---
title: "Newtonian or non-Newtonian fluid from data"
subject: "Fluid Mechanics"
chapter: 1
key: "semester_3/fluid_mechanics:newtonian-or-not-table"
source: https://www.bctengineer.com/q/semester_3/fluid_mechanics/newtonian-or-not-table
site: BCT Engineering
---

# Newtonian or non-Newtonian fluid from data

Fluid Mechanics · Chapter 1: Fluid and its physical properties

- Asked in: 2078 Kartik, 4 marks
- Video: [Understanding Viscosity](https://www.youtube.com/watch?v=VvDJyhYSJv8) — The Efficient Engineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/fluid_mechanics/newtonian-or-not-table
- Whole chapter: https://www.bctengineer.com/md/semester_3/fluid_mechanics/chapter-1

## Question

The viscosity of one of the liquids in a laboratory is determined by measurements of shear stress $\tau$ and rate of shearing strain $\frac{du}{dy}$ tested in a suitable viscometer. Based on the following observations, determine if the given liquid is Newtonian or Non-Newtonian fluid. Explain how you arrive at your answer.

| $\tau$ (N/m²) | 0.04 | 0.06 | 0.12 | 0.18 | 0.3 | 0.52 | 1.12 | 2.1 |
|---|---|---|---|---|---|---|---|---|
| $\frac{du}{dy}$ (s⁻¹) | 2.25 | 4.5 | 11.25 | 22.5 | 45 | 90 | 225 | 450 |

## Short answer

The apparent viscosity μ_a = τ/(du/dy) is not constant, decreasing from 0.0178 to 0.0047 Pa·s as shear rate increases. This indicates non-Newtonian, shear-thinning (pseudoplastic) behavior with power-law index n ≈ 0.74.

## Answer

A Newtonian fluid obeys $\tau=\mu\,\dfrac{du}{dy}$, so the ratio $\tau/(du/dy)$ is constant and $\tau$ against $du/dy$ is a straight line through the origin.

Apparent viscosity $\mu_a=\tau\big/\dfrac{du}{dy}$ for each reading:

| $du/dy$ (s⁻¹) | 2.25 | 4.5 | 11.25 | 22.5 | 45 | 90 | 225 | 450 |
|---|---|---|---|---|---|---|---|---|
| $\tau$ (N/m²) | 0.04 | 0.06 | 0.12 | 0.18 | 0.30 | 0.52 | 1.12 | 2.10 |
| $\mu_a$ (Pa·s) | 0.0178 | 0.0133 | 0.0107 | 0.0080 | 0.0067 | 0.0058 | 0.0050 | 0.0047 |

The ratio is **not constant**: it falls steadily from 0.0178 to 0.0047 Pa·s as the shear rate rises, so the plot of $\tau$ against $du/dy$ is a curve, not a straight line.

A log-log fit of the data gives the power-law (Ostwald-de Waele) form

$$
\tau=K\left(\frac{du}{dy}\right)^{n},\qquad n\approx0.74,\quad K\approx0.0196\ \text{Pa·s}^{n}
$$

Since $n<1$ and the apparent viscosity decreases with shear rate, the liquid is **non-Newtonian, of the pseudoplastic (shear-thinning) type**.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What characterises a Newtonian fluid in tau versus du/dy data?
   A. tau/(du/dy) is constant, a straight line through the origin
   B. tau is constant for all du/dy
   C. tau/(du/dy) rises steadily with shear rate
   D. tau is proportional to the square of du/dy
   Answer: A. Newton's law tau = mu du/dy means a constant ratio, i.e. a linear plot through the origin. (Key point: Test for Newtonian fluid)

2. How does the apparent viscosity tau/(du/dy) behave in the given data?
   A. It stays constant at 0.0178 Pa·s
   B. It rises from 0.0047 to 0.0178 Pa·s
   C. It falls from 0.0178 to 0.0047 Pa·s
   D. It is zero at low shear
   Answer: C. The ratio decreases steadily as shear rate rises, so the liquid is not Newtonian. (Key point: Apparent viscosity trend)

3. With tau = K (du/dy)^n and n about 0.74, which fluid type is this?
   A. Dilatant (shear-thickening)
   B. Bingham plastic
   C. Pseudoplastic (shear-thinning)
   D. Ideal fluid
   Answer: C. n < 1 with apparent viscosity decreasing with shear rate is pseudoplastic behaviour. (Key point: Type of non-Newtonian fluid)

## Related in Fluid Mechanics

- [Determination of viscosity by viscometer](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aviscometer-viscosity-determination) — Fluid Mechanics, chapter 1, asked 2×
- [Model liquid viscosity, Froude and Reynolds](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Amodel-liquid-viscosity-froude-reynolds) — Fluid Mechanics, chapter 10
- [Shear stress, displacement thickness, drag on plate](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aflat-plate-shear-displacement-drag) — Fluid Mechanics, chapter 8
- [Metacentre and laboratory determination of height](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Ametacentre-importance-lab-determination) — Fluid Mechanics, chapter 3, asked 2×
- [Viscosity from torque on rotating cylinder](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aconcentric-cylinders-torque-viscosity) — Fluid Mechanics, chapter 1
- [Wall shear stress as dimensionless function](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Awall-shear-stress-dimensionless-pi) — Fluid Mechanics, chapter 10

## Related in other subjects

- [Max shear stress and volumetric strain in thin cylinder](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Amax-shear-half-longitudinal-volumetric-strain) — Strength of Materials, chapter 5
- [Stress-strain curves: linear and non-linear cases](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Astress-strain-nonlinear-cases) — Concrete Technology and Masonry Structure, chapter 4
- [Navier-Stokes equations for Newtonian fluid](https://www.bctengineer.com/question.md?key=semester_4%2Ffluid_mechanics_mechanical%3Anavier-stokes-newtonian-fluid) — Fluid Mechanics, chapter 4
- [Fluid properties and flow description methods](https://www.bctengineer.com/question.md?key=semester_4%2Ffluid_mechanics_mechanical%3Afluid-newtonian-lagrangian-eulerian) — Fluid Mechanics, chapter 1