
Explanation
Introduction / Context:Rheology classifies fluids by the relationship between shear stress and rate of deformation. Correctly identifying Newtonian versus non-Newtonian behavior is essential in pipeline design, food processing, drilling muds, and biomedical flows.
Given Data / Assumptions:
- Shear flow between parallel plates (canonical reference).
- Steady shear; temperature constant.
- “Plastic” refers to materials exhibiting a yield stress (e.g., Bingham or Herschel–Bulkley types).
Concept / Approach:
Newtonian fluids obey τ = μ * (du/dy) where μ is constant at given conditions (e.g., water, air, light oils). Non-Newtonian fluids have a non-linear or rate-dependent relation (shear-thinning, shear-thickening, thixotropy, rheopexy). Viscoplastic materials (commonly referred to as “plastics” in older terminology) require a yield stress to initiate flow and then may behave Newtonian or otherwise.
Step-by-Step Solution:
Define Newtonian: linear proportionality, constant μ.Define non-Newtonian: τ is not linear in du/dy or μ is not constant.Define viscoplastic: τ < τ_y → no flow; τ ≥ τ_y → flow per constitutive law.Verification / Alternative check:
Examples: Water (Newtonian), ketchup/paints (shear-thinning non-Newtonian), corn starch in water (shear-thickening), drilling muds (Bingham plastic with yield stress).
Why Other Options Are Wrong:
Options (a), (b), and (c) are each correct; therefore (d) “All of the above” is the best single choice. (e) is false.
Common Pitfalls:
Confusing yield stress with yield strain; assuming viscosity is constant for all fluids; ignoring temperature dependence even in Newtonian fluids.
Final Answer:
All of the above